2021 year 10 (5.1/5.2/5.3) topic tests information sheet (nsw)

2021 Year 10 (5.1/5.2/5.3) Topic Tests Information Sheet (NSW)

2021 Year 10 (5.1/5.2/5.3) Topic Tests are sets of short answer questions and their

solutions. We offer the following sets:

Year 10 (5.1) set

● Financial Mathematics (3 questions)

● Indices and Numbers of Any Magnitude (2 questions)

● Linear Relationships (3 questions)

● Measurement (3 questions)

● Trigonometry (3 questions)

● Geometrical Figures (2 questions)

● Probability (2 questions)

● Single Variable Statistics (3 questions)

Year 10 (5.2) set

● Financial Mathematics (2 questions)

● Algebraic Expressions and Indices (3 questions)

● Linear Relationships (3 questions)

● Quadratics and Non-Linear Relationships (3 questions)




● Probability (2 questions)

● Single Variable and Bivariate Statistics (2 questions)

Year 10 (5.3) set

● Indices and Surds (2 questions)

● Expressions, Equations and Linear Relationships (2 questions)


● Quadratic Expressions, Quadratic Equations and Parabolas (3 questions)



● Non-linear Relationships, Functions and Their Graphs (2 questions)

● Logarithms and Polynomials (2 questions)

● Single Variable and Bivariate Statistics (2 questions)

The structure of each Mid-year Test is:

● 15 multiple choice questions

● 5 short answer questions

● 2 extended response questions

Distribution We will email electronic copies

File format MS Word DOCX format and PDF format

Sample We have attached sample questions

Release date 1st of March 2021

Price $105 per set

2021 Year 10 (5.1) Mathematics

Financial Mathematics Test

Time allowed: 1 hour Total marks: 25 marks

Question 1 (10 marks) a. Marcus earns $427.50 for 38 hours of work. 2 marks What is his hourly pay rate? ______________________________________________________________________________ ______________________________________________________________________________ b. A holiday package is normally priced at $8,520. 2 marks If this package is discounted by 12%, what will be the discounted price? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Dean works as a salesman who earns an annual salary of $74,516, plus 5% commission on his sales. i. What is Dean’s base fortnightly salary, before the commission on his sales is added? 2 marks ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ii. Dean’s sales were $2,700 last week. 2 marks What was his gross income last week? ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

4 2021 Year 10 (5.1) Mathematics

Financial Mathematics

Question 3 (7 marks) Michael made the following notes about the 2020-21 financial year.

Gross income from employer ?

Work-related expenses $1,750

Interest on investments $380

Tax paid for the financial year $19,250.50

The amount of Michael’s 2% Medicare levy is $1,708.40.

Resident tax rates 2020–21

Taxable income Tax on this income

0 – $18,200 Nil

$18,201 – $45,000 19 cents for each $1 over $18,200

$45,001 – $120,000 $5,092 plus 32.5 cents for each $1 over $45,000

$120,001 – $180,000 $29,467 plus 37 cents for each $1 over $120,000

$180,001 and over $51,667 plus 45 cents for each $1 over $180,000

Source: ATO website a. Show that Michael’s taxable income is $85,420. 1 mark ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ b. Find Michael’s gross income from his employer. 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Use the tax table above to calculate the amount of Michael’s income tax payable. 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Indices and Numbers of Any Magnitude Test


Question 1 (10 marks) a. Simplify 2 22 .a a 2 marks ______________________________________________________________________________ ______________________________________________________________________________ b. Write 1 22 x x x z in index form. 2 marks ______________________________________________________________________________ ______________________________________________________________________________

c. Simplify 36

2

33 .

3

2 marks

Write your answer in the form 3 ,n where n is an integer. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

d. Simplify 125x

y

using positive indices only. 2 marks

______________________________________________________________________________ ______________________________________________________________________________ e. Simplify 3 2 32 ( 3 ).e f ef 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Linear Relationships Test


Question 1 (6 marks) The number of unemployed people in a particular suburb over a period of 9 months is shown on the graph below.

a. What was the number of unemployed people initially? 1 mark _______________________________________________________________________________ b. When did the number of unemployed people reach 1,000? 1 mark _______________________________________________________________________________ c. Find the rate of decrease of the number of unemployed people during the 9-month period. 2 marks Express your answer in terms of the unit ‘thousands of unemployed people per month’. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

3 2021 Year 10 (5.1) Mathematics Linear Relationships

Question 2 (7 marks) A straight line passes through the points (0, 1) and ( 3, 4).

The gradient of this line is 5

.3

a. What is the y -intercept of the line? 1 mark

_______________________________________________________________________________ b. Complete the table below using the coordinates given. 1 mark

x

y

c. Sketch the straight line on the set of axes below. 2 marks

d. Find the equation of the straight line. 1 mark _______________________________________________________________________________ _______________________________________________________________________________ e. Write down the equation of another line that is parallel to the original line. 2 marks _______________________________________________________________________________


Measurement Test


Question 1 (8 marks) a. A true blind snake is 11 inches long. 2 marks What is the length of the true blind snake in centimetres? 1 inch is 2.54 cm. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. The storage capacity of a USB flash drive is 2 TB. 2 marks

Use the conversion table above to find the storage capacity of the USB flash drive in MB. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. The mass of a coffee table is measured as 13.5 kg. 2 marks Give the limits of accuracy for the mass of the coffee table. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

1 MB 1024 KB

1 GB 1024 MB

1 TB 1024 GB

4 2021 Year 10 (5.1) Mathematics Measurement

Question 3 (10 marks) Nicholas has an open rectangular box, which is shown below.

a. Complete the diagram below for the net of the rectangular box. 3 marks Include any relevant measurements.

b. The outer faces of the box, including the base, are painted. 2 marks Find the painted area. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Trigonometry Test


Question 1 (8 marks)

a. Point X is 4.5 km west from point .O

i. Write down the bearing of O from .X 1 mark _________________________________________________________________________ _________________________________________________________________________ ii. Write down the bearing of X from .O 2 marks _________________________________________________________________________ _________________________________________________________________________ iii. What is the shortest distance, in metres, between point X and point O? 3 marks Round your answer to the nearest whole number. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

3 2021 Year 10 (5.1) Mathematics Trigonometry

Question 2 (7 marks) The diagram below shows a rectangular cricket pitch with measurements as shown.

a. Find the value of . 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. Find the value of .y 2 marks

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Geometrical Figures Test


Question 1 (9 marks) Part of a truss bridge is shown below. It is given that 19.2 mAD and 16.5 m.DE The ratio of AB to BD is 3:1. Triangle ABC and triangle ADE are similar.

a. Which of the following angles is common to triangle ABC and triangle ?ADE 1 mark Circle the correct answer.

CED CAB ADE b. What is the scale factor? 1 mark _______________________________________________________________________________ c. Write down the appropriate mathematical symbol in each box. 3 marks

Since AB and AD are parallel, we can write .AB AD

Since triangle ABC and triangle ADE are similar, we can write .ABC ADE

If triangle X and triangle Y are congruent, we write .X Y

4 2021 Year 10 (5.1) Mathematics Geometrical Figures

d. Complete the following paragraph by writing down the appropriate words or numbers. 3 marks The squares are __________ but __________ congruent. This is because even though the

squares are not identical, the lengths of the corresponding sides are __________.

e. How many times greater is the area of the larger square than the area of the smaller square? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Probability Test


Question 1 (10 marks) The fair spinner shown below is spun 110 times, and the colour which the spinner lands on each time is recorded.

The following table shows the results.

Colour White Grey Black

Frequency 17 42 51

a. How many times did the spinner land on grey or black in the experiment? 1 mark _______________________________________________________________________________ _______________________________________________________________________________ b. What is the theoretical probability of the spinner landing on black? 1 mark _______________________________________________________________________________ _______________________________________________________________________________ c. What is the theoretical probability of the spinner not landing on black? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

3 2021 Year 10 (5.1) Mathematics Probability


A number is chosen from the set {1, 2, 3, 4, 5, 6, 7, 8}. Let the events A and B be defined as follows.

{1, 2, 3, 4, 5, 6}A

{2, 3, 5, 7}B a. Complete the following Venn diagram by writing down the appropriate numbers. 1 mark

b. Describe event B in words. 1 mark _______________________________________________________________________________ _______________________________________________________________________________ c. Suppose that a number is randomly selected from the first 8 positive integers. i. Find ( ).P A 2 marks Write your answer as a fraction in its simplest form. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ ii. Find ( ).P A B 2 marks Write your answer as a fraction in its simplest form. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

2021 Year 10 (5.1) Mathematics Single Variable Statistics Test

Time allowed: 1 hour

Total marks: 25 marks Question 1 (10 marks) a. Here are some terms used in statistics.

population census survey sample variable confidentiality

For each of the following descriptions, choose the most appropriate word from the list above. i. An element or feature that can vary. 1 mark _______________________________________________________________________ ii. All the people or objects of interest. 1 mark _______________________________________________________________________ iii. A collection of questions designed to collect data on subsets of the population. 1 mark _______________________________________________________________________ b. Determine the type of data each of the following questions would generate. i. “How many cousins do you have?” 1 mark

Categorical Numerical ii. “What company is your internet service provider?” 1 mark

Categorical Numerical c. An SMS survey about the number of hours high school students spend on sports is to be 2 marks conducted. Briefly describe two potential problems with this survey. _______________________________________________________________________________ _______________________________________________________________________________

3 2021 Year 10 (5.1) Mathematics Single Variable Statistics

Question 2 (10 marks) The following histogram shows the weight of rubbish put out by some households in Armadale last week.

a. Show that the histogram includes data from 120 households. 1 mark _______________________________________________________________________________ _______________________________________________________________________________ b. What percentage of households put out between 2.5 kg and 10 kg of rubbish last week? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. What percentage of households put out at least 5 kg of rubbish last week? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

2021 YEAR 10 (5.1) MATHEMATICS MIDYEAR TEST

Reading time: 15 minutes Writing time: 2 hours

QUESTION BOOK

Structure of book

Section Number of questions

Number of questions to be answered

Number of marks

A 15 15 15 B 5 5 25 C 2 2 20

Total 60


Midyear Test

SECTION A - Continued

SECTION A

Question 1 Eric's annual income is $96,200. If Eric saves 20% of his income, the amount of money he saves per week is

A. $370 B. $1,480 C. $1,850 D. $8016 E. $19,240 Question 2

A shop is offering a 20% discount on shoes.

Sam buys a pair of shoes for $126.90, after receiving a further 10% discount for being a member with the shop.

The original price of the shoes is

A. $101.52

B. $114.21

C. $151.20

D. $152.28

E. $176.25

Instructions for Section A Answer all questions. Choose the response that is correct for the question. A correct answer scores 1, an incorrect answer scores 0. Marks will not be deducted for incorrect answers. No marks will be given if more than one answer is completed for any question.


Midyear Test


Question 9 Which one of the following statements is false?

A. The total distance that Dylan travelled is 25 km

B. Dylan stopped moving for 2 hours

C. Dylan travelled 3 times faster in the last hour than he did in the first 2 hours

D. Dylan travelled at a constant speed for his entire journey

E. Dylan’s speed during the first 2 hours is approximately 83.3 metres per minute

The following information relates to Questions 10 – 11. In the given diagram, BC is parallel to .DE Triangles ABC and ADE are similar.

Question 10 The scale factor is

A. 0.25

B. 0.75

C. 1

D. 1.5

E. 2

Question 11 Which one of the following statements is false?

A. ABC ADE

B. 1

2

BC

DE

C. AB AD

BC DE

D. 2AD

AB

E. A is common for triangle ABC and triangle ADE


Midyear Test

SECTION B - Continued

SECTION B

Question 1 (5 marks) a. Emma’s normal pay is $525 per week. 2 marks If Emma takes 4 weeks of leave, what will be her total holiday pay including leave loading? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. A retail store gives its employees commission based on the amount of sales they make. 3 marks The employees receive a 5% commission on sales less than $300, and 9% on the amount in excess of $300. A store employee sold $755 worth of goods during a particular week. Find the commission that the store employee earned. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Instructions for Section B Answer all questions. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown. Unless otherwise indicated, the diagrams in this book are not drawn to scale.


Midyear Test


Question 3 (5 marks) The diagram below shows a wall with height h m. Point S is on the ground 13 m away from the base of the wall. The angle of elevation to the top of the wall from point S is 57º.

a. Find the height of the wall, ,h correct to one decimal place. 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. Find the horizontal distance between point U and point .S 2 marks Round your answer to one decimal place. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. What is the angle of depression to point S from the top of the wall? 1 mark _______________________________________________________________________________


Midyear Test


Question 4 (5 marks) In the diagram below, the larger trapezium is formed by enlarging the smaller trapezium by a factor of .k

a. Find the value of .k 2 marks _______________________________________________________________________________ _______________________________________________________________________________ b. Find the ratio of the area of the smaller trapezium to the area of the larger trapezium. 2 marks Write the ratio in its simplest form. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. How many times longer is the perimeter of the larger trapezium than the perimeter of the smaller 1 mark trapezium? _______________________________________________________________________________ _______________________________________________________________________________


Midyear Test

SECTION C - Continued

SECTION C

Question 1 (10 marks) The distance-time graph below shows Dominic’s cycling trip from his home to the beach. On the way to the beach, Dominic stops at some shops to buy snacks.

a. How long did Dominic stop at the shops for? 1 mark _______________________________________________________________________________ b. At what speed did Dominic travel during the first 10 minutes? 2 marks Write your answer in in kilometres per minute, as a decimal. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Instructions for Section C Answer all questions. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown. Unless otherwise indicated, the diagrams in this book are not drawn to scale.


Midyear Test


Question 2 (10 marks) The diagram below shows a rectangular campsite. A tent has been set up at each of the points ,A ,B C and .D

a. A scale drawing of the campsite is drawn in the ratio of 1.5 cm : 20 m. i. What is the length, in cm, of the scale drawing of the campsite? 2 marks _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ ii. How many times greater is the perimeter of the actual campsite than the perimeter of the 2 marks scale drawing of the campsite? Round your answer to the nearest whole number. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ b. Are the rectangular campsite and the scale drawing similar or congruent? 1 mark Circle the correct answer.

Similar Congruent


Midyear Test (answers)

2021 YEAR 10 (5.1) MATHEMATICS MIDYEAR TEST SOLUTIONS SECTION A

Question Answer 1 A2 E3 C4 B5 A6 D7 C8 B9 D10 E11 A12 D13 C14 D15 B

Question 1

Eric earns $96200

$185052

per week.

He saves 20

$1850 $370.100

Answer is A. Question 2 Let x be the original price of the shoes.

0.8 0.9 $126.9

$126.9

0.8 0.9

$176.25

x

x

Answer is E.



Question 4 (5 marks) a. 2 marks

(A1)

(A1)

10.5

52.1

k

b. 2 marks The area of the smaller trapezium is

2

1

8

(3 5)

m

22

c

The area of the larger trapezium is

2

1(6.3 10.5)

8

4

35.2 c

.2

m

2

● Correct areas of the trapezia. (A1) Therefore, the ratio of the area of the smaller area to the larger area is

18 35.28 1: : 4.4 (A1) c. 1 mark k (A1) ● Accept 2.1. Question 5 (5 marks) a. 2 marks

2 2

2 )

A 6 (A1

11 )

A

rea 2 6.25

10 1.5 c

2

(m

b. 3 marks

2 )

Surface area 2 6.25 14.4 12 14 (A1

(

. )

A1

4 2 10.5

373.8 cm

Since 372 cm2 is less than 373.8 cm2, there is not enough paper to completely wrap the chocolate. (A1)


Financial Mathematics Test


Question 1 (12 marks) a. Lily invests money into a savings account and does not make any additions or withdrawals.

The value of Lily’s investment at the end of n years is given by 12

6 17550 1 .

100 12

n

i. How much money did Lily invest? 1 mark _______________________________________________________________________ ii. What is the annual interest rate, as a percentage? 1 mark _______________________________________________________________________ iii. How many times per year is the interest compounded? 1 mark _______________________________________________________________________ iv. Find the value of Lily’s investment at the end of 3 years. 2 marks _______________________________________________________________________ _______________________________________________________________________ b. A heater loses 12% of its value every year. 2 marks The value of the heater will be $960 at the end of 5 years. Calculate the initial value of the heater. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Financial Mathematics

Question 2 (8 marks) Pro Technology offers two deals on a plasma TV worth $8,750.

Option A: Pay a 30% deposit now and make monthly repayments of $185 for 3 years

Option B: Make a cash payment to buy the plasma TV outright with a 12% discount

a. Julian purchases the plasma TV with Option A. i. Show that the deposit that Julian pays is $2,625. 1 mark _______________________________________________________________________ _______________________________________________________________________ ii. Find the total amount paid for the plasma TV. 2 marks _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ iii. Find the total interest charged. 2 marks _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ b. Another customer buys the plasma TV with Option B. 3 marks How much less did this customer pay than Julian, as a percentage? Round your answer to the nearest whole number. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Algebraic Expressions and Indices Test


Question 1 (12 marks) a. Factorise 2 24 4 .x y xy 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

b. Simplify 2 4 5 20

.7 14

x x x 2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

c. Write 2 1

3 7

z z as a single fraction. 3 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Algebraic Expressions and Indices

Question 2 (10 marks) a. In the diagram below, angle ABC and angle DBE are equal. 2 marks

Find the value of .x ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

b. If 1 1 1

,f u v 0.75u and 0.4,v find the value of .f 2 marks

Write your answer as a fraction in its simplest form. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

c. Solve the inequality 3

2 3.4

x 2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Linear Relationships Test


Question 1 (11 marks) A train travels:

● 4 km in 2 minutes at a constant speed

● then at a constant speed of 8

3 km per minute for 3 minutes

then stops for 1 minute to complete its journey. a. What was the total time taken for the train to complete its journey? 1 mark _______________________________________________________________________________ b. What was the total distance travelled? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ c. Sketch a graph that represents the journey of the train on the set of axes below. 3 marks

6 2021 Year 10 (5.2) Mathematics Linear Relationships

b. Consider the lines A - E shown below.

i. How many lines have a negative gradient? 1 mark _________________________________________________________________________

_________________________________________________________________________ ii. Write down the equation of line .C 1 mark _________________________________________________________________________ _________________________________________________________________________ iii. Which two lines are perpendicular to line C ? 1 mark _________________________________________________________________________

_________________________________________________________________________

_________________________________________________________________________


Quadratics and Non-linear Relationships Test


Question 1 (14 marks) a. Factorise 2 20 64.x x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ b. Factorise 25 125.x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Expand (2 7)(2 7).y y 2 marks Simplify your answer. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

d. Simplify 2 6 9

.3

x x

x

2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Quadratics and Non-linear Relationships

e. Solve 2 1 4,

5 25x where 0.x 2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ f. Richard kicks a ball during a footy game. 4 marks The height of the ball above the ground, in metres, is given by 0.2(8 )( 1),x x where x is the

horizontal distance of the ball from Richard. What is the horizontal distance of the ball from Richard on the two instances where the ball reaches a height of 4 metres? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Quadratics and Non-linear Relationships

Question 3 (6 marks) a. Consider the equations labelled from i - iv below. 4 marks Match each graph with the most appropriate equation (i - iv) using the table below, if the equation is present. Write N/A otherwise.

Graph Label (i-iv)

A.

B.

C.

D.


Measurement Test


Question 1 (8 marks) The following diagram shows an open cylindrical can.

a. Show that the circumference of the circular cross-section is 12 cm. 1 mark _______________________________________________________________________________ _______________________________________________________________________________ b. Complete the diagram below for the net of the can. 2 marks Include any relevant measurements.


b. The following composite solid is made up of a rectangular prism with a smaller cube put on top.

i. This composite solid has the same volume as the container in part a. 3 marks Find the side length of the cube. Round your answer to two decimal places. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ ii. Find the surface area of the composite solid, including the bottom side. 2 marks Round your answer to two decimal places. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________


Trigonometry Test


Question 1 (10 marks) In the diagram shown below, the distance between points F and G is 15 km.

a. Write down the bearing of F from .O 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. Write down the bearing of O from .F 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. What is the shortest distance between point O and point F ? 2 marks Round your answer to one decimal place. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Question 3 (5 marks) The diagram below shows David initially standing at point ,A looking at the top of a tower with a height of ( 1.7)h m.

The angle of elevation to the top of the tower from David’s eye level is 20º.

David then walks 120 m towards the tower to reach point ,B where the angle of elevation to the top of the tower from David’s eye level is 40º.

David’ eye height is 1.7 m at both points.

a. Show that tan 20 .120

tan(40 )

hh

2 marks

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________




Question 1 (10 marks) a. Consider the polygon shown below.

i. What is the name of the polygon? 1 mark _________________________________________________________________________ ii. Find the perimeter of the polygon. 2 marks _________________________________________________________________________ _________________________________________________________________________ iii. Find the value of .x 2 marks _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ iv. Find the size of an exterior angle of the polygon. 2 marks _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________


b. In the diagram below, AB CB and AC is perpendicular to .BD 4 marks

Prove that BD bisects .ABC _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Probability Test


Question 1 (8 marks) a. For events A and ,B consider “the probability of A given B ”. i. Write down an expression for this probability using symbols. 1 mark _________________________________________________________________________ ii. State a formula used to evaluate this probability. 1 mark _________________________________________________________________________ _________________________________________________________________________ b. The two-way table below shows the number of elements in the events X and .Y

X not X

Y 1 6 7

not Y 5 4 9

6 10 16

i. Find ( ).P X Y 1 mark _________________________________________________________________________ _________________________________________________________________________ ii. Find ( | ).P X Y 1 mark _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

3 2021 Year 10 (5.2) Mathematics Probability

Question 2 (12 marks) A jar has 7 black marbles and 5 white marbles. Two marbles are randomly drawn one after another with replacement.

a. Complete the following tree diagram by drawing in any missing features and writing down any 2 marks missing probabilities.

b. Will the outcome of the first draw affect the outcome of the second draw? 2 marks Justify your answer. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Single Variable and Bivariate Statistics Test


Question 1 (10 marks) Some students from two schools, Westlake and Avondale, were surveyed about the amount of time they usually spend per week studying Mathematics. The results were displayed using box plots, as shown below.

a. What percentage of Avondale students spent 4 or more hours of Mathematics per week? 1 mark _______________________________________________________________________________ b. What is the interquartile range for Westlake students? 1 mark _______________________________________________________________________________ _______________________________________________________________________________ c. What statistical measure do the box plots have in common? 2 marks Find the value of this statistical measure. _______________________________________________________________________________ _______________________________________________________________________________ d. At which school do students spend more time studying Mathematics per week? 2 marks Refer to two different features of the box plots that support your answer. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

3 2021 Year 10 (5.2) Mathematics Single Variable and Bivariate Statistics

Question 2 (10 marks) The scatter plot below shows the hours spent studying or a particular test and the score received in the test. The test was out of 50 marks.

a. State the type of the data shown by the scatter plot. 1 mark _______________________________________________________________________________ b. Briefly describe the strength of the correlation between study time and the test score. 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. The scatter plot shows that the study time and the test score have a positive correlation. 2 marks Give an interpretation of this. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________



QUESTION BOOK

Structure of book



Number of marks

A 15 15 15 B 5 5 25 C 2 2 20

Total 60


Midyear Test


SECTION A

Question 1 Julia borrows $5,750 from her bank at a rate of 12% per annum compounding monthly. The expression that gives the value of her loan at the end of 5 years is

A. 55750 1 0.12

B.5

0.125750 1

100

C. 605750 1 0.12

D. 60

0.12 15750 1

100 12

E. 60

15750 1 0.12

12

Question 2 Jason worked for 38 hours at a normal hourly rate of pay and 6 additional hours at double time.

He earned $1036 in total for his work.

Jason's normal hourly rate of pay is

A. $16.71

B. $20.72

C. $23.55

D. $25.90

E. $27.50



Midyear Test


Question 3

The number line that best represents the solution set to the inequality 2

52

xx

, where x is a real

number, is

Question 4

4 227 3x y is equal to

A. 2 29 3 3x y x y

B. 223 3x y

C. 223 3x y

D. 2 23 3 3x y x y

E. 2 23 3x y x y

Question 5 22 4 4 4

3 6

x x x simplifies to

A. 3( 2)

9

x

B. 4

2x

C. 1

4( 2)x

D. 3( 2)x

E. 2

4

x


Midyear Test


The following information relates to Questions 12– 13. Consider the graph with the equation 2( 2) 1.y x Question 12 Which one of the following statements is true about the x -intercept(s) of the graph?

A. The x -intercepts are 0 and 4

B. The graph has no x -intercepts

C. The only x -intercept is 8

D. The only x -intercept is 16

E. The x -intercepts are 4 and 0

Question 13 Which one of the following statements is true?

A. The equation for the axis of symmetry is 2y

B. The graph is not a parabola

C. The coordinates of the minimum point of the graph are (2,1)

D. The graph has no y -intercept

E. When the graph of 2 1y x is translated to the left by 2 units, the graph 2( 2) 1y x is obtained

Question 14

In the diagram above, the bearing of O from A is

A. 071º

B. 109º

C. 180º

D. 251º

E. 289º


Midyear Test


SECTION B

Question 1 (5 marks) A washing machine worth $900 is bought in December 2018. The value of the washing machine is depreciated by 14.5% at the end of each year, beginning in 2019.

a. Show that the value of the washing machine after n years is 900 0.855 .n 1 mark _______________________________________________________________________________ _______________________________________________________________________________ b. Find the value of the washing machine at the end of 2020. 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. In which year will the depreciated value of the washing machine first fall below $350? 2 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________



Midyear Test


Question 3 (5 marks) An open rectangular prism and a closed cylinder are shown below.

a. Find an expression for the surface area of the cylinder in the form ( ),r a bhr where 2 marks a and b are integers. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. If the volume of the rectangular prism and the volume of the cylinder are equal, find a rule 3 marks that relates r and .h _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Midyear Test


SECTION C

Question 1 (10 marks) The following diagram shows a photo with length 3 cm longer than its width, w cm. The photo sits inside a frame that is 2 cm wide on each side of the photo.

a. Write down the length of the photo in terms of .w 1 mark _______________________________________________________________________________ b. Write an inequality that represents a sensible restriction on .w 1 mark _______________________________________________________________________________ c. Find an expression for the combined area of the photo and the frame in the form 2 marks

2aw bw c where ,a b and c are integers.

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________





Question Answer 1 E2 B3 A4 D5 B6 C7 E8 C9 D10 E11 A12 B13 C14 D15 C

Question 1

12 5 6012 1 1

5750 1 5750 1 0.12100 12 12

Answer is E. Question 2 Let x be the normal hourly rate of pay.

38 2 6 $1036

$1036

50

$20.72

x x

x

Answer is B.



Question 11 2 3.5 58

58 2

3.516

d

d

The distance travelled is 16 kilometres. Answer is A. Question 12

The graph of 2( 2) 1y x is shown below.

It is clear that the graph has no x -intercepts.

Showing that the equation 2( 2) 1 0x has no solutions is another method to reach the same conclusion.

All other statements are false. Answer is B. Question 13 The coordinates of the minimum point of the graph are (2,1). All of the other statements are false. Answer is C.



Question 5 (5 marks) a. 2 marks

(A1)

(A1)

(10 2) 18

4

10

14

0

b. 3 marks

1.2.DF

AC

1.2.DE

AB (A1)

1.2.EF

BC (A1)

Therefore, by the SSS test, triangle ABC and triangle DEF are similar. (A1)


Indices and Surds Test



a. Simplify 32 18. 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

b. Expand and simplify 2

2 3 2 . 2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. The area of a circle is 72 cm2. 3 marks

Find the radius of the circle. Express your answer in surd form. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Indices and Surds


a. What type of number is 3

2 ? 1 mark

Circle the correct answer(s).

Integer Rational number Irrational number

b. Solve the equation 2 2

1

497

7

n

n

for .n 3 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. 3 marks

Find the perimeter of the rectangle above in surd form.

Express your answer in the form ,a b c where ,a b and c are integers. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Expressions, Equations and Linear Relationships Test



a. Solve the equation 1 1

1.3 2

x x 2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

b. Rearrange the equation 1 1 1

t u v to make v the subject. 3 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Consider the equation ( ) ,a b x c where ,a b and c are constants. Under what condition does this equation i. have a unique solution? 1 mark ________________________________________________________________________ ii. have no solution? 1 mark ________________________________________________________________________


Expressions, Equations and Linear Relationships

Question 2 (10 marks) A straight line with equation 2y x is shown below. Another line, ,L that is perpendicular to this line is also shown. The two lines intersect at the point (2,4).

a. Find the equation of line .L 3 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ b. Find the midpoint of the line segment formed by the axis intercepts of line .L 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Measurement Test


Question 1 (8 marks) Consider the hemisphere shown below.

a. Find the volume of the hemisphere. 2 marks Write your answer in exact form in terms of R and . _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. A sphere of radius r has the same volume as the hemisphere. 3 marks Express r in terms of .R Write your answer in surd form. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


c. The diagram below shows the hemisphere placed on top of an upside down cone. 3 marks

How many times greater is the combined volume of the hemisphere and the cone than the volume of the hemisphere alone? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Quadratic Expressions, Quadratic Equations and Parabolas Test


Question 1 (12 marks) a. Expand and simplify (4 2) 2 (3 5).x x x x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ b. Factorise 218 3 6.x x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Factorise 2 25 ( 4) .x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ d. If 22 2 6 1A x x and 22 4 3,B x find A B in terms of .x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Quadratic Expressions, Quadratic Equations and Parabolas

Question 3 (11 marks) A rectangular field is enclosed and divided into zone A and zone B using 120 metres of string, as shown in the diagram below. Zone A is a square with a side length of x metres, and the width of zone B is y metres.

a. Find the combined area, ,S of zone A and zone B in terms of .x 2 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

b. Complete the square to show that 23( 20) 600.

2S x 3 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Trigonometry Test



a. What is the exact value of tan(45 ) ? 1 mark

_______________________________________________________________________________ _______________________________________________________________________________ b. For what obtuse angle is the equation sin(25 ) sin( ) true? 1 mark

_______________________________________________________________________________ _______________________________________________________________________________

c. It is given that 2

sin( )5

x and 1

cos( ) ,5

x where 90 180 .x 2 marks

Find the exact value of tan( ).x _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


d. i. Complete the graph of cos( )y for 0 360 on the set of axes below. 2 marks

ii. Show that one solution of the equation cos( ) 0.75 for 0 360 is 41.4º, correct 2 marks to one decimal place. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ iii. Find the other solution of the equation cos( ) 0.75 for 0 360 . 2 marks Round your answer to one decimal place. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________




In each question, ensure your responses are supported with geometric reasoning. Question 1 (8 marks) a. Consider the circle below.

i. What is the size of the reflex angle at point O ? 2 marks _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ ii. Find the value of .a 2 marks _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________


c. In the diagram below, DE is a tangent to the circle and .DOE 3 marks

Find OED in terms of . _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Non-linear Relationships, Functions and Their Graphs Test


Question 1 (8 marks) a. Each of the following graphs (i, ii and iii) shows how the population, ,P of a city varies over time .t For each graph, describe whether the population is increasing or decreasing, and if the population is changing at an increasing, decreasing or constant rate. i. 2 marks

________________________________________________________________________ ________________________________________________________________________ ii. 2 marks

________________________________________________________________________ ________________________________________________________________________


Non-linear Relationships, Functions and Their Graphs

b. The graph below shows the amount of current flowing, ,I in an electrical circuit t seconds after it is switched off. The equation of the graph is in the form ,tI a b where a and b are integers.

i. State the values of a and .b 2 marks ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ii. How long does it take for the current to reach 0.5 amps? 2 marks ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ iii. What happens to the current after a long time? 1 mark ________________________________________________________________________ ________________________________________________________________________


Non-linear Relationships, Functions and Their Graphs

d. 2 marks

Use the vertical line test to determine if the graph above represents a function. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Logarithms and Polynomials Test


Question 1 (13 marks) a. Simplify 2log (32). 2 marks

______________________________________________________________________________ ______________________________________________________________________________

b. Simplify 2 2

1 1log log .

2 8

2 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

c. Solve the equation 4 5x using logarithms. 3 marks ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ d. Write 10log (24)P in terms of a and ,b where 10log (2)a and 10log (3)b . 3 marks

______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________


Logarithms and Polynomials

Question 2 (12 marks) a. Is 2 4x x a polynomial? 1 mark Circle the correct answer.

Yes No b. Consider the polynomial 3 2( ) 2 2,Q x x x kx where k is an integer. 2 marks If ( 1)x is a factor of ( ),Q x find the value of .k ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ c. Consider the polynomial 3 2( ) 2 2.P x x x x Find the remainder when ( )P x is divided by ( 3)x using each of the following two methods: i. long division. 2 marks ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ii. the remainder theorem. 2 marks ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________


Single Variable and Bivariate Statistics Test


Question 1 (9 marks) a. The back-to-back stem and leaf plot below shows the maximum daily temperature for Melbourne and Sydney over a 10-day period one summer. A data summary table is also shown.

i. Which city would you expect to have a greater standard deviation of the maximum daily 2 marks temperatures recorded? Justify your answer. _________________________________________________________________________ _________________________________________________________________________ ii. Calculate the standard deviation of the maximum daily temperatures recorded for 2 marks Sydney over the 10-day period. Round your answer to one decimal place. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ b. In general, is the standard deviation affected by outliers? 2 marks Justify your answer. _______________________________________________________________________________ _______________________________________________________________________________

Melbourne Sydney

Minimum 23 18

Median 29 34 Mean 30.7 31.6

Maximum 41 44

Range 18 26

3 2021 Year 10 (5.3) Mathematics Single Variable and Bivariate Statistics

Question 2 (11 marks) A design business collects data on the profit made on each project and the budget allocated for marketing. This bivariate data is displayed in the scatter plot below. A least squares line has been sketched on the scatter plot. This line passes through the point (0, 445).

a. Describe the correlation between the profit made and the budget allocated for marketing in 2 marks terms of strength and direction. _______________________________________________________________________________ _______________________________________________________________________________ b. Show that equation of the least squares line is 2 marks

profit 445 0.3875 budget

_______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________



QUESTION BOOK

Structure of book



Number of marks

A 15 15 15 B 5 5 25 C 2 2 20

Total 60


Midyear Test


SECTION A

Question 1 Which one of the following statements about 4 8 is true?

A. 4 8 is an irrational number

B. 4 8 is a rational number

C. 4 8 is a natural number

D. 4 8 is an integer

E. 4 8 can be written in the form ,a

b where a and b are integers

Question 2

If the area of a semicircle is 7

2

cm2 then its radius is

A. 1.75 cm

B. 3.5 cm

C. 7 cm

D. 7 cm

E. 14 cm



Midyear Test


The following information relates to Questions 5 – 6.

Question 5

The surface area of this sphere is S m2.

Which equation is true?

A. 4R S

B. 4

SR

C. 4S

R

D. 1

4

SR

E. 4S

R

Question 6

If the combined volume of two of these spheres is 720 m3, the value of R is closest to

A. 2.56

B. 3.23

C. 4.07

D. 5.65

E. 8.14


Midyear Test


SECTION B


A sheet of paper has a length of 3 12 cm and a width of 7 cm.

A smaller rectangle with a length of 7 cm and a width of 3 cm is cut out from the middle of the paper.

a. Find the area of the remaining paper in exact form. 3 marks _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. Express the area of the remaining paper as a percentage of the original area of the paper. 2 marks Round your answer to one decimal place. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________



Midyear Test


Question 4 (5 marks) In the diagram below, AB and CB are tangents to the circle.

a. Find the angle . 3 marks Give a reason for each step of working. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ b. If 4.5AB cm, what is the area of quadrilateral OABC ? 2 marks Round your answer to one decimal place. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________


Midyear Test


SECTION C

Question 1 (10 marks) A bank charges interest on loans at the rate of 20% per annum, compounding annually. Suppose that Luke takes up a loan of $300 with the bank at the start of 2020. No repayments are made by Luke. a. Find the rule for the value of Luke’s loan n years after the loan was first issued in the form 1 mark ,nA a b where a and b are positive constants. _______________________________________________________________________________ _______________________________________________________________________________ b. Calculate the value of Luke’s loan at the start of 2022. 1 mark _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ c. Use logarithms to find when the value of Luke’s loan will exceed triple its initial value for the 3 marks first time. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________





Question Answer 1 A2 C3 B4 E5 D6 B7 C8 C9 A10 B11 C12 E13 D14 C15 A

Question 1

4 8 2 2 2, which is an irrational number.

Answer is A. Question 2 If r is the radius of the semicircle

2

2

7

2 2

7

7

r

r

r

Answer is C.



Question 2 (10 marks) a. 2 marks The surface area of the composite solid is

2 2

2 2 )

2 3 3 4 3 2 2 2

30 8

2(15

(A1)

) cm (4 A1

y y y y y y

y y

y

b. 2 marks The volume of the composite solid is

2

3 3

3 38

(2 2 3 3

98

( 9) c )m

A1)

(A1

y y y y y

y y

y

c. 3 marks

3 3

3 3 3

3

3

3

4

)

( ) (8 9)34

(8 9)3

4(8 9

)

(A1)

(A1)

(A1

3

)3

(8 94

3(8 9)

42

ky y

k y y

k

k

k

d. 3 marks The initial (full) volume of the container is

3 3(8 9) (4.1) cm (A1)

The volume remaining in the container after t minutes is

3(8 9) (4.1) dt (A1)

where d is the rate at which the water is being drained. Therefore

3

3

)

(8 9) (4.1) 10 1879

1879 (8 9)

A

(4.1)

10

47 mL per minute ( 1

d

d

2021 year 10 (5.1/5.2/5.3) topic tests information sheet (nsw)

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