year 10 mathematics examination semester 2018 · 2018-06-21 · kinross college year 10 mathematics...

Year 10 Mathematics Examination

SEMESTER 2018

QUESTION AND ANSWER BOOKLET

STUDENT NAME:

TEACHER:

DATE:

TIME ALLOWED FOR THIS PAPER Reading time before commencing work: 10 minutes Working time for this paper: 105 minutes

MATERIAL TO BE PROVIDED BY THE SUPERVISOR This Question/Answer Booklet

MATERIAL TO BE PROVIDED BY THE CANDIDATE Pen/pencil for answering questions

Erasing stationery

Up to two scientific calculators

Written notes on one unfolded A4 sized paper; can be double-sided

Year 10 Mainstream (100 Total Marks) Year 10 Academic Extension (120 Total Marks)

Section 1: Non - Calculator -

assumed 50 minutes (47 marks)

Section 2: Calculator

55 minutes (53 marks)

(Additional 20 marks AE)

AT THE END OF THE EXAMINATION Attach any extra sheets used to this Question/Answer booklet.

IMPORTANT NOTE TO CANDIDATES No other items may be taken into the examination room. It is your responsibility to ensure that you do not have any unauthorised notes or other items of a non-personal nature in the examination room. If you have any unauthorised material with you, hand it to the supervisor BEFORE reading any further.

Kinross College Year 10 Mathematics Exam, Semester 1 2018 1


1.

What is the expanded form of 5a2b3:

(A) 5 × a × b (B) 5 × a2 × b3 (C) 5 × a × a × b × b × b (D) 5a2 × b3

2.

What is the simplified form of x2 × (x3)4?

(A) x9 (B) x24 (C) x20 (D) x14

3.

What does 36x3y3

4xy2

simplify to?

(A) 9

xy3 (B) 9x2y (C)

9x-1y-3 (D)

9

xy

4.

The area of the following shape is:

(A) 216m2 (B) 100 m2 (C) 140 m2 (D) 37.7 mm

Section 1: Multiple choice NON- CALCULATOR(Total 10 marks, one mark per question)


5. The volume of the following solid is:

(A) 25 m3 (B) 250 m3 (C) 75 m3 (D) 320 m3

6.

An experiment involves tossing three biased coins and counting the number of heads. Here are the results after running the experiment 100 times.

Number of heads 0 1 2 3

Frequency 15 20 29 36

The experimental probability of obtaining at least one heads is: (A) 35% (B) 29% (C) 20% (D) 65%

7.

lf a = 4, b = 5 and c = –3 then a2 + 2bc evaluates to:

(A) –46 (B) –12 (C) –38 (D) 14


8.

Consider a set of cards numbered 1 to 10. If one card is chosen, what is the probability it is a odd

number?

(A) 1

3 (B)

1

4 (C)

1

2 (D)

1

10

9.

The solution to x - 4

2= -3 is:

(A) 1

2 (B) 2 (C)

1

2 (D) -2

10.

Which equation has a solution of x = 5?

(A) 3x-7 =8

(B) 2x+3

13=1

(C) 3

2 - x=1

(D -2x+5=11


Section 1: Non Calculator – assumed (Total 37 marks)

11. 2,2,2,2,2,3

Simplify the following: a) 3xy+6x+9xy-4x b) -8a´7b

Expand and simplify: c) 5(x- 7) d) -3(x- 7)

Factorise the following:

e) 35-5b f) 4x2 -16x

12. 1,2,3,4

Simplify the following using the index laws.

a) 2p5q´7p2q3 b) (4x2)2

c) a3

b2c

æ

èçç

ö

ø÷÷

5

d) 6a3

b-4c2

æ

èçç

ö

ø÷÷

2

x3a4

b-3c2

æ

èçç

ö

ø÷÷

3


13. 2,1,1,1,1

Two four-sided dice, numbered 1 to 4, are rolled.

a) List the sample space using a table using the following table.

Die 2

1 2 3 4

Die

1 1

2

3

4

b) Find:

i Pr(a 4 is rolled at least once) __________________________________________

ii Pr(sum is equal to 4) __________________________________________

iii Pr(sum is not equal to 4) __________________________________________

iv Pr(sum is at most 4) __________________________________________

14. 1,1,2,2

Solve the following linear equations for x: a) x - 7 = 11 b) 4x + 7 = 15

c) x

2+ 9 =13 d)

x - 7

4= 3


15. 2

Solve the following inequality and show your solution on this number line.

2x+11< 21

STOP


Section 2: CALCULATOR (Total 53 marks)

1. 1,2,2,3

Find the area of these basic shapes, rounding to two decimal places where necessary.

a) Please use centimetres for your units. b)

c) d)


2. 4,4

Find (i) the total surface area, and (ii) the volume of these solids a)

b)


3. 3,2

A 13m-high storage tank was constructed from stainless steel (including the lid and the base). The diameter was 3 metres as shown.

a) What is the surface area of the tank? (Round your answer to two decimal places)

b) How much did the steel cost for the side of the tank if it comes in sheets 1 m wide that cost $6 a metre ?

4. 2

Calculate the volume of the cylinder below. Give your answers correct to 2 decimal place.


5. 1,2,2,3

Simplify each of the following :

a) 4k0 +3 b) (c3d)5

c) 3w5

z3

æ

èç

ö

ø÷

4

d) 3h9k5 ´ 5h4k

5h7k5

6. 2,2

a) Find the gradient of the line segment joining each pair of points:

i) (2, 3) and (−2, −3) ii) (−3, −2) and (−2, −3)

b) Find the coordinates of the midpoint for the line segment joining each pair of points:

i) (2, 3) and (8, 7) ii)(−4, 6) and (−3, 5)


7. 1,1

For each of the following statements, write an equation and then solve it for the pronumeral.

a) When 4 is added to the product of 3 and x, the result is 25.

b) When 6 less than 3 lots of x is doubled, the result is 12.

8. 3

Solve the following inequality and graph the solution on a number line.

-11x+4 ³ 48


9. 1,1,1,2

The Venn diagram shows the distribution of elements in two sets A and B.

Find: a) n(A∩B) :

b) n(A ∪ B) :

c) n(A′∩B′) :

d) Transfer the information in the Venn diagram into a two-way table.

TOTAL

TOTAL


10. 3,1,1,1,1,1

From a group of 50 adults, 35 enjoy reading fiction (F), 20 enjoy reading non- fiction (N) and 10 enjoy reading both fiction and non- fiction.

a) Illustrate the information in a Venn diagram:

State the number of people who enjoy:

b) Fiction only?

c) Neither fiction nor non-fiction?

Find the probability that a person chosen at random will enjoy reading:

d) Non-fiction?

e) Non-Fiction only?

f) Both fiction and non-fiction?


ACADEMIC EXTENSION

1. 3,2

Find the surface area of the shape below: a)

b) Determine the surface area of the following object.


2. 2,3

Use index laws to simplify each of the following: a)

8m-5n

(2mn)4¸

12m3n-2

-(2mn)0

b)

4a1

3

b3

æ

è

ççç

ö

ø

÷÷÷

1

2

3. 2,2

Determine the equation of the line that: a) Passes through (3,7) with a gradient of 4 b) Passes through (-5,2) and (1, -4)


4. 3,1,1,1

Mr. Avenell is creating the timetable for year 12 students. The request forms have been entered online:

163 want to study Mathematics, 95 Physics, 124 Chemistry

61 requested Mathematics and Physics

67 requested Mathematics and Chemistry

49 requested Physics and Chemistry

27 want to study all three subjects

17 want to study none of these subjects a) Draw a Venn diagram to illustrate the situation. b) How many students requested only Mathematics? c) How many students requested only Physics? d) What was the total number of requests?

**END OF EXAM***

year 10 mathematics examination semester 2018 · 2018-06-21 · kinross college year 10 mathematics...

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