year 10 mathematics examination semester 2 2017 · b) factorise by completing the square: 2+8 +3 7....

Year 10 Mathematics Examination

SEMESTER 2 2017

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: 100 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

TOTAL QUESTIONS: TOTAL MARKS:

Year 10 Mainstream

(100 Total Marks)

Year 10 Academic Extension

(120 Total Marks)

Section 1: Non - Calculator -

assumed 45 minutes (53marks)

Attempt questions

Section 2: Calculator

55 minutes (47 marks)

(Additional 20 marks AE)

Attempt questions

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 2017 1

1.

Complete the factorization: y2 - y-6 = (y-3)(y+?)

(A) 8 (B) 2 (C) 3 (D) -2

2.

Which expression is the factorised form of: k2 -8k+ 7 (A) (k -1)(k - 7) (B) (k +1)(k - 7) (C) (k -1)(k + 7) (D) (k +1)(k + 7)

3.

Expand and simplify: (3a-5b)(3a+5b)

(A) (9a+25b) (B) (9a-25b) (C) 9a2 +25b2 (D) None of these

4.

The turning point of the graph could onlybe:

(A) (-3,3) (B) (4,-2) (C) (3,4) (D) (-3,-2)

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


5.

The median of the set of data is: (10,16,28,13,25,17,19,21,16,14)

(A) 15 (B) 16.5 (C) 16 (D) 17

6.

The interquartile range of the data displayed in the boxplot above is: (A) 15 (B) 25 (C) 20 (D) 35

7.

What is the total number of people who participated in this data set.

(A) 25 (B) 30 (C) 34 (D) 15


8.

Which congruency test applies to these triangles?

(A) AAS (B) RHS (C) SAS (D) SSS

9.

The scale factor of the pair of similar triangles below is:

(A) 5

2 (B)

4

3 (C)

5

3 (D)

3

2

10.

Which similarity test proves that the given pair of triangles is similar?

(A) SSS (B) SAS (C) AAS (D) RHS


Section 1: Non Calculator – assumed (Total 43 marks)

11. 2,1,1,1,1,1,1,1,1

Consider the given data set:

9 , 6, 17, 8, 4, 13, 10, 12, 24, 8, 11, 5, 13 a) List the data in order, from smallest to largest. ________________________________________________________________ b) For the data, find: i the minimum and maximum values ___________________________ ii the range ___________________________ iii the mode ___________________________ iv the mean, correct to one decimal place ___________________________ v the median (Q2) ___________________________ vi the lower and upper quartiles ___________________________

(Q1 and Q3) vii the interquartile range (IQR) ___________________________ viii any outliers ___________________________

12. 1,2,3,4

Expand and simplify the following.

a) 3 + 2(2x – 3) b) 4(3x – 8) + 5

c) 4(5x – 6x) + 7(3x – 1) d) (𝑥 + 3)(𝑥2 + 4𝑥 − 2)


13. 2,2,3

Simplify:

a)

2x

3+

2x

4=

b)

3

10-

3b

2=

c) -8a

7´

7

2a=

14. 2,2

Questions a and b refer to the pair of triangles below.

a) The value of x above is: b) The scale factor of the pair of similar triangles above is:


15. 2,2

Decide whether the pairs of triangles are similar, giving reasons.

a b

________________________________ ________________________________

________________________________ ________________________________

________________________________ ________________________________

16. 4,2,2

Consider the variables x and y and the corresponding bivariate data.

x 1 2 3 4 5 6 7 8

y 7 6 1 4 5 3 3 2

a) Draw a scatter plot for the data. (4 marks)

b) Is there positive, negative or no correlation between x and y? c) Is the correlation between x and y strong or weak?


STOP


Section 2: CALCULATOR (Total 47 marks)

1. 1,1,1,2,1,1,3

Here are the names of the last ten prime ministers of Australia together with the ages at which they

became prime minister. (Hint: place ages in numerical order )

William McMahon 63

Gough Whitlam 56

Malcolm Fraser 45

Bob Hawke 53

Paul Keating 47

John Howard 56

Kevin Rudd 50

Julia Gillard 49

Tony Abbott 55

Malcom Turnbull 60

a) Calculate:

i) the Median. ii) the lower quartile. iii) the upper quartile.

b) Determine the interquartile range.

c) Determine the range.

d) Determine the mean age.

e) Draw a median boxplot to represent the above data above the scale below.

40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70


2. 2,2,2

Joshua buys a $6000 car on the following terms:

30% deposit

monthly repayments of $210 for 2 years.

Find:

a the deposit paid.

______________________________________________________________________

______________________________________________________________________

b the total amount paid for the car.

______________________________________________________________________

______________________________________________________________________

c the interest charged.

______________________________________________________________________

______________________________________________________________________

3. 2,2,3

a) 3

4+

2

a=

b) 3

2y-

7

9=

c) x + 4

10´

2

x=


4. 1,1,2,3

Factorise the following by finding the highest common factor:

a) 5𝑏 + 30

b) 10𝑥𝑦 + 16𝑥

c) −34𝑗𝑘2 + 24𝑗2𝑘

d) 45𝑎𝑏2 − 15𝑎2𝑏 + 25𝑎𝑏

5. 2,2,2

Determine the following key features of the given graph.

a) Coordinates of the turning point and whether it is a maximum or minimum. b) Coordinates of the x-intercepts. c) Coordinates of the y-intercept.


6. 2,2

a) Rearrange the equation below and then solve using the quadratic formula. Round your answers to two decimal places: 𝑥2 − 4𝑥 = 9

b) Factorise by completing the square: 𝑥2 + 8𝑥 + 3

7. 2,2,3

Find the interest paid on a $5000 loan under the following conditions.

a) 8% p.a. simple interest over 4 years

b) 7% p.a. simple interest over 3 years and 4 months

Find the interest paid on a $9000 loan under the following conditions.

a) 4% p.a. compounded bi-annually over 6 years


ACADEMIC EXTENSION

1. 2

Find the exact solutions to

x2 10x 7 0 by first completing the square.

2. 2

b) Find the exact solutions to

2x2 7x 4 0 using the quadratic formula.

3. 3,3

Simplify these expressions:

a) 6x -3

x¸

1- 2x

4

b) x

(x - 2)2-x

x - 2


4. 4

$5000 is borrowed for 4 years with interest compounding 6-monthly. At the end of the 4 years the loan

is worth $6842.85. Determine the interest rate (per annum) at which the money is borrowed.

5. 1,2,3

The Cats and The Mice basketball teams compare their number of points per match for a season. The data is presented in this back-to-back stem-and-leaf plot.

a) the higher range

b) the higher mean10

c) The Cats have the higher standard deviation. What is the standard deviation for “The Mice”?

year 10 mathematics examination semester 2 2017 · b) factorise by completing the square: 2+8 +3 7....

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