Year 10 Mathematics Examination SEMESTER 2 2018 QUESTION ... · Kinross College Year 10 Mathematics...

Year 10 Mathematics Examination

SEMESTER 2 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: 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: 28

TOTAL MARKS: Year 10 Mainstream (115 Total Marks) Year 10 Academic Extension (135 Total Marks)

Section 1: Non - Calculator -

assumed 45 minutes

(50 marks)

Section 2: Calculator

55 minutes (65 marks)

(Additional 20 marks AE)

Kinross College Year 10 Mathematics Exam, Semester 2 2018 1


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.

..…DO NOT TURN THIS PAGE UNTIL ASKED TO DO SO…..


1.

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

2.

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

3.

Which of the following mathematical statements is true?

(A) a2 = b2 + c2 (B) 2 2b a c (C) 2 2c a b (D) c2 = a2 – b2

4.

Which of the following triangles has its sides labelled correctly?

(A) (B) (C) (D)

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


5.

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

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

6.

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)

7.

For the given triangle:

(A) sin = a

θb

(B) sin = b

θa

(C) sin = c

θb

(D) sin = b

θc

8.

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

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


9.

Helen invests $10 000 in a simple interest bank account that pays 5% annually. How much will be in her bank account after 3 years? (A) $10 150 (B) $11 500 (C) $12 000 (D) $12 500

10.

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

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


Section 1: Non Calculator – assumed (Total 40 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) 4(3𝑥 − 8)+5 b) (𝑥 + 7)(𝑥 + 5) c) (4𝑥 − 3)(4𝑥 + 5) d) 2(𝑥 + 3)(𝑥 + 4)

13. 2,2,3

Factorise these quadratic trinomials: a) 𝑥2 + 6𝑥 + 9 b) 𝑥2 − 3𝑥 − 10 c) 4𝑥2 − 16𝑥 − 20


14. 1.5,1.5

Label the sides of each triangle by using the letters H (hypotenuse), O (opposite) and A (adjacent):

a) b)

15. 2,2

Place the angle 𝜃 in the following triangles to match the labels:

a) b)


16. 4,1,1

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 65 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

Use each diagram to help expand the expressions.

a) (x+3)(x+1) b) (x+ 4)2


4. 3,3

Find the lengths of the missing sides, rounding the answers to 2 decimal places; all lengths are given in

centimetres:

a) b)

5. 3

Find the perimeter of this shape correct to 2 decimal places:


6. 2,1,1

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.

7. 2,2

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

b) Factorise by completing the square or the quadratic formula: 2𝑥2 + 22𝑥 + 32 = 0


8. 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 $5000 loan under the following conditions.

a) 4% p.a. compounded bi-annually over 3 years

9. 3,2

Jacqui is saving money to purchase a racing bike like the one shown. She has saved $1980 and wishes

to earn the remaining amount in interest on an investment. The best simple interest rate she can find

is 7.2% p.a.

a) For how long must Jacqui invest

the money in order to earn the

extra amount she needs?

b) Jacqui wants to investigate ways to

earn the money more quickly

through a shorter investment.

What interest rate does she need if

she wishes to have the money in 18

months?


10. 3,3

Find the lengths of the sides marked x, for these triangles correct to 2 decimal places:

a) b)

11. 3,3

Find the unknown angles correct to 2 decimal places:

a) b)


12. 4

A plane flying at 1850 m starts to climb at an angle of 18 degrees to the horizontal when the pilot sees a mountain peak 2450 m high, 2600 m away from him in a horizontal direction. Will the pilot clear the mountain (yes or no) by how much?


ACADEMIC EXTENSION (20 Marks)

1. 2

Find the exact solutions to

x210x 7 0 by first completing the square.

2. 2

Find the exact solutions to

2x2 7x 4 0 by completing the square or using the quadratic formula.

3. 3

A sailor on a yacht at sea sights the bottom of a lighthouse on a cliff at an angle of elevation of 43°

from sea level. The angle of depression from the top of the lighthouse to the yacht is 65°. If the yacht is

125 metres from the base of the cliff, find the height of the lighthouse.


4. 4

An aeroplane flies 138 km in a southerly direction from a military air base to a drop-off point. The drop-off point is 83 km west of the air base. Find the bearing correct to the nearest degree of:

a) The drop-off point from the air base

b) The air base from the drop-off point

5. 3

$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.


6. 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 mean

c) The higher standard deviation

Year 10 Mathematics Examination SEMESTER 2 2018 QUESTION ... · Kinross College Year 10 Mathematics...

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