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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 2
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…..
Kinross College Year 10 Mathematics Exam, Semester 2 2018 4
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)
Kinross College Year 10 Mathematics Exam, Semester 2 2018 5
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 6
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 7
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 ___________________________
Kinross College Year 10 Mathematics Exam, Semester 2 2018 8
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 9
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)
Kinross College Year 10 Mathematics Exam, Semester 2 2018 10
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…
Kinross College Year 10 Mathematics Exam, Semester 2 2018 11
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 12
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 13
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:
Kinross College Year 10 Mathematics Exam, Semester 2 2018 14
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
Kinross College Year 10 Mathematics Exam, Semester 2 2018 15
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?
Kinross College Year 10 Mathematics Exam, Semester 2 2018 16
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)
Kinross College Year 10 Mathematics Exam, Semester 2 2018 17
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?
Kinross College Year 10 Mathematics Exam, Semester 2 2018 18
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.
Kinross College Year 10 Mathematics Exam, Semester 2 2018 19
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.