year 10 mathematics examination semester one 2017

Year 10 MATHEMATICS EXAMINATION

SEMESTER ONE 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 (45 marks)

Attempt questions

Section 2: Calculator

55 minutes (55 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

The expanded and simplified form of 4(2x – 3) – 7 is:

(A) 8x-7 (B) 6x-11 (C) 8x-19 (D) 8x-8

2.

0 04 (5 )x x evaluates to:

(A) 1 (B) 2 (C) 5 (D) 4

3.

2 1

5 3

6

9

x y

x y

expressed with positive indices is:

(A) 3

2

3

2

x

y (B)

3

4

2

3

x

y (C)

4

7

3

2

y

x (D)

7

2

2

3

x

y

4.

2 The circumference of a circle with radius 3 mm correct to one decimal place is:

(A) 9.4 mm (B) 18.8 mm (C) 28.3 mm (D) 37.7 mm

5.

The volume of the following solid is:

(A) 25 m3 (B) 50 m3 (C) 75 m3 (D) 175 m3

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

1.


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 two heads is: (A) 35% (B) 29% (C) 36% (D) 65%

7.

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

(A) –46 (B) –14 (C) –38 (D) 14

8.

Which of the following points does not lie on the line y = –2x + 7?

(A) (4, –1) (B) (1, 3) (C) (0, 7) (D) (–1, 9)

9.

The gradient of the line joining the points (–2, 1) and (6, –3) is:

(A) 1

2 (B) 2 (C)

1

2 (D) -2

10.

The inequality representing the x values on the number line below is:

(A) 5 ≤ x < 7 (B) x ≤ 7 (C) 5 < x ≤ 7 (D) x > 5


Section 1: Non Calculator – assumed (Total 35 marks)

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

Simplify the following: a) 2xy+5x+ 7xy-3x b) -5a´7b

Expand and simplify: c) 4(x -3) d) - 4(x -8)

Factorise the following:

e) 21- 7b f) 3x2 -12x

12 1,2,3,4

Simplify the following using the index laws.

a) 3 2 24 3p q p q b) (5x3)2

c)

34

5

a

b c

d) 6a3

b-4c2

æ

èçç

ö

ø÷÷

2

¸3a4

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 3 is rolled at least once) __________________________________________

ii Pr(sum is equal to 3) __________________________________________

iii Pr(sum is not equal to 3) __________________________________________

iv Pr(sum is at most 3) __________________________________________

14. 2,2

a) If F ma , find m when 7, 56a F

b) If v u at , find t when v = 24, u = 8 and a = 2.


15. 1,1,2,2

Solve: a) x + 8 = 13 b) 3x – 7 = 14

c) x

3+ 6 =10 d)

x 9

5 2

16. 2

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

2x+5<11


Section 2: CALCULATOR (Total 55 marks)

1 2,2,3,3

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

a) b)

c) d)


2 4,4,4

Find (i) the total surface area, and ii) the volume of these solids, rounding to two decimal places

where necessary. a)

b)

c)


3 2,3,3

Answer the following questions for this triangular prism.

i Draw a labelled diagram of the surface area net.

ii Calculate the total surface area (TSA).

iii Calculate the volume.


4. 1,1,2,3

Simplify:

a) 0 03 5k b) 2 3 5( )a b

c)

34

2

2w

r

d) 7 3 2

3 5

5 4

8

h k h k

h k

5 3,3

Sketch the graph of the line of each given equation.

a) 3y x b) 2 3 6y x by plotting the x- and

y-intercepts.


6. 2,2,3

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

a) When 8 is added to the product of 4 and x, the result is 20.

b) When 6 less than 3 lots of x is doubled, the result is 18.

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

7 3,1,1

Boxes A and B contain 4 marbles each.

Box A contains three red and two white marbles.

Box B contains one red and four white marbles.

a) A box is chosen at random and then a single marble is selected. Represent this information in a tree diagram. b) What is the probability of selecting a red counter? c) What is the probability of selecting a white counter?


ACADEMIC EXTENSION

1 1,1,1,2

Determine the surface area of this cube with a cylindrical hole, including the inner surface area. Surface area of cube: Circumference of circle: Area of circle: Inner surface area of cylinder: Total surface area:


2 2,1,1,1

A group of 50 students were asked whether they liked vegemite or peanut butter. 27 liked vegemite,

19 liked peanut butter and 11 did not like either vegemite or peanut butter.

i) Represent this information on a Venn diagram.

If a student is selected at random from the group what is the probability that they:

ii) like vegemite but not peanut butter

iii) like both peanut butter and vegemite

iv) like peanut butter given that they like vegemite

V P


3. 2,2

Simplify the following using the index laws. a)

3m3n4

2m-6n-5¸

2m4n6

m-1n

æ

èç

ö

ø÷

-2

2a1

2b1

3

6a1

3b1

2

´

4a1

4bæ

èç

ö

ø÷

b1

4a

1

2


4. 3,3

Find the gradient and x- and y-intercepts for these linear relations and sketch their graph.

a) 1

12

y x

b) 5 2 10x y


Spare sheet if required:

END OF EXAMINATION

year 10 mathematics examination semester one 2017

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