Year 10 Mathematics Examination SEMESTER 1 2019...SEMESTER 1 2019 QUESTION AND ANSWER BOOKLET STUDENT NAME: TEACHER: DATE: TIME ALLOWED FOR THIS PAPER Reading time before commencing

Year 10 Mathematics Examination

SEMESTER 1 2019

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

TOTAL QUESTIONS: TOTAL MARKS:

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

Section 1: Non - Calculator -

assumed 50 minutes (47 marks)

Attempt questions

Section 2: Calculator

55 minutes (53 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 2018 1


1.

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

number?

(A) 1

3 (B)

1

4 (C)

1

2 (D)

1

10

2.

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) 85% (B) 29% (C) 20% (D) 65%

3.

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)


4.

The volume of the following solid is:

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

5.

What does 18x3y3

2xy2

simplify to?

(A) 9

xy3 (B) 9x2y (C)

9x-1y-3 (D)

9

xy

6.

What is the expanded form of 5a2b4 :

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

7.

What is the simplified form of x2 × (x4)2 ?

(A) x9 (B) x24 (C) x10 (D) x14


8.

Which equation has a solution of x = 5?

(A) -2x+5=11

(B) 2x+3

13=1

(C) 3

2 - x=1

(D) 3x-7 =8

9.

The solution to x - 4

2= -3 is:

(A) 1

2 (B) 2 (C)

1

2 (D) -2

10.

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

(A) –12 (B) –46 (C) -14 (D) -38


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

11. 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) __________________________________________

12. 2,2,2,2,2,3

Simplify the following:

a) 5xy+6x+9xy-3x b) -5a´7b

Expand and simplify: c) 4(x -8) d) -6(x- 4)

Factorise the following:

e) 45-9b f) 4x2 -16x


13. 1,2,3,4

Simplify the following using the index laws.

a) (5x3)2

b) (-3x10)2

c) a4

b2c

æ

èçç

ö

ø÷÷

4

d) 6a3

b-4c2

æ

èçç

ö

ø÷÷

2

x3a4

b-3c2

æ

èçç

ö

ø÷÷

3

14. Question 1,1,2,2

Solve the following linear equations for x: a) x - 8 = 15 b) 5x + 7 = 37

c) x

2+ 9 =14 d)

x - 7

2= 7


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. 1,1,1,2

The Venn diagram shows the distribution of elements in two sets Gears (Set A) and Suspension (Set B).

Suppose that, in a group of 18 bicycles, 9 have gears, 11 have suspension and 5 have both gears and suspension.

Find: a) n(A∩B):

b) n(A ∪ B):

c) n(A′∩B′):

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


2. 1,2,2,3

Simplify each of the following:

a) 7k0 +8 b) (c9d )7

c) 4w5

z7

æ

èç

ö

ø÷

4

d) 3h9k5 ´ 5h4k

5h7k5

3. 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)


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)


5+

5. 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.

b) What is the surface area of the tank?

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?

6. 2

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


7. 2,2

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

i) (-3, 7) and (4, −1) ii) (−4, −3) and (−5, −2)

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

i) (2, 4) and (6, 8) ii) (−5, 7) and (−1, -2)

8. 1,1,3

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

a) When 7 is added to the product of 3 and x, the result is 25.

b) A number of lollies “l” is decreased by 5 and then shared equally among three friends so that they each get 7.

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

-11x+4 ³ 48


9. 3,1,1,1,1,1

One hundred people were surveyed regarding their use of water for their garden. Of that group, 23 said that they use rainwater (RW), 48 said that they used tap water (TW) and 41 said that they did not water at all.

Illustrate the information in a Venn diagram:

State the number of people who:

a) Used rainwater only?

b) Neither rainwater nor tap water? Find the probability that a person watering their garden will use:

c) Tap water?

d) Rainwater only?

e) Both Rainwater and Tap water?


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

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

163 want to study Mathematics, 124 Chemistry 95, Physics

67 requested Mathematics and Chemistry

61 requested Mathematics and Physics

49 requested Physics and Chemistry

27 want to study all three subjects

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

***END OF EXAM***

Documents

Year 10 Mathematics Examination SEMESTER 1 2019...SEMESTER 1 2019 QUESTION AND ANSWER BOOKLET STUDENT NAME: TEACHER: DATE: TIME ALLOWED FOR THIS PAPER Reading time before commencing