GRADE 10

MATHEMATICS ASSESSMENT BOOKLET

TERM 2

i

MATHEMATICS (MATHC1002)

Mathematics (MATHC1002) ASSESSMENT TASK COVER PAGE

Topic STS Performance criteria

Assessment Event Date Time

Project/Investigation

Student Name Teacher Class Total Mark

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Marked and feedback provided by: Signature: Date:

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Student Comment/s:

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1. Look at the sequence of numbers

7, 11, 15, 19,……….

(a) Write down the next number in the sequence.

Answer (a) ……….…………………….…… [1]

(b) Find the 10th number in the sequence.

Answer (b) ……….…………………….…… [1]

(c) Write an expression, in terms of n, for the nth number in the sequence.

Answer (c) ……….…………………….…… [1]

2.

The first three patterns in a sequence are shown above.

(a) Complete the table.

Pattern number 1 2 3 4

Number of dots 5

[1]

(b) Find a formula for the number of dots, d, in the nth pattern.

Answer (b) d = ………………………….…… [1]

Pattern 1 Pattern 2 Pattern 3

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(c) Find the number of dots in the 60th pattern.

Answer (c) …….…..………………….…… [1]

(d) Find the number of the pattern that has 89 dots.

Answer (d) …….…..………………….…… [1]

3. The diagram below shows a sequence of patterns made from dots

and lines.

(a) Draw the next pattern in the sequence in the space above. [1]

(b) Complete the table for the numbers of dots and lines.

Dots 1 2 3 4 5 6

Lines 4 7 10

[2]

(c) How many lines are in the pattern with 99 dots?

Answer (c) ……………………..….……… [2]

(d) How many lines are in the pattern with n dots?

Answer (d) ………………….….….……… [2]

(e) Complete the following statement.

There are 85 lines in the pattern with ……………… dots. [2]

1 dot 3 dots2 dots 4 dots

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4. (a) 4𝑝 × 45 = 415. Find the value of 𝑝.

Answer (a) 𝑝 = ………..……..………………

[1]

(b) 27 ÷ 2𝑞 = 24. Find the value of 𝑞.

Answer (b) 𝑞 = ………..……..………………

[1]

5. (a) 3𝑝 × 35 = 314. Find the value of 𝑝.

Answer (a) 𝑝 = ………..……..………………

[1]

(b) 28 ÷ 2𝑞 = 23. Find the value of 𝑞.

Answer (b) 𝑞 = ………..……..………………

[1]

6. Simplify

(a) (1

𝑝)0,

Answer (a) ………..……..………………

[1]

(b) 𝑞3 × 𝑞5,

Answer (b) ………..……..………………

[1]

(c) (𝑟4)−2.

Answer (c) ………..……..………………

[1]

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7. Simplify 3𝑥2𝑦 × 𝑥4𝑦2

Answer ………..……..………………

[2]

8. Simplify

(a) 4𝑑 × 6𝑑4

Answer (a) ………..……..………………

[2]

(b) 28𝑡3 ÷ 7𝑡−4

Answer (b) ………..……..………………

[2]

9. In the diagram AB is parallel to CD.

Calculate the value of 𝑎.

NOT TO SCALE

Answer 𝑎 = ………..………………….

[2]

A

B

C

D

a°

5a°

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10.

NOT TO SCALE

In the diagram BC is parallel to DE. ABD and ACE are straight lines.

Angle BDE = 35o.

Calculate the size of angle DBC

Answer (b) Angle DBC = ………..…………….

[1]

11.

NOT TO SCALE

In the diagram, AB, CD and EF are parallel lines.

Angle ABC = 25o and angle CEF = 130o.

Calculate angle BCE.

Answer Angle BCE = ………..…………….

[2]

12.

NOT TO SCALE

A

B

CD

E

35°

25

130

A B

E F

C D

r°

q°130° p°

F B C G

t°s°

AD E

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In the diagram above, DAE and FBCG are parallel lines.

AC = BC and angle FBA = 130o.

(i) What is the special name given to triangle ABC?

Answer (i) ………..…………………….

[1]

(ii) Work out the values of p, q, r, s and t.

Answer (ii) ……….. 𝑝 = …………. 𝑞 = …………… 𝑟 =…………..

𝑠 = …………… 𝑡 =…….…….

[5]

13. In the diagram below, AB and CD are straight lines which intersect at M.

LMN and PQRS are parallel straight lines.

Angle QMR = 35o and angle BMN = 64o.

NOT TO SCALE

Find the value of 𝑥, 𝑦 and 𝑧.

Answer 𝑥 = ………..…………………….

[1]

64°

35°

x°

y° z°

P Q R S

L N

D B

A C

M

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Answer 𝑦 = ………..…………………….

[2]

Answer 𝑧 = ………..…………………….

[2]

14.

NOT TO SCALE

In the diagram PQ is parallel to SR, and QR is parallel to PT.

PQ = QR, angle PRS = 63o and angle RST = 100o.

Find the value of

(i) 𝑥,

Answer (i) 𝑥 = ………..…………………….

[1]

(ii) 𝑦,

Answer (ii) 𝑦 = ………..…………………….

[2]

(iii) 𝑧.

Answer (iii) 𝑧 = ………..…………………….

[2]

63100

z

yxP

T

S R

Q

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15. A square ABCD, of side 8 cm, has another square, PQRS, drawn inside it.

P, Q, R and S are at the midpoints of each side of the square ABCD, as

shown in the diagram.

NOT TO SCALE

(a) Calculate the length of PQ.

Answer (a) ………..……………………. cm

[2]

(b) Calculate the area of the square PQRS.

Answer (b) ………..……………………. cm2

[1]

16. Each interior angle of a regular polygon is 150o.

(a) Work out the size of each exterior angle.

Answer (a) ………..…………………….

[1]

(b) Work out the number of sides of this polygon.

Answer (b) ………..…………………….

[2]

A B

D C

P

S

R

Q

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17. ABCDE is a regular polygon with centre O.

NOT TO SCALE

(i) What is the special name for the polygon?

Answer (i) ………..…………………….

[1]

(ii) Calculate angle EOD.

Answer (ii) Angle EOD = ………..………

[2]

(iii) Calculate angle AED.

Answer (iiI) Angle AED = ………..………

[2]

18. (i) Calculate the interior angle of a regular heptagon (seven-sided

polygon).

Write down all the figures on your calculator display.

Answer (i) ………..…………………….

[2]

A

B

C

DE

O

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(ii) Round your answer to part (a)(i) to 1 decimal place.

Answer (ii) ………..…………………….

[1]

19. The area of a square is 42.25 cm2.

Work out the length of one side of the square.

Answer …………….…………… cm

[1]

20.

NOT TO SCALE

For the shape above, work out

(a) the perimeter,

Answer (a) …………….…………… cm

[2]

(b) the area.

Answer (b) …………….…………… cm2

[2]

21. Find the circumference of a circle of radius 5.7 cm.

Write down your answer

(a) exactly as it appears on your calculator,

10 cm

14 cm

22 cm

6 cm

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Answer (a) …………….…………… cm

[1]

(b) correct to the nearest centimetre.

Answer (b) …………….…………… cm

[1]

22. Calculate the circumference of a circle of diameter 13 cm.

Answer …………..….…………… cm

[2]

23. Calculate the area of a circle with radius 3.7 centimetres.

Answer ………..……..……… cm2

[2]

24.

NOT TO SCALE

The solid shown is a cuboid with length 4 cm, width 2 cm and height 3

cm.

(a) Draw an accurate net of the cuboid on the grid below.

3cm

2cm

4cm

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[2]

(b) Using your net, calculate the total surface area of the cuboid.

Answer (b) …………………………. cm2

[2]

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25.

NOT TO SCALE

A cube of side l metres has a volume of 20 cubic metres.

Calculate the value of 𝑙.

Answer 𝑙 = …………………………………….

[2]

26.

NOT TO SCALE

l m

lm

lm

A B

C

AB

C

4 cm

6 cm

8 cm

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The diagram above shows a cuboid and its net.

(a) Calculate the total surface area of the cuboid.

Answer (a) …………………………. cm2

[3]

(b) Calculate the volume of the cuboid.

Answer (b) …………………………. cm3

[2]

(c) An ant walks directly from A to C on the surface of the cuboid.

(i) Draw a straight line on the net to show this route.

[1]

(ii) Calculate the length of the ant’s journey.

Answer (c)(ii) …………………………. cm

[3]

27. A candle, made from wax, is in the shape of a cylinder.

The radius is 1.5 centimetres and the height is 20 centimetres.

NOT TO SCALE

(a) Calculate, correct to the nearest cubic centimetre,

the volume of wax in the candle.

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[The volume of a cylinder, radius r, height h, is πr2h.]

Answer (a) …………………………. cm2

[2]

(b) The candle burns 0.8 cm3 of wax every minute.

How long, in hours and minutes, will it last?

Write your answer correct to the nearest minute

Answer (b) …….……… h …….….…. min

[3]

28.

NOT TO SCALE

An old Greek coin is a cylinder with a diameter of 30 millimetres and a

thickness of 2 millimetres.

Calculate, in cubic millimetres, the volume of the coin.

[The volume of a cylinder, radius r, height h, is πr2h.]

Answer ……………………………………. mm3

[2]

29.

NOT TO SCALE

30 mm

2 mm

ON

M

1200m

900m

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A hot air balloon, M, is 900 metres vertically above a point N on the

ground.

A boy stands at a point O, 1200 metres horizontally from N.

(a) Calculate the distance, OM, of the boy from the balloon.

Answer (a) OM = ………..……. m

[2]

(b) Calculate angle MON.

Answer (b) Angle MON = ………..…….

[2]

30.

NOT TO SCALE

ABC is a right angled triangle.

AB = 4.2 m and BC = 1.5 m.

Calculate the length of AC.

Answer AC = ………..……. m

[2]

1.5m

4.2m

A

B C