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STS\G10\Term 2\Further_Maths Booklet\CDAU\ADVETI Version 1.0 2013 1 | 28
GRADE 10
FURTHER MATHEMATICS ASSESSMENT
BOOKLET
TERM 2
STS\G10\Term 2\Further_Maths Booklet\CDAU\ADVETI Version 1.0 2013 2 | 28
MATHEMATICS (MATHE1002)
Mathematics (MATHE1002) 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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STS\G10\Term 2\Further_Maths Booklet\CDAU\ADVETI Version 1.0 2013 3 | 28
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. Simplify
(a) 𝑝2 × 𝑝3
Answer (a) ………..……..………….
[1]
(b) 𝑞3 ÷ 𝑞−4
Answer (b) ………..……..………….
[1]
(c) (𝑟2)3
Answer (c) ………..……..………….
[1]
5. Write down the value of 𝑥 when
(a) 2𝑥 = 8
Answer (a) 𝑥 = ………..……..………………
[1]
(b) 3𝑥 = 1
81
Answer (b) 𝑥 = ………..……..………………
[1]
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6. (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]
(c) 5𝑟 =1
25. Find the value of 𝑟.
Answer (c) 𝑟 = ………..……..………………
[1]
7. (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]
(c) 6𝑟 =1
36. Find the value of 𝑟.
Answer (c) 𝑟 = ………..……..………………
[1]
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8. Simplify
(a) (1
𝑝)
0,
Answer (a) ………..……..………………
[1]
(b) 𝑞3 × 𝑞5,
Answer (b) ………..……..………………
[1]
(c) (𝑟4)−2.
Answer (c) ………..……..………………
[1]
9. Simplify 3𝑥2𝑦 × 𝑥4𝑦2
Answer ………..……..………………
[2]
10. Simplify
(a) 4𝑑 × 6𝑑4
Answer (a) ………..……..………………
[2]
(b) 28𝑡3 ÷ 7𝑡−4
Answer (b) ………..……..………………
[2]
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11. In the diagram AB is parallel to CD.
Calculate the value of 𝑎.
NOT TO SCALE
Answer 𝑎 = ………..………………….
[2]
12.
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]
A
B
C
D
a°
5a°
A
B
CD
E
35°
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13.
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]
14.
NOT TO SCALE
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]
25
130
A B
E F
C D
r°
q°130° p°
F B C G
t°s°
AD E
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15. 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]
Answer 𝑦 = ………..…………………….
[2]
Answer 𝑧 = ………..…………………….
[2]
64°
35°
x°
y° z°
P Q R S
L N
D B
A C
M
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16.
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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17. 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]
18. 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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19. 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]
20. (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]
21. The shape of a flower bed is a regular octagon, ABCDEFGH, with sides of
4 metres.
Show that the interior angle of a regular octagon is 135o.
Answer ………..…………………….
[2]
22. (a) Write down the name of a polygon with 8 sides.
Answer (a) ………..…………………….
[1]
(b) Find the size of the interior angle of a regular polygon with 8 sides.
Answer (b) ………..…………………….
[2]
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23. The area of a square is 42.25 cm2.
Work out the length of one side of the square.
Answer …………….…………… cm
[1]
24.
NOT TO SCALE
For the shape above, work out
(a) the perimeter,
Answer (a) …………….…………… cm
[2]
(b) the area.
Answer (b) …………….…………… cm2
[2]
10 cm
14 cm
22 cm
6 cm
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25.
NOT TO SCALE
A model ship is flying two flags.
The first is a rectangle 5 centimetres by 6 centimetres.
The second is an isosceles triangle with base 8 centimetres and height h
centimetres.
The flags are equal in area.
Find the value of h.
Answer h = …………….……………….
[2]
26.
NOT TO SCALE
A builder estimates the number of bricks in a wall by dividing the area of
the wall by the area of the face of a brick.
A brick wall is 10 metres long and 1.5 metres high.
6 cm
h cm
5 cm
8 cm
Part of the wall
brick face
20cm
10cm
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Each brick is 20 centimetres long and 10 centimetres high.
Calculate how many bricks the builder estimates are in the wall.
Show all your working.
Answer …………..….…………… bricks
[3]
27. Find the circumference of a circle of radius 5.7 cm.
Write down your answer
(a) exactly as it appears on your calculator,
Answer (a) …………….…………… cm
[1]
(b) correct to the nearest centimetre.
Answer (b) …………….…………… cm
[1]
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28.
NOT TO SCALE
(a) The diagram shows the plan for a new soccer field.
The length of the pitch is 90 metres.
The ratio length : width is 5 : 3.
Calculate the width of the pitch.
Answer (a) …………..….…………… m
[2]
(b) The centre circle has a circumference of 57.5 metres.
Calculate the radius.
Answer (b) …………..….…………… m
[2]
90 m
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29. The diagram shows a square tile of side 10 centimetres with 4 identical
quarter circles shaded.
Calculate the area of the unshaded region.
Answer …………..….…………… cm2
[4]
30. Calculate the circumference of a circle of diameter 13 cm.
Answer …………..….…………… cm
[2]
10 cm
10 cm
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31. Calculate the area of a circle with radius 3.7 centimetres.
Answer ………..……..……… cm2
[2]
32.
NOT TO SCALE
3cm
2cm
4cm
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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.
[2]
(b) Using your net, calculate the total surface area of the cuboid.
Answer (b) …………………………. cm2
[2]
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33.
NOT TO SCALE
A cube of side l metres has a volume of 20 cubic metres.
Calculate the value of 𝑙.
Answer 𝑙 = …………………………………….
[2]
l m
lm
lm
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34.
NOT TO SCALE
NOT TO SCALE
The diagram above shows a cuboid and its net.
(a) Calculate the total surface area of the cuboid.
Answer (a) …………………………. cm2
[3]
A B
C
AB
C
4 cm
6 cm
8 cm
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(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]
35. 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.
[The volume of a cylinder, radius r, height h, is πr2h.]
Answer (a) …………………………. cm2
[2]
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(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]
36.
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]
37.
NOT TO SCALE
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.
30 mm
2 mm
ON
M
1200m
900m
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(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]
38.
NOT TO SCALE
ABC is a right angled triangle.
AB = 3.9 m and BC = 2.4 m.
Calculate the length of AC.
Answer AC = ………..……. m
[2]
2.4m
3.9m
A
B C
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39.
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]
40. Town E is 14 kilometres due east of D.
Town F is due south of E, and DF = 17 kilometres.
Calculate the distance from E to F.
NOT TO SCALE
Answer …………………………. km
[2]
1.5m
4.2m
A
B C
D E
F
14km
16km
North
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41.
NOT TO SCALE
A physics teacher uses a set of identical triangular glass prisms in a
lesson.
Diagram 1 shows one of the prisms.
Diagram 2 shows the cross-section of one prism.
The triangle ABC is equilateral, with sides of length 3 cm and height AD.
(a) (i) Calculate the length of AD.
Answer (a)(i) …………………. cm
[2]
(ii) Calculate the area of triangle ABC.
Answer (a)(ii) …………………. cm2
[2]
(iii) The length of the prism is 8 cm. Calculate the volume of the
prism.
Answer (a)(iii) …………………. cm3
[2]
A
CB D
3cm
3cm3cm
8cm
A
CB 3cm
3cm3cm
Diagram 1 Diagram 2
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(b) After the lesson, the glass prisms are put into a box, which is also a
triangular prism.
The cross-section is an equilateral triangle, with sides of length 9 cm.
The length of the box is 16 cm.
NOT TO SCALE
(i) Work out the largest number of glass prisms that can fit into
the box.
Answer (b)(i) ………………………
[2]
(ii) Sketch a net of the box. (Accurate construction is not
required.)
[1]
(iii) Calculate the surface area of the box.
Answer (b)(iii) ……………………… cm2
[6]
(iv) The box was made out of plastic, which cost 6 cents per
square centimetre.
To make the box, 540 cm2 of plastic was bought.
Calculate the total cost of the plastic, giving your answer in
dollars.
Answer (b)(iv) $ ………………….
[2]
16cm9cm
9cm9cm
