Download GRADE 10 MATHEMATICS ASSESSMENT BOOKLET

GRADE 10
MATHEMATICS ASSESSMENT BOOKLET
TERM 2
MATHEMATICS (MATHC1002)
Topic
Mathematics (MATHC1002) ASSESSMENT TASK COVER PAGE
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1.
Look at the sequence of numbers
7,
11,
15,
19,……….
(a) Write down the next number in the sequence.
23
Answer (a) ……….…………………….……
[1]
(b) Find the 10th number in the sequence.
43
Answer (b) ……….…………………….……
[1]
(c)
Write an expression, in terms of n, for the nth number in the
sequence.
4n + 3
Answer (c) ……….…………………….……
[1]
2.
Pattern 1
Pattern 2
Pattern 3
The first three patterns in a sequence are shown above.
(a) Complete the table.
Pattern number
1
2
Number of dots
5
8
3
11
4
14
[1]
(b) Find a formula for the number of dots, d, in the nth pattern.
3n + 2
Answer (b) d = ………………………….……
[1]
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(c)
Find the number of dots in the 60th pattern.
182
Answer (c) …….…..………………….……
[1]
(d) Find the number of the pattern that has 89 dots.
29
Answer (d) …….…..………………….……
[1]
3.
The diagram below shows a sequence of patterns made from dots
and lines.
draw here
1 dot
2 dots
3 dots
4 dots
(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
Lines
4
7
10
5
13
16
6
19
[2]
(c)
How many lines are in the pattern with 99 dots?
298
Answer (c) ……………………..….………
[2]
(d) How many lines are in the pattern with n dots?
3n + 1
Answer (d) ………………….….….………
[2]
(e) Complete the following statement.
28
There are 85 lines in the pattern with ………………
dots.
[2]
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4.
(a)
4𝑝 × 45 = 415 . Find the value of 𝑝.
10
Answer (a) 𝑝 = ………..……..………………
[1]
(b)
27 ÷ 2𝑞 = 24 . Find the value of 𝑞.
3
Answer (b) 𝑞 = ………..……..………………
[1]
5.
(a)
3𝑝 × 35 = 314 . Find the value of 𝑝.
9
Answer (a) 𝑝 = ………..……..………………
[1]
(b)
28 ÷ 2𝑞 = 23 . Find the value of 𝑞.
5
Answer (b) 𝑞 = ………..……..………………
[1]
6.
Simplify
(a)
1 0
(𝑝) ,
1
Answer (a) ………..……..………………
[1]
(b)
𝑞3 × 𝑞5 ,
q8
Answer (b) ………..……..………………
[1]
(c)
(𝑟 4 )−2 .
r -8
Answer (c) ………..……..………………
[1]
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7.
Simplify 3𝑥 2 𝑦 × 𝑥 4 𝑦 2
6
3x y 3
Answer ………..……..………………
[2]
8.
Simplify
(a) 4𝑑 × 6𝑑4
24d 5
Answer (a) ………..……..………………
[2]
28𝑡 3 ÷ 7𝑡 −4
(b)
4t 7
Answer (b) ………..……..………………
[2]
9.
In the diagram AB is parallel to CD.
Calculate the value of 𝑎.
B
a°
D
A
5a°
C
NOT TO SCALE
30
Answer 𝑎 = ………..………………….
[2]
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10.
A
B
D
C
35°
NOT TO SCALE
E
In the diagram BC is parallel to DE. ABD and ACE are straight lines.
Angle BDE = 35o.
Calculate the size of angle DBC
145
Answer (b) Angle DBC = ………..…………….
[1]
11.
A
B
25
C
D
130
E
NOT TO SCALE
F
In the diagram, AB, CD and EF are parallel lines.
Angle ABC = 25o and angle CEF = 130o.
Calculate angle BCE.
75
Answer Angle BCE = ………..…………….
[2]
12.
D
A
E
s° r° t°
130° p°
F
B
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C
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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?
isosceles
Answer (i) ………..…………………….
[1]
(ii)
Work out the values of p, q, r, s and t.
50
50
80 𝑟 =…………..
Answer (ii) ……….. 𝑝 = ………….
𝑞 = ……………
80
50
𝑠 = ……………
𝑡 =…….…….
13.
[5]
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.
D
L
B
M
x°
64°
N
35°
P
Q
y°
A
R
S
z°
NOT TO SCALE
C
Find the value of 𝑥, 𝑦 and 𝑧.
35
Answer 𝑥 = ………..…………………….
[1]
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64
Answer 𝑦 = ………..…………………….
[2]
81
Answer 𝑧 = ………..…………………….
[2]
14.
Q
P
x
y
T z
100
63
S
R
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,
63
Answer (i) 𝑥 = ………..…………………….
[1]
(ii)
𝑦,
54
Answer (ii) 𝑦 = ………..…………………….
[2]
(iii)
𝑧.
134
Answer (iii) 𝑧 = ………..…………………….
[2]
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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.
A
P
Q
S
D
(a)
B
R
C
NOT TO SCALE
Calculate the length of PQ.
5,66
Answer (a) ………..……………………. cm
[2]
(b)
Calculate the area of the square PQRS.
32
Answer (b) ………..……………………. cm2
[1]
16.
Each interior angle of a regular polygon is 150o.
(a)
Work out the size of each exterior angle.
30
Answer (a) ………..…………………….
[1]
(b)
Work out the number of sides of this polygon.
12
Answer (b) ………..…………………….
[2]
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17.
ABCDE is a regular polygon with centre O.
B
A
E
(i)
C
O
D
NOT TO SCALE
What is the special name for the polygon?
pentagon
Answer (i) ………..…………………….
[1]
(ii)
Calculate angle EOD.
72
Answer (ii) Angle EOD = ………..………
[2]
(iii)
Calculate angle AED.
108
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.
128.571...
Answer (i) ………..…………………….
[2]
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(ii)
Round your answer to part (a)(i) to 1 decimal place.
128.6
Answer (ii) ………..…………………….
[1]
19.
The area of a square is 42.25 cm2.
Work out the length of one side of the square.
6.5
Answer …………….……………
cm
[1]
20.
14 cm
6 cm
10 cm
NOT TO SCALE
22 cm
For the shape above, work out
(a)
the perimeter,
64
Answer (a) …………….…………… cm
[2]
(b)
the area.
172
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,
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35.81415...
Answer (a) …………….……………
cm
[1]
(b)
correct to the nearest centimetre.
36
Answer (b) …………….……………
cm
[1]
22.
Calculate the circumference of a circle of diameter 13 cm.
40.8
Answer …………..….……………
cm
[2]
23.
Calculate the area of a circle with radius 3.7 centimetres.
43
Answer ………..……..……… cm2
[2]
24.
3 cm
2 cm
4 cm
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.
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*DRAW THE NET HERE
**NET OF THE CUBOID
[2]
(b)
Using your net, calculate the total surface area of the cuboid.
52
Answer (b) …………………………. cm2
[2]
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25.
lm
lm
NOT TO SCALE
lm
A cube of side l metres has a volume of 20 cubic metres.
Calculate the value of 𝑙.
2.71...
Answer 𝑙 = …………………………………….
[2]
26.
C
A
NOT TO SCALE
B
6 cm
C
4 cm
*DRAW A LINE FROM A - C
B
A
8 cm
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The diagram above shows a cuboid and its net.
(a)
Calculate the total surface area of the cuboid.
208
Answer (a) ………………………….
cm2
[3]
(b)
Calculate the volume of the cuboid.
192
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.
12.8
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.]
141
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
56
2
Answer (b) …….………
h …….….…. min
[3]
28.
30 mm
2 mm
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.]
1413
Answer …………………………………….
mm3
[2]
29.
M
900 m
O
N
1200 m
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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.
1500
Answer (a) OM = ………..…….
m
[2]
(b)
Calculate angle MON.
XXX
MNO
MNO
90
Answer (b) Angle MON
XXX = ………..…….
[2]
30.
A
4.2 m
B
1.5 m
C
NOT TO SCALE
ABC is a right angled triangle.
AB = 4.2 m and BC = 1.5 m.
Calculate the length of AC.
4.46
Answer AC = ………..……. m
[2]
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