Section 3: Revision tests
Section 3 provides additional resources for the Chapter and Term revision tests found
in the Student’s Book. The Chapter and Term tests have been recreated into easy to
print test sheets that you can use for formal assessment with your class.
The answers to the Chapter and Term tests were not given in the Student’s Book
answer section, so you can conduct your assessments knowing that the students can’t
copy the answers from their Student’s Book.
There are four subsections:
1 chapter revision test sheets for printing
2 answers to the chapter revision tests
3 term revision test sheets for printing
4 answers to the term revision tests.
76
Section 3: Revision tests
Chapter revision test sheets
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 1 Revision Test
1a Write down all the factors of 60.
_______________________________________________________________________
b Which factors of 60 are prime numbers?
_______________________________________________________________________
c Write 60 as a product of its prime factors in index form.
_______________________________________________________________________
2Find the HCF of:
a 45 and 105 _____________b
60, 108 and 156 _____________
3Find the LCM of:
a 20 and 25 _____________b
6, 7 and 8 _____________
4Which of the numbers 4, 6 and 9 divide exactly into 51 420?
_______________________________________
5In the number 5 41*, the * stands for a missing
digit. Find values for * that make the number
divisible by:
a 5 _____________
b 6 _____________
c 9 _____________
6Find the next three terms of the
sequence 1, 9, 25, 49,
_____________,
_____________,
_____________.
What is the rule for the sequence?
_______________________________________
_______________________________________
_______________________________________
7Look at Figure 1.7.
Figure 1.7
Section 3: Revision tests
77
Draw a graph like Figure 1.7 to show the factors of 24.
______
8Express 11 664 as a product of its factors in index form. Hence find √​  11 664 ​. 
__________________________________________________________________________
9Given: 23 × 52 × 11 × n, where n is a whole number. What is the smallest value of n that will
make this number into a perfect square?
__________________________________________________________________________
10 Find the square root of 5.
__________________________________________________________________________
78
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 2 Revision Test
1A cloth curtain has an area of 1.2 m2. Express this as a number of mm2.
__________________________________________________________________________
2Simplify.
a 4n5 × 7n
_______________________________________________________________________
b 6 × 103 × 3 × 104
_______________________________________________________________________
3Simplify.
a 20a8 ÷ 5a3
_______________________________________________________________________
b (9 × 106) ÷ (2 × 102)
_______________________________________________________________________
4Remove negative indices and simplify:
a 10–5
_______________________________________________________________________
b y0 × y–7
_______________________________________________________________________
5Express these numbers in standard form.
a 6 700 000 _____________b 29 _____________
c 290 ______________
6Change these numbers to ordinary form.
a 8.4 × 105 _____________b6 × 104 _____________
c 6.3 × 101 __________
7Express these numbers in standard form.
a 0.000 07 _____________b0.8 _____________
c 0.002 4 ___________
8Change these numbers to decimal fractions.
a 6 × 10–4 _____________
b
4.8 × 10–2 _____________ c 1.7 × 10–1 _________
9Round off these numbers.
a 8 348 to 3 s.f. _____________ b0.007 96 to 2 s.f. _____________
c 6.329 to 1 d.p. _____________ d 0.056 84 to 3 d.p. _____________
10 In 2013, the estimated population of Nigeria was 173.6 million. If current birth rates stay the
same, the population will rise to 440.4 million by 2050.
a What will be the increase in Nigeria’s population during this time?
_______________________________________________________________________
b Express the increase in standard form to 2 s.f.
_______________________________________________________________________
Section 3: Revision tests
79
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 3 Revision Test
In Figure 3.20, PQRS is a parallelogram with diagonals PR and SQ. Four angles are marked a, b, c, d.
Figure 3.20
Use Figure 3.20 to answer Questions 1–4.
ˆ P = a. Name another angle the same size as a.
1S​ R​
__________________________________________________________________________
2R​ˆ
S ​ Q = b. Name another angle the same size as b.
__________________________________________________________________________
3P​ˆ
S ​ Q = c. Name another angle the same size as c.
__________________________________________________________________________
ˆ
4S​ P​
 R = d. Name another angle the same size as d.
__________________________________________________________________________
5Make a rough copy of Figure 3.11.
Figure 3.11
80
Replace the 27° with 32° and fill in the sizes of all the other angles.
Section 3: Revision tests
6Make a rough copy of Figure 3.14.
Figure 3.14
Replace 112° and 40° with 115° and 39°.
What will then be the sizes of the two other angles of the kite?
__________________________________________________________________________
7Make a rough copy of Figure 3.15.
Figure 3.15
Section 3: Revision tests
81
Replace the 31° and 52° with 29° and 63°. Fill in the sizes of all the other angles.
8Daudu says, ‘A kite always has at least one pair of opposite angles that are equal.’ Is Daudu
correct?
__________________________________________________________________________
9In general, which of these do not have a line of symmetry: kite, parallelogram, rectangle,
rhombus, square, trapezium?
__________________________________________________________________________
10 Rosebelle says, ‘It is impossible for a trapezium to have a pair of equal angles.’
Barbara says, ‘I disagree. In fact I can draw a trapezium with two pairs of equal angles.’
Who is correct?
__________________________________________________________________________
82
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 4 Revision Test
1Simplify these expressions:
a (+8) – (–1) _____________
b 16 – (+7) – 14 _____________
c (–7) + (–7) + (–7) _____________
d –5 + (–1) – (–14) _____________
2+30, +20, +10, _____________, _____________, _____________, _____________
3(+10) × (+3)= _____________
(+10) × (+2)= _____________
(+10) × (+1)= _____________
(+10) × 0 = _____________
(+10) × (–1)= _____________
(+10) × (–2)= _____________
(+10) × (–3)= _____________
4a 8 × (+7) _____________
b 8 × (–7) _____________
c 7 × (+8) _____________
d 7 × (–8) _____________
5–30, –20, –10, _____________, _____________, _____________, _____________
6(+3) × (–10) = _____________
(+2) × (–10) = _____________
(+1) × (–10) = _____________
0 × (–10) = _____________
(–1) × (–10) = _____________
(–2) × (–10) = _____________
(–3) × (–10) = _____________
7a –8 × 6 _____________b
8 × (–6) _____________
c –8 × (–6) _____________
d –6 × (–8) _____________
8a +16, +12, +8, +4, 0, _____________, _____________, _____________, _____________
b (+4) × 4, (+3) × 4, (+2) × 4, (+1) × 4, 0 × 4, _____________, _____________,
_____________, _____________
Section 3: Revision tests
83
c (+4) × 4 = +16
(+3) × 4 = +12
(+2) × 4 = +8
(+1) × 4 = +4
0 × 4 = 0
_____________ × _____________ = _____________
_____________ × _____________ = _____________
_____________ × _____________ = _____________
_____________ × _____________ = _____________
9Simplify these expressions:
a (–5) × 6 _____________
b (–3) × (–8) _____________
c 7 × (–4) _____________
d (–6) × (–6) _____________
e (–15) ÷ 3 _____________
f
(–18) ÷ (–2) _____________
g 36 ÷ (–9) _____________
10 In an experiment, a scientist records a temperature of –120°C. Later the temperature rises to a
value one-twentieth of this. What is the new temperature?
__________________________________________________________________________
84
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 5 Revision Test
Table 5.6 is shows the shoe sizes of a group of men.
Shoe size
6
7
8
9
10
Frequency
4
5
9
4
2
Table 5.6 Shoe sizes
Use Table 5.6 to answer Questions 1–6.
1How many men are in the group?
__________________________________________________________________________
2If you owned a shoe shop, which size of shoe would you order most of?
__________________________________________________________________________
3Draw pictogram of this information.
4Draw a bar chart of the information in Table 5.6.
Section 3: Revision tests
85
5Table 5.7 shows how a student began to calculate the angles of sectors when drawing a bar chart
of the shoe sizes. Complete the table.
Shoe size
6
7
8
9
10
Totals
Frequency
4
5
9
4
2
24
Angle of sector
× 360° = 60°
× 360° = 75°
× 360° = _____________
× 360° = _____________
× 360° = _____________
360°
Table 5.7
6Hence, draw a pie chart of the information in Table 5.7.
Figure 5.6 shows how a student spent last Thursday (24 hours).
Use Figure 5.6 to answer Questions 7–10.
7What fraction of the student’s time was spent in bed?
_________________________________________
_________________________________________
8How many sectors in Figure 5.6 are connected
with school?
_________________________________________
_________________________________________
9How much time does this come to?
_________________________________________
_________________________________________
10 Thursday is market day. How much time do the
mother and student spend at the market?
_________________________________________
_________________________________________
86
Section 3: Revision tests
Figure 5.6
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 6 Revision Test
Find the sizes of the lettered angles in Figure 6.24.
1
2
3
4
5
6
Figure 6.24
a _____________b
_____________
c_____________
d
_____________
e_____________f_____________
g_____________h _____________
i_____________
j_____________
k
_____________l_____________
m
_____________n_____________
7The angles of a quadrilateral are m, 3m, 2m and 3m in that order.
a Write an equation in m.
_______________________________________________________________________
b Find m.
_______________________________________________________________________
c Find the angles of the quadrilateral.
_______________________________________________________________________
Section 3: Revision tests
87
d Make a sketch of the quadrilateral.
e What kind of quadrilateral is it?
_______________________________________________________________________
8Calculate the size of each angle of a regular octagon.
__________________________________________________________________________
9
Figure 6.25
In Figure 6.25:
a Find the value of x.
_______________________________________________________________________
b Find the unknown angles in the hexagon.
_______________________________________________________________________
10 a How many sides does a polygon have, if the sum of its angles is 18 right angles?
_______________________________________________________________________
b If the polygon is regular, what is the size of each angle in degrees?
_______________________________________________________________________
88
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 7 Revision Test
1Simplify:
a (–3y) × (–7y) ____________________________________________________________
b _​  13 ​of (–42a)______________________________________________________________
c 63a2b ÷ 9ab2_____________________________________________________________
Use a = 2, b = –8, x = 3, y = –5 to find the value of the expressions in Questions 2–4.
2ax2 – b ____________________________________________________________________
3ax + by ____________________________________________________________________
(a – 2b)
4​ _____
  
​ _____________________________________________________________________
3(x + y)
5Remove the brackets from:
a 3a(2a – b)_______________________________________________________________
b (4x – y)3x _______________________________________________________________
6Remove the brackets from:
a –a(5a – 9)_______________________________________________________________
b –3(–5x – 7)______________________________________________________________
7 Remove the brackets and simplify these expressions:
a 4 – 5(7 – 3x)_____________________________________________________________
b16a – 7(2a – 3b)__________________________________________________________
8 Remove the brackets and simplify these expressions:
a x(x – 6) – (x + 8)__________________________________________________________
b x(2x – 3) – 4(2x – 3)_______________________________________________________
9 Expand these expressions:
a(p + q)(r – s)_____________________________________________________________
b(4a – b)(a + 2b)___________________________________________________________
10 Expand these expressions:
a(a + 4b)(a – 2b)___________________________________________________________
b(6x – 7y)(3x + y)__________________________________________________________
c(5x – 6)2________________________________________________________________
d(9a + 1)(9a – 1)___________________________________________________________
Section 3: Revision tests
89
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 8 Revision Test
Complete the empty boxes.
1
39 273
2
45 197
3
5.55555
4
8.97
5
0.05844
3 s.f.
s.f.
45 000
3 d.p.
1 d.p.
d.p.
0.06
6‘Our village is 127.49 m above sea level.’ What is wrong with this statement? Make it more
sensible.
__________________________________________________________________________
__________________________________________________________________________
In Questions 7–10, round the given numbers to 1 s.f., before estimating the answer. Then use a
calculator to see if your estimates are reasonable.
7a book has 334 pages. There are about 460 words per page. Estimate how many words are in the
book.
_______________________________________________________________________
8Two friends have their 14th birthday on the same day. Estimate their age in minutes.
__________________________________________________________________________
9A boy counts the number of paces he takes to walk between two villages. His pace is about
82 cm. Estimate in km how far the villages are apart, if he takes 6 854 paces.
_______________________________________________________________________
10 A bucket contains 8.8 ℓ. A water tank contains 10 000 ℓ at the beginning of a week. During the
week a school draws 848 buckets of water from the tank. Approximately how many ℓ are left?
__________________________________________________________________________
90
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 9 Revision Test
1aConvert 32% to:
ia common fraction. _____________
b
__
​  14
 ​ to:
25
Convert
i a decimal fraction. _____________
c Convert 0.85 to:
i a percentage. _____________
ii a decimal fraction. _____________
ii a percentage. _____________
ii a common fraction. _____________
2 A 3 kg pack of vaccine is sufficient to vaccinate 120 children. How many children would a 10 kg
pack vaccinate?
__________________________________________________________________________
3 ‘A 30-year old woman has a body mass of 50 kg. What will be her body mass when she is 60?’ Is
it possible to use mathematics to answer this question? Give reasons.
__________________________________________________________________________
4 Write the ratio N450 : N810 as simply as possible.
__________________________________________________________________________
5 Fill the boxes:
24 ___
a​ __
  ​ = ​     ​
8
5
b
: 42 = 2 : 12
6Share N5 200 in the ratio:
a 13 : 27
_______________________________________________________________________
b 2 : 4 : 7
_______________________________________________________________________
7If N1 000 is equivalent to R68 (South African rand), how many rands are equivalent to N3 500?
__________________________________________________________________________
8 Complete these statements:
a 17% of 400 is _____________.
b 0.5 cm is _____________ of 4 cm.
c _____________ is 150% of 14 kg.
9 In a village, there are 375 children under the age of 10. If 68% of them have had malaria, how
many children have escaped the disease?
__________________________________________________________________________
10 A State has an area of 9 970 km2 and a population of 2 458 000. Round these numbers to 2 s.f.
and estimate the population density of the state in people per km2.
__________________________________________________________________________
Section 3: Revision tests
91
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 10 Revision Test
1 Find the simple interest on N40 000 for 3 years at 2​ _12 ​ % per annum.
__________________________________________________________________________
2 How much must I pay back if I borrow N120 000 for 2 years at 12% simple interest?
__________________________________________________________________________
3 Use the PAYE tax system in Table 10.1 and the tax allowances to answer this question.
Tax bands on taxable income (N)
First N200 000
Over N200 000 and up to N400 00
Over N400 000 and up to N600 000
Over N600 000
Rate of tax
10%
15%
20%
25%
Table 10.1 Tax bands for PAYE system
A person with two children and no dependent relatives earns N180 000 per month before tax.
Calculate:
a The tax allowance.
_______________________________________________________________________
b The taxable income.
_______________________________________________________________________
c The total tax paid.
_______________________________________________________________________
d The money left after paying tax.
_______________________________________________________________________
4 In a market, a clothing trader has a sign that says:
‘TODAY ONLY!! 15k in the N off all marked prices!!’
a What is the percentage discount?
_______________________________________________________________________
b What would be the cost of a shirt that is marked as N2 800?
_______________________________________________________________________
5 To buy a TV set by hire purchase requires a 20% deposit with the balance payable in equal
monthly instalments over two years. If the hire purchase price is N93 600, calculate:
a The amount of the deposit.
92
_______________________________________________________________________
Section 3: Revision tests
b The remainder to be paid.
_______________________________________________________________________
c The amount of each monthly instalment.
_______________________________________________________________________
6 A boutique has a sign that says: ‘ALL PRICES INCLUDE 5% VAT’.
How much VAT does the Government receive on a wedding dress that costs N94 500?
__________________________________________________________________________
7 Refer to Table 10.3.
Cost per unit
N15
Standing charge
N750 per quarter
VAT
5% of total bill
Table 10.3 Typical electricity charges
Calculate the monthly electricity bill for a family that uses 824 units in a month.
__________________________________________________________________________
8 Refer to Table 10.4.
Letters up to 20 g:
Letters within a State
Letters between States
Letters outside Nigeria
Parcels within Nigeria:
≤ 1 kg
> 1 kg and ≤ 2 kg
N20
N50
N100
N200
N400
Table 10.4 Typical postal charges
A company based in Lagos State posts these items at the end of a day’s business:
• 5 letters to Abuja and 8 letters to Kano.
• 2 letters to Calcutta and 4 letters to Beijing.
• 3 parcels weighing 0.2 kg each to Enugu.
What is the total postage bill?
__________________________________________________________________________
9 A villager bought 11 goats for N76 000. A year later he sold them at a profit of 32%. What was
the average selling price per goat?
__________________________________________________________________________
10 A customer deposits a cheque for N50 000. Her bank charges 2% commission for clearing the
cheque. Calculate how much money is credited to her account.
__________________________________________________________________________
Section 3: Revision tests
93
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 11 Revision Test
1 Write down all the factors of:
a12p _____________b16ax2 _____________
2 Find the HCF of:
a pq and 5pr _____________ b2x2 and 10x _____________
3 Find the LCM of:
a3a and 4b _____________ b5xy and 3x2 _____________
4 Complete the brackets in 18ax2 – 12x = 6x(_____________)
5Factorise:
a2a2b + 5ab
b–3mn – 15m
6 Complete the boxes in:
5k ____
5m ____
15mn
a​ __
  ​ = ​ 
  
 b​ __
​
 
  
​
n  ​ = ​ 
8
40
7Simplify:
​  20x  ​
a​ _5x ​ – __
b​ _n5 ​ + _​  n3 ​
8Simplify:
a​ _7x ​ + 1
3
4
b​ __
  ​ – __
​  4b
  ​
5a
9Simplify:
(a + 2b) ______
– 3b)
b​ _____
   
 
​ – ​  (2a15
   
​ 
5
4x – 1
   
​ + 5x
a​ ____
3
(x – 2y)
(x + 8y)
10 Simplify ​ _____
   
​ – _____
​  –6   
​ as far as possible.
2
__________________________________________________________________________
94
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 12 Revision Test
1 aOn the graph paper below, draw a number line from –5 to +14.
b On the line mark the points A(2), B(–2), C(+7), D(–4.5), E(13.5).
c What is the distance between B and C?
_______________________________________________________________________
Figure 12.23 is a Cartesian graph,
showing points A, B, C, D, E, F, G.
Use Figure 12.23 to answer Questions 2–6.
2a What is the scale on the axes?
___________________________
___________________________
___________________________
___________________________
3 Which point is at the origin?
Figure 12.23
__________________________________________________________________________
4 What is another name for the y-axis?
__________________________________________________________________________
5 Write down the co-ordinates of points A, B, C, and D. What do you notice?
__________________________________________________________________________
6 Write down the co-ordinates of points D, E, F, G. What do you notice?
__________________________________________________________________________
Section 3: Revision tests
95
7 On a Cartesian graph, plot these points:
A(0; 4), B(–3; –1), C(–2; –4), D(1; 1), E(3; 2), F(4; 0) and G(2; –1).
Take the origin near the middle of your graph paper. Let 2 cm represent 1 unit on both axes.
96
Section 3: Revision tests
Use your graph in Question 7 to answer Questions 8–10.
8 Draw quadrilateral ABCD. What kind of quadrilateral is it?
__________________________________________________________________________
Let its diagonals cross at X. Find the co-ordinates of X.
__________________________________________________________________________
9 What do you notice about points B, X, D and E?
__________________________________________________________________________
10 Draw quadrilateral DEFG. What kind of quadrilateral is it?
__________________________________________________________________________
Let its diagonals cross at Y. Find the co-ordinates of Y.
__________________________________________________________________________
Section 3: Revision tests
97
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 13 Revision Test
Solve the equations in Questions 1–6. Check your solutions.
1 31 = 7x – 4
__________________________________________________________________________
25y + 8 = 3y
__________________________________________________________________________
3 10(9 – z) = 0
__________________________________________________________________________
47(m – 2) = 3(2m – 3)
__________________________________________________________________________
6a
1
5​ __
  ​ – 4​ _ ​= 0
2
5
__________________________________________________________________________
(b + 3) _____
6​ ____
   
​ = ​  (3b3+  3) 
​ 
5
__________________________________________________________________________
7 A rectangle has a perimeter of 40 cm. Its longer side is 17 cm and its shorter side is k cm.
Find the value of k.
__________________________________________________________________________
8 Find two consecutive odd numbers such that 6 times the smaller plus 3 times the larger comes
to 105.
__________________________________________________________________________
9 The age gap between a father and his daughter is y years.
a Express two-thirds of the age gap in terms of y.
_______________________________________________________________________
b Express three-quarters of the age gap in terms of y.
_______________________________________________________________________
c If the daughter is 5 and the age gap is 5 times the age of the daughter what is age of the
father?
_______________________________________________________________________
10 I am thinking of a number. I add 62 to the number and divide the total by 7. The result is 4 less
than the number I thought of. What was the number?
__________________________________________________________________________
98
Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 14 Revision Test
Solve the equations in Questions 1–6. Then check your solutions.
1 Sugar costs N240 per kg.
a
Complete Table 14.18.
Sugar (kg)
Cost (N)
1
2
3
240
480
720
4
5
6
Table 14.18
b Using a scale of 2 cm to 1 kg on the horizontal axis and 1 cm to N100 on the vertical axis,
draw a graph of this information.
Section 3: Revision tests
99
c Use your graph to find:
i
The cost of 22 kg of sugar.
___________________________________________________________________
ii How much sugar can be bought for N900.
___________________________________________________________________
2 The drill of an oil well drills downwards at a rate of 7.5 m/h.
a
Complete Table 14.19.
Time (h)
Distance (m)
1
2
3
–7.5
–15
–22.5
4
5
6
Table 14.19
b Draw the origin near the top left corner of your graph paper. Using a scale of 2 cm to 1 h on
the horizontal axis and 1 cm to 5 m on the vertical axis, draw a graph of the information.
c Use the graph to find:
i
How long it takes the drill to drill down through 25 m.
___________________________________________________________________
ii The distance of the drill below ground level after 90 min.
___________________________________________________________________
100 Section 3: Revision tests
3 Sun shades cost N900 each.
a Make a table of values showing the cost of 0, 1, 2, 3, 4 and 5 sunshades.
b Use scales of 2 cm to 1 sunshade on the horizontal axis and 2 cm to N500 on the vertical
axis. Draw a graph to show this information.
Section 3: Revision tests 101
c Is your graph continuous or discontinuous?
_______________________________________________________________________
4 A baby was 3.4 kg when he was born. For his first 6 weeks, his mass increased by about 0.3 kg
per week.
a
Complete Table 14.20.
Week
0
1
2
3
Mass (kg)
3.4
3.7
4.0
4.3
4
5
6
Table 14.20
b Choose a suitable scale and draw a graph of this information.
c Approximately how many days old was the baby when his mass was 5 kg?
_______________________________________________________________________
102 Section 3: Revision tests
5 Use Figure 14.14 to find the US$ equivalent of:
a N300 _____________
b N550 _____________
6 Use Figure 14.14 and scaling to find the naira
equivalent of:
a US$400 _____________
b US$2 400 _____________
7 Use Figure 14.16 as a model to make a conversion
graph for changing marks out of 60 to percentages.
Figure 14.14
Use your graph to change these marks out of 60 to percentages.
a 54 _____________
b 28 _____________
c 38 _____________
Section 3: Revision tests 103
Figure 14.33 is a graph of the journeys of two
students, Mary and Kojo.
• They leave their university at different
times and travel 6 km to the nearest
hospital.
• Mary walks and the line ABCD shows
her journey.
• Kojo cycles and the line FD shows his
journey.
8 Use Figure 14.33 to answer these questions:
a What time did Mary leave the university?
_________________________________
_________________________________
b What time did Mary arrive at the hospital?
_________________________________
_________________________________
Figure 14.33 Travel graph for Mary and Kojo
c Mary stopped for a rest during her journey. How long did she stop for?
_______________________________________________________________________
d During part AB of Mary’s journey, how far did she walk?
_______________________________________________________________________
How long did part AB take?
_______________________________________________________________________
e During part CD of Mary’s journey, how far did she walk?
f
_______________________________________________________________________
How long did part CD take?
_______________________________________________________________________
At 11:15, how far was Mary from the hospital?
_______________________________________________________________________
g What time did Kojo leave the university?
_______________________________________________________________________
h What time did Kojo arrive at the hospital?
i
j
_______________________________________________________________________
When Kojo leaves the university, how far is Mary from the hospital?
_______________________________________________________________________
At 12:15, how far apart were the students?
_______________________________________________________________________
104 Section 3: Revision tests
9 Use Figure 14.33 to find these speeds:
a Mary’s speed between A and B.
_______________________________________________________________________
b Mary’s speed between C and D.
_______________________________________________________________________
c Mary’s average speed for the whole journey.
_______________________________________________________________________
d Kojo’s average speed for his whole journey.
_______________________________________________________________________
10 Figure 14.34 shows the speed–time graph of a car.
Figure 14.34
a Calculate the acceleration of the car during the first 20 s.
_______________________________________________________________________
b Calculate the distance the car travels from rest before it begins to decelerate.
_______________________________________________________________________
c Given that the car decelerates at 0.5 m/s2, calculate the total time taken for the journey.
_______________________________________________________________________
Section 3: Revision tests 105
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 15 Revision Test
ˆ C = 75°.
In Questions 1–3, △ABC is such that AB = 6 cm, BC = 9 cm and A​ B​
1Construct △ABC accurately.
ˆ B.
2 Measure AC and A​ C​
__________________________________________________________________________
3 Construct the bisector of BC.
In Q4–6, △XYZ is such that YZ = 8 cm, Y​
​ ˆ = 28° and Z​
​ ˆ  = 118°.
4 Make a rough sketch of △XYZ.
106 Section 3: Revision tests
5Construct △XYZ accurately.
6 Measure the shortest side of △XYZ.
__________________________________________________________________________
In Questions 7–9, △PQR is such that PQ = QR = 7 cm and PR = 9 cm.
Section 3: Revision tests 107
7 Make a rough sketch of △PQR. What can you say about this triangle?
8Draw △PQR accurately.
108 Section 3: Revision tests
9 Measure the largest angle of △PQR, then bisect it.
10 a Construct △XYZ in which XY = 9 cm, YZ = 12 cm and XZ = 60°.
ˆ Y to meet YZ at D.
b Construct the bisector of Z​ X​
c Measure DZ.
_______________________________________________________________________
Section 3: Revision tests 109
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 16 Revision Test
Complete the boxes in Table 16.3.
Actual length
Scale
Length on scale drawing
1
400 m
1 to 5 000
 cm
2
3.2 km
2 cm to 1 km
 cm
3
km
5 cm to 1 km
9.4 cm
4
m
1 : 500
6.8 cm
5
200 km
1 cm to
km
2.5 cm
Table 16.3
6 In Figure 16.17 use measurement to find the scale of
the inner square (shaded) compared to the outer square.
Figure 16.17
7 An architect uses a scale of 1 : 200 to draw the plan of a building. A corridor in the building is
12.2 m long. How long will it be on the plan?
__________________________________________________________________________
110 Section 3: Revision tests
8 Figure 16.18 is a small scale map of Central African Republic (CAR).
Figure 16.18
a What is the scale on a map?
_______________________________________________________________________
b How many countries surround CAR?
_______________________________________________________________________
c Assume that the scale on the map is 1 cm to 200 km. How far, to the nearest 100 km, is it
from Bangui to Bangassou?
_______________________________________________________________________
9 You will need a metre rule or a measuring tape. Make suitable measurements to draw a plan of
your classroom.
Your plan should show the position of the door(s), the window(s) and the chalk board. Include
the position of your desk (but not the others).
Section 3: Revision tests 111
Compare your drawing with someone who sits at least two desks from you.
112 Section 3: Revision tests
10 Figure 16.19 shows the plan of a postgraduate student apartment.
Figure 16.19
a What is the length, breadth and area of the apartment?
_______________________________________________________________________
b How many rooms does it contain?
_______________________________________________________________________
Which room is the smallest?
_______________________________________________________________________
c How many doors and windows has the apartment?
_______________________________________________________________________
d Estimate the length and breadth of the shower.
_______________________________________________________________________
e What tells you that this apartment is above ground level?
_______________________________________________________________________
Section 3: Revision tests 113
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 17 Revision Test
ˆ R = 90°, PQ = 7 km, QR = 24 km. Sketch △PQR and use Pythagoras’ rule to
1In △PQR, P​ Q​
calculate PR.
114 Section 3: Revision tests
Find the value of m in each part of Figure 17.21.
All measurements are in cm.
2
3
In each case, find the value of y2 before
finding the value of m.
2 m = _____________
3 m = _____________
4 m = _____________
5 m = _____________
4
5
6 Here are Pythagorean triples. Reduce them
to their simplest terms.
Figure 17.21
a (24, 45, 51)
_______________________________________________________________________
b (24, 10, 26)
_______________________________________________________________________
c (24, 18, 30)
_______________________________________________________________________
7 Find out which of these are Pythagorean triples.
a (24, 58, 62)
b (14, 49, 50)
c (15, 36, 39)
d (32, 60, 68)
_______________________________________________________________________
8 Calculate, to 2 s.f., the length of a diagonal of a square that measures 20 cm by 20 cm.
__________________________________________________________________________
9 A ladder 7 m long leans against a wall as shown in Figure 17.22.
Figure 17.22
The ladder’s foot is 2 m from the wall. Calculate how far up the wall the ladder reaches.
__________________________________________________________________________
10 A student cycles from home to school, first eastwards to a road junction 12 km from home, then
southwards to school. If the school is 19 km from home, how far is it from the road junction?
__________________________________________________________________________
Section 3: Revision tests 115
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 18 Revision Test
Month
City
J
F
M
A
M
J
J
A
S
O
N
D
Sokoto
0
0
0
10
48
91
155
249
145
15
15
0
Jos
3
3
28
56
203
226
330
292
213
41
3
3
Ibadan
10
23
89
137
150
188
160
84
178
155
46
10
Port Harcourt
66
109
155
262
404
660
531
318
516
460
213
81
Table 18.1 Mean monthly rainfall (mm)
1 Refer to Table 18.1.
a Which city had the highest rainfall in March?
_______________________________________________________________________
b Which city had the lowest rainfall in August?
_______________________________________________________________________
c What is the average rainfall for Jos in June?
_______________________________________________________________________
d For every city, the rainfall increases from April to May. Is this true?
_______________________________________________________________________
Refer to Table 18.8 for Questions 2–6.
Table 18.8 shows how a SUBEB (State UBE Board) allocated its budget to provide basic education
for the years 2014/15 and 2015/16.
Area of public UBE provision
Budget allocation (%)
2014/15
72%
2015/16
74%
Non-formal education
2%
1%
Nomadic education
12%
12%
Schools for physically challenged
4%
2%
Pre-school (nursery) education
10%
11%
Total
100%
100%
Formal primary and JSS schools
Table 18.8 UBE budget allocations
2 Which area accounts for most of the budget?
__________________________________________________________________________
116 Section 3: Revision tests
3 On which area is least money spent?
__________________________________________________________________________
4 In 2015, the SUBEB decided that as many children with physical challenges as possible should
attend ‘normal’ schools. How does this show in Table 18.8?
__________________________________________________________________________
5 Find out what non-formal education includes.
__________________________________________________________________________
6 If you were the SUBEB director, how would you allocate the budget?
__________________________________________________________________________
Use this information to answer
Questions 7–10:
To keep fit Gbenga decides to do a long
walk every day. His target is to walk at least
8 000 paces each day. He records his daily
walk to the nearest 1 000 paces. Figure 18.8
shows Gbenga’s walking performance for
one week.
Figure 18.8
7 On which day(s) did Gbenga achieve his target?
__________________________________________________________________________
8 On which day(s) did Gbenga not go for a walk?
__________________________________________________________________________
9 On which other days did Gbenga not meet his target?
__________________________________________________________________________
10 What was Gbenga’s average number of paces per day for the week?
__________________________________________________________________________
Section 3: Revision tests 117
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 19 Revision Test
Use the value 3.1 for π, unless told otherwise. Give your answers to a suitable degree of accuracy.
1 Calculate the curved surface area of cylinder of radius 6 cm and height 15 cm.
__________________________________________________________________________
2 Calculate the total surface area of the cylinder in Question 1.
__________________________________________________________________________
3 A plastic container is in the shape of an open cylinder.
It has a lid which is also an open cylinder.
Figure 19.32 gives the dimensions of the container
and lid.
Use the value 3.1 for π to find:
a The surface area of the container.
____________________________________
____________________________________
b The surface area of the lid.
____________________________________
____________________________________
c The total area of plastic needed to make both.
____________________________________
____________________________________
Figure 19.32
4 A cylindrical wooden column is 3 m high and 28 cm in diameter. Use the value for π
to calculate:
a The volume of the column.
_______________________________________________________________________
b The mass, in kg, of the column if the density of the wood is 0.8 g/cm3.
_______________________________________________________________________
5 Use Pythagoras’ rule to find the slant height of a cone with base diameter 16 cm and height
17 cm.
__________________________________________________________________________
6 Calculate the area of a sector of a circle of radius 12 cm and angle 150°.
__________________________________________________________________________
118 Section 3: Revision tests
7 Calculate the base radius of a cone made from the sector of a circle in Question 6.
__________________________________________________________________________
8 Calculate the total surface area of the cone in Question 5.
__________________________________________________________________________
9 A round house is made of two basic shapes: a cylinder and a cone. Calculate the volume of air in
22
a round house with dimensions as given in Figure 19.33. Use the value ​ __
  ​for π.
7
Figure 19.33
__________________________________________________________________________
10 An oil drum is cut in half. One half is used as a water trough as shown in Figure 19.34. Use the
dimensions in Figure 19.34 to estimate the capacity of the water trough in litres.
Figure 19.34
__________________________________________________________________________
Section 3: Revision tests 119
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 20 Revision Test
Use Figure 20.21 to answer Questions 1–3.
1 Name three things in Figure 20.21
that are horizontal.
___________________________
___________________________
___________________________
2 Name three things in Figure 20.21
that are vertical.
___________________________
___________________________
___________________________
3 Name three things in Figure 20.21
that are neither horizontal nor vertical.
___________________________
Figure 20.21
___________________________
___________________________
4 Make a sketch of something in your classroom. It must have a some edges that are horizontal and
vertical, b at least one edge that is neither horizontal nor vertical.
Discuss your drawing with your classmates.
120 Section 3: Revision tests
se Figure 20.22 and a protractor
U
to answer Questions 5 and 6.
Figure 20.22
5 Measure the angle of elevation of Person P from Person E.
__________________________________________________________________________
6 Measure the angle of depression of Person D from Person P.
__________________________________________________________________________
7 The angle of elevation of the Sun is 45°. A tree has a shadow 12 m long. Find the height of
the tree.
__________________________________________________________________________
8 The angle of elevation of the Sun is 27°. A man is 180 cm tall. How long is his shadow?
Give your answer to the nearest 10 cm.
__________________________________________________________________________
9 The angle of elevation of the top of a radio mast from a point 53 m from its base on level ground
is 61°. Find the height of the mast to the nearest 5 m.
__________________________________________________________________________
10 Figure 20.21 shows the angles of elevation of an
aircraft from two points 1 100 m apart.
Find the height of the aircraft above the ground
to the nearest 100 m.
_____________________________________
_____________________________________
_____________________________________
_____________________________________
Figure 20.23
Section 3: Revision tests 121
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 21 Revision Test
1 The rainfall records of a town gives these totals for February for the past ten years:
0 mm
2 mm
0 mm
0 mm
0 mm
3 mm
0 mm
0 mm
0 mm
0 mm
Table 21.10
a What is the probability that there no rain in February? Give your answer in three different
ways.
_______________________________________________________________________
b Someone says, ‘It never rains in this town In February.’ Are they correct? Why do you think
they said that?
_______________________________________________________________________
2 Open this book at any page. Look at the page number on the left-hand page. Is the number
divisible by 3? (That is, is the sum of its digits divisible by 3?)
Record this as ‘yes’ or ‘no’. Do this thirty times.
What is the experimental probability that if someone opens this book at random, the left-hand
page number is:
a An even number?
_______________________________________________________________________
b An odd number?
_______________________________________________________________________
c Divisible by 3?
_______________________________________________________________________
3 The annual birth rate in a village is 3%. This means that for every 100 people, there are 3 live
births. How many live births would you expect in a year for a village with a population of 731?
__________________________________________________________________________
4 Mark a pencil like that in Figure 21.5.
Figure 21.5
122 Section 3: Revision tests
Roll the pencil across your desk 50 times and note the number on the top face. What is the
experimental probability of getting a number that is a perfect square?
__________________________________________________________________________
5 A teacher records the number of times students arrive late for lessons. Table 21.11 shows the
number of latecomers in a month.
Total latecomers
48
Total on time
552
Table 21.11
a How many students did he record altogether?
_______________________________________________________________________
b What percentage of students were late?
_______________________________________________________________________
c What is the probability that at the beginning of a lesson some students will be late?
_______________________________________________________________________
6 A packet of sweets contains 15 red sweets, 8 green sweets and 7 yellow sweets. I pick a sweet at
random. What is the probability that it is:
aRed?
_______________________________________________________________________
bYellow?
_______________________________________________________________________
c Either green or yellow?
_______________________________________________________________________
dWhite?
_______________________________________________________________________
Table 21.12 shows the student distribution a university. Use the table to answer Questions 7 to 9.
Students aged 21 years and over
Students aged 21 years and under
Female
621
Male
807
1 398
1 684
Total
Total
Table 21.12
Section 3: Revision tests 123
7 Round the numbers in Table 21.12 to the nearest 100 and complete the empty boxes.
Female
Male
Total
Students aged 21 years and over
Students aged 21 years and under
Total
Use the table you made in Q7 to answer Questions 8 and 9:
8 A student walks out of the gate of the university. What is the probability that the student is:
aFemale?
_______________________________________________________________________
b 21 years or older?
_______________________________________________________________________
9 The Dean of the university picks a student at random. What is the probability that the student
is:
a Male and younger than 21?
_______________________________________________________________________
b Female and 21 years or older?
_______________________________________________________________________
10 Approximately 26 000 people at a football match are wearing red supporters shirts. The
probability of picking someone from the crowd wearing a red shirt is 0.4. Roughly how many
people were at the football match?
__________________________________________________________________________
124 Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 22 Revision Test
1 Replace the words with the correct symbol.
a 4 is not equal to –9. _____________
b 4 is greater than –9. _____________
c 4 is greater than or equal to x. _____________
d y is less than 4. _____________
e z is less than or equal to 4. _____________
2 Insert a > or < on the line to make each statement true.
a –12 ÷ 4 _____________ 3
b 6 × –2.9 _____________ –18
3 Choose a letter for the unknown and change the following statement to algebra.
The student got less than 10 for her homework.
__________________________________________________________________________
4 The qualifying time for a 100 m-race is 11 seconds or less. An athlete did m seconds and did not
qualify. Another athlete did n seconds and qualified. Write down three different inequalities in m
or n or both.
__________________________________________________________________________
5 Write down the inequalities shown in the graphs in Figure 22.7.
a
4
b
0
Figure 22.7
__________________________________________________________________________
6 Sketch graphs to show these inequalities:
a x ≥ –4
Section 3: Revision tests 125
b x < 5
7 aSolve the inequality 7 ≥ 5x – 13.
_______________________________________________________________________
b Sketch a graph of the inequality.
8 Given that x is an integer, solve the inequality: x – 9 < 6x + 19.
__________________________________________________________________________
9 Solve these inequalities.
–1
a​ __
 ​ ≤ –5
3y
_______________________________________________________________________
b 8 – 3h > 41
_______________________________________________________________________
10 The angles of a triangle are x°, y° and z°, where y > 90°.
a What kind of triangle is it?
_______________________________________________________________________
b Write down an inequality in terms of x.
_______________________________________________________________________
c Write down an inequality in terms of x and y.
_______________________________________________________________________
d What is the range of values of x?
_______________________________________________________________________
126 Section 3: Revision tests
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 23 Revision Test
1 Complete this table of values:
x
y = 2x – 3
–3
0
+3
Table 23.8
2 aUse your table of values and a suitable scale to draw the graph of y = 2x – 3.
b Use your graph (or otherwise) to find the value of y when x = 2.
_______________________________________________________________________
Section 3: Revision tests 127
c Use your graph (or otherwise) to find the value of x when y = –2.
_______________________________________________________________________
3P(–2;p), Q(0;q) and R(r;10) are three points on the straight line y = 3x + 4.
a Find the values of p, q and r.
_______________________________________________________________________
b Hence plot the points and draw the line through P, Q and R.
4 aDraw the graphs of these lines on the same axes for values of x from –3 to +3.
i
y = –x – 2
ii y = –x + 2
iii y = –x + 5
128 Section 3: Revision tests
b What do you notice about the three lines you have drawn?
_______________________________________________________________________
5 y = _​  23 ​x – 4 is the equation of a line.
a Re-write the equation in the form ax + by + c = 0
_______________________________________________________________________
bIf a = 2, what are the values of b and c?
_______________________________________________________________________
Section 3: Revision tests 129
6 aUse the method in Example 2 to draw the graph of 5x – 2y = 6.
b Find where the line crosses the x-axis.
_______________________________________________________________________
7 What are the coefficients of x and y in each of these equations?
a y = 9x – 2
_______________________________________________________________________
b 2x – 7y – 2 = 0
_______________________________________________________________________
8 Write down the equations of any two lines that are parallel to y = 5x – 1.
__________________________________________________________________________
9 Write down the equations of any two lines that are parallel to 3x + 6y – 4 = 0.
__________________________________________________________________________
130 Section 3: Revision tests
10 a Complete Table 23.9 for the equation y = 3x – 5.
x
–1
+1
+2
y = 3x – 5
Table 23.9
b Using scales of 2 cm to 1 unit on the x-axis and 1 cm to 1 unit on the y-axis, draw the graph
of the equation.
c Find the x- and y-intercepts.
_______________________________________________________________________
d Draw any line through the origin that is parallel to y = 3x – 5.
Section 3: Revision tests 131
Teacher’s name: _________________________
Class name: _________________________
Student’s name: _________________________
Date:
_________________________
Chapter 24 Revision Test
1 What is the angle between these directions?
a N and SE. _____________
b N and SW. _____________
2 X is on a compass bearing of NW from Y. Show this on a sketch, similar to those in Figure 24.6.
3 What is the acute-angle bearing of X from Y in each part of Figure 24.31?
Figure 24.31
__________________________________________________________________________
4 Change your answers to Question 3 to three-figure bearings.
__________________________________________________________________________
5 If the bearing of P from Q is 298°, what is the three-figure bearing of Q from P?
__________________________________________________________________________
132 Section 3: Revision tests
6 In Figure 24.32 ON points north. Give the bearings
of J, K, L, M from O as three-figure bearings.
___________________________________________
___________________________________________
___________________________________________
___________________________________________
7 Make sketches of these bearings. Each sketch must show
a line pointing north (↑N) and details of the sizes of
the angles.
a The bearing of P from Q is 055°.
b C is on a bearing 190° from D.
Figure 24.32
c R is on a bearing 320° from S.
Figure 24.25
8 Make a rough copy of Figure 24.25, but change distance AB to 80 m. Given this information
make a scale drawing and hence estimate the width of the river to 2 s.f.:
• The tree is due north of A.
• B is due east of A.
• The tree is on bearing 300° from B.
Section 3: Revision tests 133
9 A car leaves P and drives 20 km north to Q. From Q it drives 15 km on a bearing N45°E to R.
Find the distance and bearing of R from P.
__________________________________________________________________________
10 Ikeja is approximately 60 km due south of Abeokuta. Ibadan is approximately 110 km from
Ikeja on a bearing 036°. Use scale drawing to find:
a The bearing and distance of Ibadan from Abeokuta.
_______________________________________________________________________
b How far north and how far east Ibadan is from Ikeja.
_______________________________________________________________________
134 Section 3: Revision tests