section 3: revision tests - pearson africa · 76 section 3: revision tests section 3: revision...

76 Section 3: Revision tests

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.

77Section 3: Revision tests

Teacher’s name: _________________________ Class name: _________________________

Student’s name: _________________________ Date: _________________________

Chapter 1 Revision Test

1 a 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. _______________________________________________________________________ 2 Find the HCF of:

a 45 and 105 _____________ b 60, 108 and 156 _____________ 3 Find the LCM of:

a 20 and 25 _____________ b 6, 7 and 8 _____________ 4 Which of the numbers 4, 6 and 9 divide exactly into 51 420? _______________________________________ 5 In 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 _____________ 6 Find the next three terms of the

sequence 1, 9, 25, 49, _____________,

_____________, _____________. What is the rule for the sequence? _______________________________________ _______________________________________ _______________________________________ 7 Look at Figure 1.7.

Figure 1.7

Chapter revision test sheets

78 Section 3: Revision tests78

Draw a graph like Figure 1.7 to show the factors of 24.

8 Express 11 664 as a product of its factors in index form. Hence find √ ______

11 664 . __________________________________________________________________________ 9 Given: 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. __________________________________________________________________________

79Section 3: Revision tests 79




1 A cloth curtain has an area of 1.2 m2. Express this as a number of mm2. __________________________________________________________________________ 2 Simplify.

a 4n5 × 7n _______________________________________________________________________

b 6 × 103 × 3 × 104

_______________________________________________________________________ 3 Simplify.

a 20a8 ÷ 5a3

_______________________________________________________________________b (9 × 106) ÷ (2 × 102)

_______________________________________________________________________ 4 Remove negative indices and simplify:

a 10–5

_______________________________________________________________________b y0 × y–7

_______________________________________________________________________ 5 Express these numbers in standard form.

a 6 700 000 _____________ b 29 _____________ c 290 ______________ 6 Change these numbers to ordinary form.

a 8.4 × 105 _____________ b 6 × 104 _____________ c 6.3 × 101 __________ 7 Express these numbers in standard form.

a 0.000 07 _____________ b 0.8 _____________ c 0.002 4 ___________ 8 Change these numbers to decimal fractions.

a 6 × 10–4 _____________ b 4.8 × 10–2 _____________ c 1.7 × 10–1 _________ 9 Round off these numbers.

a 8 348 to 3 s.f. _____________ b 0.007 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.

_______________________________________________________________________




Chapter 3 Revision TestIn 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. 1 S ̂ R P = a. Name another angle the same size as a. __________________________________________________________________________ 2 R ̂ S Q = b. Name another angle the same size as b. __________________________________________________________________________ 3 P ̂ S Q = c. Name another angle the same size as c. __________________________________________________________________________ 4 S ̂ P R = d. Name another angle the same size as d. __________________________________________________________________________ 5 Make a rough copy of Figure 3.11.

Figure 3.11

Replace the 27° with 32° and fill in the sizes of all the other angles.


6 Make 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? __________________________________________________________________________

7 Make a rough copy of Figure 3.15.

Figure 3.15


Replace the 31° and 52° with 29° and 63°. Fill in the sizes of all the other angles.

8 Daudu says, ‘A kite always has at least one pair of opposite angles that are equal.’ Is Daudu correct?

__________________________________________________________________________ 9 In 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? __________________________________________________________________________





1 Simplify 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) = _____________ 4 a 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) = _____________ 7 a –8 × 6 _____________ b 8 × (–6) _____________

c –8 × (–6) _____________ d –6 × (–8) _____________ 8 a +16, +12, +8, +4, 0, _____________, _____________, _____________, _____________

b (+4) × 4, (+3) × 4, (+2) × 4, (+1) × 4, 0 × 4, _____________, _____________, _____________, _____________


c (+4) × 4 = +16 (+3) × 4 = +12 (+2) × 4 = +8 (+1) × 4 = +4 0 × 4 = 0 _____________ × _____________ = _____________ _____________ × _____________ = _____________ _____________ × _____________ = _____________ _____________ × _____________ = _____________ 9 Simplify 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?

__________________________________________________________________________




Chapter 5 Revision TestTable 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. 1 How many men are in the group? __________________________________________________________________________ 2 If you owned a shoe shop, which size of shoe would you order most of? __________________________________________________________________________ 3 Draw pictogram of this information.

4 Draw a bar chart of the information in Table 5.6.


5 Table 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 Frequency Angle of sector6 4 × 360° = 60°7 5 × 360° = 75°8 9 × 360° = _____________9 4 × 360° = _____________

10 2 × 360° = _____________Totals 24 360°

Table 5.7

6 Hence, 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. 7 What fraction of the student’s time was spent in bed? _________________________________________ _________________________________________ 8 How many sectors in Figure 5.6 are connected

with school? _________________________________________ _________________________________________ 9 How much time does this come to? _________________________________________ _________________________________________ 10 Thursday is market day. How much time do the

mother and student spend at the market? _________________________________________ _________________________________________

Figure 5.6




Chapter 6 Revision TestFind 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 _____________

7 The 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.

_______________________________________________________________________


d Make a sketch of the quadrilateral.

e What kind of quadrilateral is it? _______________________________________________________________________ 8 Calculate 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? _______________________________________________________________________





1 Simplify:a (–3y) × (–7y) ___________________________________________________________b 1 _ 3 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. 2 ax2 – b ___________________________________________________________________ 3 ax + by ___________________________________________________________________ 4 (a – 2b)

_____ 3(x + y) ____________________________________________________________________ 5 Remove the brackets from:

a 3a(2a – b) ______________________________________________________________b (4x – y)3x ______________________________________________________________

6 Remove the brackets from:a –a(5a – 9) ______________________________________________________________b –3(–5x – 7) _____________________________________________________________

7 Remove the brackets and simplify these expressions:a 4 – 5(7 – 3x) ____________________________________________________________b 16a – 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) __________________________________________________________




Chapter 8 Revision TestComplete the empty boxes.

1 39 273 3 s.f.

2 45 197 s.f. 45 000

3 5.55555 3 d.p.

4 8.97 1 d.p.

5 0.05844 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. 7 a book has 334 pages. There are about 460 words per page. Estimate how many words are in the

book. _______________________________________________________________________ 8 Two friends have their 14th birthday on the same day. Estimate their age in minutes. __________________________________________________________________________ 9 A 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? __________________________________________________________________________





1 a Convert 32% to: i a common fraction. _____________ ii a decimal fraction. _____________b Convert 14 __ 25 to: i a decimal fraction. _____________ ii a percentage. _____________c Convert 0.85 to: i 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:

a 24 __ 8 = ___ 5 b : 42 = 2 : 12

6 Share N5 200 in the ratio:a 13 : 27

_______________________________________________________________________b 2 : 4 : 7

_______________________________________________________________________ 7 If 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. __________________________________________________________________________





1 Find the simple interest on N40 000 for 3 years at 2 1 _ 2 % 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) Rate of taxFirst N200 000 10%

Over N200 000 and up to N400 00 15%

Over N400 000 and up to N600 000 20%

Over N600 000 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.

_______________________________________________________________________


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 N20

Letters between States N50

Letters outside Nigeria N100

Parcels within Nigeria:≤ 1 kg N200

> 1 kg and ≤ 2 kg 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. __________________________________________________________________________





1 Write down all the factors of:a 12p _____________ b 16ax2 _____________

2 Find the HCF of:a pq and 5pr _____________ b 2x2 and 10x _____________

3 Find the LCM of:a 3a and 4b _____________ b 5xy and 3x2 _____________

4 Complete the brackets in 18ax2 – 12x = 6x(_____________) 5 Factorise:

a 2a2b + 5ab b –3mn – 15m

6 Complete the boxes in:

a 5k __ 8 = ____ 40 b 5m __ n = 15mn ____

7 Simplify:

a x _ 5 – x __ 20 b 5 _ n + 3 _ n

8 Simplify:

a 7 _ x + 1 b 4 __ 5a – 3 __ 4b

9 Simplify:

a 4x – 1 ____ 3 + 5x b (a + 2b) _____ 5 – (2a – 3b)

______ 15

10 Simplify (x – 2y) _____ 2 – (x + 8y)

_____ –6 as far as possible. __________________________________________________________________________





1 a On 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. 2 a What is the scale on the axes? ___________________________ ___________________________ ___________________________ ___________________________

3 Which point is at the origin? __________________________________________________________________________ 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? __________________________________________________________________________

Figure 12.23


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.


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. __________________________________________________________________________




Chapter 13 Revision TestSolve the equations in Questions 1–6. Check your solutions. 1 31 = 7x – 4

__________________________________________________________________________

2 5y + 8 = 3y

__________________________________________________________________________

3 10(9 – z) = 0

__________________________________________________________________________

4 7(m – 2) = 3(2m – 3)

__________________________________________________________________________

5 6a __ 5 – 4 1 _ 2 = 0

__________________________________________________________________________

6 (b + 3) ____ 5 = (3b + 3)

_____ 3

__________________________________________________________________________ 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? __________________________________________________________________________




Chapter 14 Revision TestSolve the equations in Questions 1–6. Then check your solutions. 1 Sugar costs N240 per kg.

a Complete Table 14.18.

Sugar (kg) 1 2 3 4 5 6

Cost (N) 240 480 720

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.


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) 1 2 3 4 5 6

Distance (m) –7.5 –15 –22.5

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.

___________________________________________________________________


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.


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 4 5 6

Mass (kg) 3.4 3.7 4.0 4.3

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? _______________________________________________________________________


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.

Use your graph to change these marks out of 60 to percentages.a 54 _____________ b 28 _____________ c 38 _____________

Figure 14.14


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? _________________________________ _________________________________

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? _______________________________________________________________________

How long did part CD take? _______________________________________________________________________

f 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 When Kojo leaves the university, how far is Mary from the hospital? _______________________________________________________________________

j At 12:15, how far apart were the students? _______________________________________________________________________

Figure 14.33 Travel graph for Mary and Kojo


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. _______________________________________________________________________




Chapter 15 Revision TestIn Questions 1–3, △ABC is such that AB = 6 cm, BC = 9 cm and A ̂ B C = 75°. 1 Construct △ABC accurately.

2 Measure AC and A ̂ C B. __________________________________________________________________________ 3 Construct the bisector of BC. In Q4–6, △XYZ is such that YZ = 8 cm, ̂ Y = 28° and ̂ Z = 118°. 4 Make a rough sketch of △XYZ.


5 Construct △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.


7 Make a rough sketch of △PQR. What can you say about this triangle?

8 Draw △PQR accurately.


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°.

b Construct the bisector of Z ̂ X Y to meet YZ at D.c Measure DZ.

_______________________________________________________________________




Chapter 16 Revision TestComplete 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?

__________________________________________________________________________


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).


Compare your drawing with someone who sits at least two desks from you.


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? _______________________________________________________________________





1 In △PQR, P ̂ Q R = 90°, PQ = 7 km, QR = 24 km. Sketch △PQR and use Pythagoras’ rule to calculate PR.


Find the value of m in each part of Figure 17.21. All measurements are in cm.

In each case, find the value of y2 before finding the value of m.2 m = _____________ 3 m = _____________4 m = _____________ 5 m = _____________ 6 Here are Pythagorean triples. Reduce them

to their simplest terms.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? __________________________________________________________________________

2 3

4 5

Figure 17.21





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 provisionBudget allocation (%)

2014/15 2015/16

Formal primary and JSS schools 72% 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%

Table 18.8 UBE budget allocations

2 Which area accounts for most of the budget? __________________________________________________________________________


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.

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? __________________________________________________________________________

Figure 18.8





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. ____________________________________ ____________________________________ 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°. __________________________________________________________________________

Figure 19.32


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

a round house with dimensions as given in Figure 19.33. Use the value 22 __ 7 for π.

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

__________________________________________________________________________





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. ___________________________ ___________________________ ___________________________ 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.

Figure 20.21


Use Figure 20.22 and a protractor to answer Questions 5 and 6.

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 20.22

Figure 20.23





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


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:a Red?

_______________________________________________________________________b Yellow?

_______________________________________________________________________c Either green or yellow?

_______________________________________________________________________d White?

_______________________________________________________________________ Table 21.12 shows the student distribution a university. Use the table to answer Questions 7 to 9.

Female Male Total

Students aged 21 years and over 621 807

Students aged 21 years and under 1 398 1 684

Total

Table 21.12


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:

a Female? _______________________________________________________________________

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?

__________________________________________________________________________





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 _____________ 3b 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


b x < 5

7 a Solve 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.

a –1 __ 3y ≤ –5 _______________________________________________________________________

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? _______________________________________________________________________





1 Complete this table of values:

x –3 0 +3

y = 2x – 3

Table 23.8

2 a Use 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. _______________________________________________________________________


c Use your graph (or otherwise) to find the value of x when y = –2. _______________________________________________________________________ 3 P(–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 a Draw 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


b What do you notice about the three lines you have drawn? _______________________________________________________________________ 5 y = 2 _ 3 x – 4 is the equation of a line.

a Re-write the equation in the form ax + by + c = 0 _______________________________________________________________________

b If a = 2, what are the values of b and c? _______________________________________________________________________


6 a Use 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. __________________________________________________________________________


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.





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? __________________________________________________________________________


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.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.

Figure 24.32


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. _______________________________________________________________________

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