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Mathematics questions, chapter 3
Nama / NameKelas / ClassTarikh / Date

Algebraic Formulae

40 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Show your working for Section B.

Section A: objective questions

12 marks
Choose the correct answer. Each question carries 1 mark.
1

Question 1

Which of the following is an algebraic formula?
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B
A formula is an equation that connects variables. 3m + 6n and 4x² − 9 are expressions (no equals sign) and 2x + 1 > 5 is an inequality.
For the teacher: Remembering, low difficulty, standard 3.1.1
Textbook p. 44
2

Question 2

In the formula P = a + 2b, which letter is the subject of the formula?
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C
The subject is the single letter with coefficient 1 on one side of the equation, written on its own: P.
For the teacher: Remembering, low difficulty, standard 3.1.2
Textbook p. 46
3

Question 3

Table 1 shows the number of dancers in a cultural club. Which formula gives L, the total number of Lion dancers?
Table of dancers. Sumazau: Malay a, Chinese 2c, Indian 2a. Kuda Kepang: Malay 2b, Chinese b, Indian 5b. Lion: Malay 2c, Chinese 3a, Indian c
Table 1
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A
Add the Lion row: 2c + 3a + c = 3a + 3c. Option C leaves out the Indian dancers. Dancers are added, not multiplied.
For the teacher: Understanding, low difficulty, standard 3.1.1
Textbook p. 45
4

Question 4

A shop sells pens at RM3 each and books at RM7 each. All items have a 20% discount. Which formula gives the selling price, z, of x pens and y books?
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D
A 20% discount means paying 100% − 20% = 80% = 0.8 of the total 3x + 7y. The 0.8 multiplies the whole bracket.
For the teacher: Applying, medium difficulty, standard 3.1.1
Textbook p. 45
5

Question 5

Make x the subject of the formula y = 3x − 5.
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B
Add 5 to both sides: y + 5 = 3x. Divide both sides by 3: x = (y + 5)/3. Option C divides only the 5.
For the teacher: Applying, low difficulty, standard 3.1.2
Textbook p. 46
6

Question 6

Given t = 125p, express p in terms of t.
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C
Multiply both sides by 5p: 5pt = 12. Divide both sides by 5t: p = 12/(5t). Option A multiplies by t instead of dividing.
For the teacher: Applying, medium difficulty, standard 3.1.2
Textbook p. 46
7

Question 7

Given k = √(m5), express m in terms of k.
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A
Square both sides: k² = m/5. Multiply both sides by 5: m = 5k². Squaring undoes a square root.
For the teacher: Understanding, medium difficulty, standard 3.1.2
Textbook p. 47
8

Question 8

Given F = 3x − 2y, find the value of F when x = 4 and y = −5.
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D
F = 3(4) − 2(−5) = 12 + 10 = 22. Option A forgets that subtracting −10 gives +10.
For the teacher: Applying, low difficulty, standard 3.1.3
Textbook p. 47
9

Question 9

Given y = √(3x − 2), find the value of x when y = 4.
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B
Square both sides: 16 = 3x − 2, so 3x = 18 and x = 6. Option A forgets to square. Option C subtracts 2 instead of adding it.
For the teacher: Applying, high difficulty, standard 3.1.3
Textbook p. 48
10

Question 10

Aiman changed the subject of h = 4k − 7 and wrote k = h − 74. Which statement is correct?
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C
To undo − 7, add 7 to both sides: h + 7 = 4k. Then divide by 4: k = (h + 7)/4.
For the teacher: Analysing, medium difficulty, standard 3.1.2
Textbook p. 46
11

Question 11

A pen costs RMx and a ruler costs RM(x + 2). Siti pays RM19 for 3 pens and 2 rulers. What is the price of a pen?
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A
3x + 2(x + 2) = 19, so 5x + 4 = 19, 5x = 15 and x = 3. A pen costs RM3 (a ruler RM5).
For the teacher: Applying, medium difficulty, standard 3.1.4
Textbook p. 49
12

Question 12

A car travels 12 km on 1 litre of petrol. Petrol costs RMp a litre. Which formula gives the cost, C, of petrol for a journey of d km?
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D
Litres used = d ÷ 12. Cost = litres × price = (d/12) × p = dp/12.
For the teacher: Understanding, medium difficulty, standard 3.1.1
Textbook p. 50

Section B: structured questions

28 marks
Answer all questions. Show your working.
13

Question 13

A shop sells notebooks at RM4 each and pens at RM2.50 each. A customer gets a 20% discount on the total price.
[2 marks] (a)Write a formula for the amount payable, z, in RM, when m notebooks and n pens are bought. Give your answer without brackets.
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Tick each point you got.
[2 marks] (b)Calculate z when m = 5 and n = 4.
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Check: (20 + 10) × 0.8 = 24.
Tick each point you got.
For the teacher: Applying, low difficulty, standard 3.1.1
Textbook p. 45
14

Question 14

Express the letter in brackets as the subject of the formula.
[2 marks] (a)3y = 7wx   [x]
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Tick each point you got.
[3 marks] (b)3a = √(3b) + 5   [b]
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 3.1.2
Textbook p. 46
15

Question 15

Given 5u = 3r − s, calculate the value of r when u = 3 and s = −6.
[2 marks] (a)Show your working.
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 3.1.3
Textbook p. 47
16

Question 16

Given Q = 2vu − v.
[3 marks] (a)Express u as the subject of the formula.
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Tick each point you got.
[1 mark] (b)Calculate the value of u when v = 2 and Q = 4.
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Tick each point you got.
For the teacher: Applying, high difficulty, standard 3.1.3
Textbook p. 52
17

Question 17

A bun costs RMx. A cup of drink costs RM3 more than a bun. Ali pays RM19 for 2 buns and 3 cups of drink.
[1 mark] (a)Write an equation in x for the total amount paid.
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Tick each point you got.
[2 marks] (b)Find the price of a bun and the price of a cup of drink.
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 3.1.4
Textbook p. 49
18

Question 18

Hafiz changed the subject of the formula 2s − m = b to m. His working is: m = b − 2s.
[1 mark] (a)Hafiz's answer is
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wrong
The sign of m is still negative after 2s − m = b, so he cannot move 2s across without changing the sign of m.
[2 marks] (b)Show the correct working and give the correct answer.
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Or: −m = b − 2s, then multiply both sides by −1 to get m = 2s − b.
Tick each point you got.
For the teacher: Evaluating, medium difficulty, standard 3.1.2
Textbook p. 46
19

Question 19

A formula is T = 5a + 3b.
[2 marks] (a)Write a short real-life situation that this formula could describe. State what T, a and b stand for.
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T is the total cost in RM of a cups of tea at RM5 each and b buns at RM3 each.
Tick each point you got.
For the teacher: Creating, medium difficulty, standard 3.1.1
Textbook p. 44
20

Question 20

Diagram 1 shows a trapezium with an area of 40 cm². The value of x + y is 10 cm.
Trapezium with parallel sides x cm at the top and 3y cm at the bottom and a height of 5 cm
Diagram 1
[2 marks] (a)Use the area to form an equation in x and y.
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Tick each point you got.
[3 marks] (b)Calculate the values of x and y.
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Check: 12 × (7 + 9) × 5 = 40.
Tick each point you got.
For the teacher: Analysing, high difficulty, standard 3.1.4
Textbook p. 51