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Mathematics questions, chapter 7
Nama / NameKelas / ClassTarikh / Date

Linear inequalities

41 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 symbol means is less than or equal to?
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C
≤ is < with a line for 'equal to'. ≥ means 'greater than or equal to'.
For the teacher: Remembering, low difficulty, standard 7.1.1
Textbook p. 153
2

Question 2

Which inequality is true?
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B
−9 is to the left of −4 on the number line, so −9 < −4. The others treat −7, −8 or −1 as if they were bigger because 7, 8 or 1 look bigger.
For the teacher: Understanding, low difficulty, standard 7.1.1
Textbook p. 150
3

Question 3

Which inequality is represented on the number line in Diagram 1?
Number line from −5 to 2 with a solid circle at −2 and an arrow to the right
Diagram 1
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D
The solid circle means −2 is included, and the arrow points right (greater). x > −2 would need an open circle.
For the teacher: Understanding, low difficulty, standard 7.1.1
Textbook p. 153
4

Question 4

What is the converse of the inequality −4 > −13?
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A
Converse: if a > b, then b < a. Swap the numbers and turn the symbol round: −13 < −4. Option B swaps the numbers but keeps the same symbol, which is false.
For the teacher: Remembering, low difficulty, standard 7.1.2
Textbook p. 154
5

Question 5

Given p < q, which of the following is true?
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C
Dividing by a positive number (4) keeps the symbol. Multiplying by −3 or by −1 reverses it, and subtracting 5 keeps it, so A, B and D are false.
For the teacher: Understanding, medium difficulty, standard 7.1.2
Textbook p. 156
6

Question 6

A lift can carry a maximum load of 900 kg. Which inequality shows the total mass, m kg, that the lift can carry?
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B
Maximum 900 means 900 kg is allowed but not more: m ≤ 900. m < 900 leaves out exactly 900 kg.
For the teacher: Applying, low difficulty, standard 7.2.1
Textbook p. 158
7

Question 7

Solve x − 7 ≥ 3.
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D
Add 7 to both sides: x ≥ 3 + 7 = 10. −4 comes from subtracting 7 instead of adding. Adding does not reverse the symbol, so x ≤ 10 is wrong.
For the teacher: Applying, low difficulty, standard 7.2.2
Textbook p. 160
8

Question 8

Solve 5 − 2x > 11.
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D
−2x > 11 − 5 = 6. Divide by −2 and reverse: x < −3. x > −3 forgets to reverse; x < −8 adds 5 instead of subtracting it.
For the teacher: Applying, medium difficulty, standard 7.2.2
Textbook p. 160
9

Question 9

Diagram 2 shows the solution of a linear inequality. Which inequality has this solution?
Number line from 1 to 7 with an open circle at 4 and an arrow to the left
Diagram 2
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A
The diagram shows x < 4. 3x + 2 < 14 gives 3x < 12, x < 4. B gives x > 4, C gives x ≤ 4 (solid circle) and D gives x > −4.
For the teacher: Analysing, medium difficulty, standard 7.2.2
Textbook p. 160
10

Question 10

Solve the simultaneous linear inequalities x + 3 > 5 and 2x ≤ 10.
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C
x > 2 and x ≤ 5. The common region is 2 < x ≤ 5. Option B mixes up which end is included; A and D give only one of the two inequalities.
For the teacher: Applying, medium difficulty, standard 7.2.3
Textbook p. 162
11

Question 11

Diagram 3 shows two linear inequalities on a number line. List all the integers that satisfy both inequalities.
Number line from −3 to 5. One arrow: solid circle at −1 pointing right. Other arrow: open circle at 3 pointing left
Diagram 3
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B
The inequalities are x ≥ −1 (solid circle, included) and x < 3 (open circle, not included). Common integers: −1, 0, 1, 2.
For the teacher: Analysing, high difficulty, standard 7.2.3
Textbook p. 162
12

Question 12

Aina has RM50. She pays a booking fee of RM6 once, and each concert ticket costs RM7.50. What is the maximum number of tickets she can buy?
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A
6 + 7.5n ≤ 50, 7.5n ≤ 44, n ≤ 5.87, so the maximum is 5 (round down). 6 comes from forgetting the fee or rounding up; 7 from adding the fee to RM50.
For the teacher: Applying, high difficulty, standard 7.2.2
Textbook p. 161

Section B: structured questions

29 marks
Answer all questions. Show your working.
13

Question 13

Diagram 4 shows two number lines.
(a) Number line from 0 to 6 with an open circle at 3 and an arrow to the right labelled y. (b) Number line from −4 to 2 with a solid circle at −1 and an arrow to the left labelled k
Diagram 4
[1 mark] (a)Write the algebraic inequality represented by number line (a).
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Tick each point you got.
[1 mark] (b)Write the algebraic inequality represented by number line (b).
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Solid circle: −1 is included.
Tick each point you got.
For the teacher: Understanding, low difficulty, standard 7.1.1
Textbook p. 153
14

Question 14

It is given that 8 > −3. Choose the correct symbol to make each statement true.
[1 mark] (a)8 + 4 ☐ −3 + 4
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>
12 > 1. Adding keeps the symbol.
[1 mark] (b)8 × (−2) ☐ −3 × (−2)
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<
−16 < 6. Multiplying by a negative number reverses the symbol.
[1 mark] (c)84 ☐ −34
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>
2 > −0.75. Dividing by a positive number keeps the symbol.
For the teacher: Understanding, medium difficulty, standard 7.1.2
Textbook p. 156
15

Question 15

Answer the following.
[1 mark] (a)A taxi can carry not more than 4 passengers. Let n be the number of passengers. Write a linear inequality.
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Tick each point you got.
[2 marks] (b)Puan Rosnah donates 3% of her monthly profit, RMp, to charity. She wants her donation to exceed RM240. Write a linear inequality and find the profit she must make.
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Tick each point you got.
[1 mark] (c)h ≥ 110, where h is the height, in cm, of a passenger allowed on a roller coaster. Write a situation for this inequality.
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Tick each point you got.
For the teacher: Applying, medium difficulty, standard 7.2.1
Textbook p. 158
16

Question 16

Solve each linear inequality.
[2 marks] (a)4x + 3 ≤ 23
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Tick each point you got.
[2 marks] (b)7 − x2 > 9
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Check x = −6: 7 − (−3) = 10 > 9.
Tick each point you got.
For the teacher: Applying, medium difficulty, standard 7.2.2
Textbook p. 160
17

Question 17

Diagram 5 shows a lift with a maximum load of 900 kg. A worker pushes a 120 kg trolley into the lift. Each box on the trolley has a mass of 35 kg. Ignore the mass of the worker.
A lift with the sign Maximum load 900 kg. A trolley of mass 120 kg carrying boxes of mass 35 kg each
Diagram 5
[1 mark] (a)Let n be the number of boxes. Write a linear inequality for the total mass.
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Tick each point you got.
[2 marks] (b)Find the maximum number of boxes that can go up in the lift with the trolley.
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Check: 120 + 35 × 22 = 890 kg ≤ 900; 23 boxes give 925 kg.
Tick each point you got.
For the teacher: Applying, high difficulty, standard 7.2.2
Textbook p. 161
18

Question 18

Diagram 6 shows two gym membership plans. Danial wants to choose the cheaper plan for v visits in a year.
Table. Plan A: yearly fee RM60, RM4 per visit. Plan B: no yearly fee, RM10 per visit
Diagram 6
[1 mark] (a)Write an expression, in terms of v, for the total cost of Plan A.
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Tick each point you got.
[3 marks] (b)Find the minimum number of visits so that Plan A is cheaper than Plan B.
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At 10 visits both cost RM100. At 11 visits Plan A costs RM104 and Plan B costs RM110.
Tick each point you got.
For the teacher: Analysing, high difficulty, standard 7.2.2
Textbook p. 162
19

Question 19

Solve the simultaneous linear inequalities 2x − 3 ≥ 1 and 5x + 2 < 32.
[3 marks] (a)Solve the simultaneous linear inequalities.
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Tick each point you got.
[1 mark] (b)List all the integers that satisfy both inequalities.
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2 is included (≥); 6 is not (<).
Tick each point you got.
For the teacher: Applying, medium difficulty, standard 7.2.3
Textbook p. 162
20

Question 20

Aiman solved 6 − 3x ≥ 18. Diagram 7 shows his working.
Aiman's working: 6 − 3x ≥ 18, −3x ≥ 18 − 6, −3x ≥ 12, x ≥ −4
Diagram 7
[1 mark] (a)Is Aiman's answer correct? Explain his mistake.
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Tick each point you got.
[1 mark] (b)Write the correct solution.
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Tick each point you got.
[1 mark] (c)Is x = 0 a solution of 6 − 3x ≥ 18?
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No
6 − 3(0) = 6, and 6 is not ≥ 18. (With Aiman's answer x = 0 would be a solution, which shows his answer is wrong.)
For the teacher: Evaluating, high difficulty, standard 7.2.2
Textbook p. 160
21

Question 21

Create a pair of simultaneous linear inequalities whose solution is −2 ≤ x < 3. Each inequality must have a term in x with a coefficient that is not 1, and a constant term.
[2 marks] (a)Write your two inequalities and show that they give −2 ≤ x < 3.
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2x + 5 ≥ 1 and 4x − 3 < 9
Tick each point you got.
For the teacher: Creating, high difficulty, standard 7.2.3
Textbook p. 162