Write down the inequality shown on the number line: a filled dot at 5 with an arrow pointing right.
(1)
2
Write down the inequality shown on the number line: an open circle at -2 with an arrow pointing left.
(1)
3
State whether x = 4 satisfies the inequality x > 3.
(1)
4
State whether x = -1 satisfies the inequality x ≤ -1.
(1)
5
Solve the inequality x + 4 > 9.
(1)
6
Solve the inequality x - 2 < 6.
(1)
7
Solve the inequality 3x > 12.
(1)
8
Solve the inequality 2x + 3 < 11.
(2)
9
Solve the inequality 5x - 4 ≥ 16.
(2)
10
Solve the inequality 7 - x > 2.
(2)
11
Solve the inequality -2x < 8.
(2)
12
Solve the inequality 3x + 5 ≤ x + 13.
(2)
13
Find all integer values of x that satisfy -3 ≤ x < 2. List them.
(2)
14
Solve the inequality 4(x - 1) > 8.
(3)
15
Solve the compound inequality and give the solution in inequality form: 3 ≤ 2x - 1 < 9.
(3)
16
A theme park ride requires riders to be at least 120 cm tall but under 200 cm tall. Using h for height in cm, write this rule as an inequality, then state whether a rider of height 118 cm is allowed on the ride.
(3)
17
Solve the inequality 3(2x - 1) ≤ 4x + 9. Then describe how the solution would be shown on a number line (state the type of dot used and the direction of the arrow).
(4)
18
A courier's box already weighs 4 kg. Extra identical items are added, each weighing 1.5 kg. The total weight must stay under 13 kg to qualify for standard postage. Using n for the number of extra items, form an inequality and solve it to find the greatest whole number of extra items that can be added.
(4)
19
Stretch. Find all integer values of x that satisfy -5 < 3x - 2 ≤ 10.
(4)
Mark scheme · KS3.M-A18D Inequalities and Number Lines: Fluency and Exam Drill
Question 1
B1 x ≥ 5 cao
Answer: x ≥ 5
Question 2
B1 x < -2 cao
Answer: x < -2
Question 3
B1 Yes, because 4 > 3
Answer: Yes
Question 4
B1 Yes, because -1 is equal to -1, which satisfies ≤
Answer: Yes
Question 5
B1 x > 5 cao
Answer: x > 5
Question 6
B1 x < 8 cao
Answer: x < 8
Question 7
B1 x > 4 cao
Answer: x > 4
Question 8
M1 correct rearrangement, e.g. 2x < 8
A1 x < 4 cao
Answer: x < 4
Question 9
M1 correct rearrangement, e.g. 5x ≥ 20
A1 x ≥ 4 cao
Answer: x ≥ 4
Question 10
M1 correct rearrangement, e.g. -x > -5
A1 x < 5 cao (inequality sign flipped correctly)
Answer: x < 5
Question 11
M1 divides both sides by -2 and identifies the sign must flip
A1 x > -4 cao
Answer: x > -4
Question 12
M1 collects x terms on one side, e.g. 2x + 5 ≤ 13
A1 x ≤ 4 cao
Answer: x ≤ 4
Question 13
M1 identifies the correct range of integers, including -3 but excluding 2
A1 -3, -2, -1, 0, 1 cao
Answer: -3, -2, -1, 0, 1
Question 14
M1 expands the bracket correctly, e.g. 4x - 4 > 8
M1 correct rearrangement, e.g. 4x > 12
A1 x > 3 cao
Answer: x > 3
Question 15
M1 adds 1 to all three parts, e.g. 4 ≤ 2x < 10
M1 divides all three parts by 2 correctly
A1 2 ≤ x < 5 cao
Answer: 2 ≤ x < 5
Question 16
B1 correct inequality: 120 ≤ h < 200
M1 compares 118 to the lower bound 120 correctly
A1 not allowed, because 118 < 120
Answer: 120 ≤ h < 200; a rider of 118 cm is not allowed
Question 17
M1 expands the bracket correctly, e.g. 6x - 3 ≤ 4x + 9
M1 collects x terms correctly, e.g. 2x ≤ 12
A1 x ≤ 6 cao
B1 correctly describes a filled (closed) dot at 6 with an arrow pointing left
Answer: x ≤ 6; filled dot at 6, arrow pointing left
Question 18
M1 correct inequality formed: 4 + 1.5n < 13
M1 correct rearrangement, e.g. 1.5n < 9
A1 n < 6 cao
A1 greatest whole number of items is 5
Answer: n < 6; the greatest whole number of extra items is 5
Question 19
M1 adds 2 to all three parts, e.g. -3 < 3x ≤ 12
M1 divides all three parts by 3 correctly
A1 -1 < x ≤ 4 cao
A1 0, 1, 2, 3, 4 cao
Answer: -1 < x ≤ 4; the integers are 0, 1, 2, 3, 4