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Chapter 2 Practice Paper: Linear Inequalities — mark scheme

QuizQuipPractice Series
QQ/S2MATH/CH2

Secondary 2 · Lower Secondary Mathematics (G2 / G3)

Mark scheme

Linear Inequalities

Chapter 2 Practice Paper · Maximum mark: 30

Notes for markers

  • Award one mark for each point marked [1], up to the marks shown for the part.
  • Accept answers worded differently that show the same understanding.
  • Units are required where the answer line shows one. ecf: allow an error carried forward.

Section A: Multiple-choice questions[10 marks]

QuestionAnswer
1BThe bar under the sign is the “or equal to” part.1
2CThe open circle excludes −1 and the rightward shading takes the larger values.1
3AAdding 6 to both sides gives x ≥ 10; adding never flips the sign.1
4DDividing by the positive 5 keeps the sign: x < 9.1
5BDividing by −4 flips ≤ into ≥, giving x ≥ −3.1
6C−x < −2, and dividing by −1 flips the sign: x > 2.1
7A4 is below the boundary; 4.5 is excluded and is not an integer anyway.1
8DThe integers are −1, 0, 1, 2, 3 — five of them.1
9B“At most” allows exactly 6, so t ≤ 6.1
10CSubtract 5 to get 2x ≤ 12, then divide by 2: x ≤ 6.1

Section B: Structured questions[20 marks]

QuestionAnswer and marking pointsMarks
1(a)

4x < 16, so x < 4.

  • 4x < 16 [1]
  • x < 4 [1]
2
1(b)

An open circle at 4, with shading to the left.

  • Open circle at 4, shading left [1]
1
1(c)

3 (the integer just below the open boundary 4). [1]

1
1(d)

No: 4(4) − 3 = 13, and 13 is not less than 13; the boundary is open.

  • Substitutes x = 4 and concludes no [1]
1
Total for Question 15
2(a)

−3x ≥ −6; dividing by −3 and flipping gives x ≤ 2.

  • −3x ≥ −6 [1]
  • Division by −3 flips the sign [1]
  • x ≤ 2 [1]
3
2(b)

The flip happened when dividing by −3; dividing by a negative number reverses which side is bigger, so the comparison must reverse.

  • Names the division by −3 [1]
  • Negative division reverses the comparison [1]
2
Total for Question 25
3(a)

−2, −1, 0, 1, 2, 3, 4.

  • Values from −2 to 4 [1]
  • Complete list with both ends right [1]
2
3(b)

4 (the closed boundary itself is a solution). [1]

1
3(c)

Four: 1, 2, 3, 4.

  • Counts positive values only [1]
  • 4 [1]
2
Total for Question 35
4(a)

120 + 6c ≤ 300.

  • 120 + 6c on one side [1]
  • ≤ 300 used [1]
2
4(b)

6c ≤ 180, so c ≤ 30.

  • 6c ≤ 180 [1]
  • c ≤ 30 [1]
2
4(c)

30 chairs [1]

1
Total for Question 45

— End of mark scheme —