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Quiz Chapter 6: Linear Inequalities in Two Variables

10 questions · Form 4 Mathematics Bab 6: Linear Inequalities in Two Variables

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Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Consider the system: y > x, y < 4, x > 0. Which of the following points lies inside this feasible region?

  1. A. (1, 3)
  2. B. (3, 2)
  3. C. (2, 5)
  4. D. (-1, 2)
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Answer: A

Testing point (1, 3): 3 > 1 (True), 3 < 4 (True), 1 > 0 (True). All three conditions hold.

2. A baker makes x butter cakes and y chocolate cakes. The total number of cakes baked is not more than 80. Write this as a linear inequality.

  1. A. x + y ≥ 80
  2. B. x + y > 80
  3. C. x + y ≤ 80
  4. D. x + y < 80
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Answer: C

'Not more than' means less than or equal to, which is represented by '≤'. Therefore, x + y ≤ 80.

3. Which inequality corresponds to the region to the right of the vertical line x = 3, excluding the line itself?

  1. A. x ≥ 3
  2. B. x > 3
  3. C. x ≤ 3
  4. D. x < 3
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Answer: B

Regions to the right of a vertical line correspond to greater values of x. Excluding the line requires the strictly greater symbol '>'.

4. Given the system x ≥ 0, y ≥ 0, x + y ≤ 6. What shape is formed by the solution region in the first quadrant?

  1. A. Circle
  2. B. Triangle
  3. C. Rectangle
  4. D. Hexagon
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Answer: B

The lines x = 0 (y-axis), y = 0 (x-axis), and x + y = 6 enclose a right-angled triangular region in the first quadrant.

5. Which of the following represents a linear inequality in two variables?

  1. A. 2x² + 3y ≤ 6
  2. B. 3x - 5y > 10
  3. C. x + 1y < 4
  4. D. xy + 2 ≥ 0
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Answer: B

A linear inequality in two variables must have both variables raised to the power of 1. Option B (3x - 5y > 10) meets this criteria. Options A, C, and D contain squared terms, variables in denominators, or products of variables.

6. Translate the statement into an inequality: 'The number of girls, y, is at least twice the number of boys, x.'

  1. A. y ≤ 2x
  2. B. y < 2x
  3. C. y ≥ 2x
  4. D. y > 2x
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Answer: C

The key term 'at least' translates to the inequality symbol '≥'. Hence, y ≥ 2x.

7. To shade the region for y < -x + 4, which area relative to the line y = -x + 4 should be shaded?

  1. A. Above the solid line
  2. B. Above the dashed line
  3. C. Below the dashed line
  4. D. Below the solid line
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Answer: C

The symbol '<' indicates the region below the boundary line, and since it is strictly less than, the line must be dashed.

8. If a point lies directly on a dashed boundary line of a shaded region, is it a solution to the inequality?

  1. A. Yes, always
  2. B. No, points on a dashed line are excluded from the solution region
  3. C. Only if x is positive
  4. D. Only if y is zero
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Answer: B

Points on a dashed line are excluded from the solution set because the inequality symbol is strict (< or >).

9. Which of the following points lies in the solution set of y > 3x - 2?

  1. A. (1, 0)
  2. B. (2, 1)
  3. C. (0, 0)
  4. D. (3, 2)
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Answer: C

Substitute (0, 0): 0 > 3(0) - 2 ⇒ 0 > -2, which is a true statement.

10. What type of line is drawn on a graph to represent the inequality y ≥ 2x + 1?

  1. A. Dashed line
  2. B. Solid line
  3. C. Dotted line
  4. D. Curved line
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Answer: B

Inequalities containing '≥' or '≤' include the points on the boundary line, so they are drawn with a solid line.

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