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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. If x represents the number of pens and y represents the number of rulers, with the condition 'the number of rulers is at most twice the number of pens', which inequality is correct?

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

'At most' corresponds to '≤'. Therefore, y (rulers) ≤ 2x (twice pens).

2. 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.

3. 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.

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. Identify the point that satisfies the system of inequalities: y ≤ x + 2 and y > -2x.

  1. A. (0, 3)
  2. B. (1, 1)
  3. C. (-2, 5)
  4. D. (0, -3)
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Answer: B

Test point (1, 1): 1 ≤ 1 + 2 = 3 (True) and 1 > -2(1) = -2 (True). Both inequalities are satisfied.

6. The difference between the number of adult tickets (x) and child tickets (y) is less than 15. Write the inequality.

  1. A. x - y ≤ 15
  2. B. x - y < 15
  3. C. x - y > 15
  4. D. x - y ≥ 15
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Answer: B

'Less than' indicates a strict inequality symbol '<'. Thus, x - y < 15.

7. Does the origin (0, 0) satisfy the inequality 3x - 4y ≥ -12?

  1. A. Yes, because 0 ≥ -12 is True
  2. B. No, because 0 < -12 is False
  3. C. Only if x is negative
  4. D. Cannot be determined
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Answer: A

Substitute (0, 0): 3(0) - 4(0) = 0. Since 0 ≥ -12 is True, the origin satisfies the inequality.

8. Which pair of inequalities defines a region entirely in the first quadrant of a Cartesian plane?

  1. A. x ≤ 0, y ≤ 0
  2. B. x ≥ 0, y ≥ 0
  3. C. x < 0, y > 0
  4. D. x > 0, y < 0
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Answer: B

The first quadrant is where both x-coordinates and y-coordinates are non-negative, defined by x ≥ 0 and y ≥ 0.

9. 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.

10. 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 >).

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