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Quiz Chapter 6: Linear Inequalities in Two Variables

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

Question 1 of 10Score: 0

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.

Full Question List & Answer Key

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

1. 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.

2. The inequality representing 'The maximum weight of x boxes of type A and y boxes of type B is 500 kg' is:

  1. A. ax + by > 500
  2. B. ax + by ≥ 500
  3. C. ax + by < 500
  4. D. ax + by ≤ 500
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Answer: D

The phrase 'maximum' or 'at most' corresponds to the inequality symbol '≤'.

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. 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.

5. 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.

6. Which region defines the solution to a system of linear inequalities on a Cartesian graph?

  1. A. The unshaded region on the graph
  2. B. The common overlapping shaded region satisfying all inequalities
  3. C. Any region above the x-axis
  4. D. The region enclosed only by the y-axis
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Answer: B

The solution region (feasible region) of a system of linear inequalities is the region where the shaded areas of all individual inequalities overlap.

7. 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.

8. 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.

9. 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.

10. 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.

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