Question 1: Solve for x: 3x + 5 < 20. Show your working.

Answer: x < 5

Question 2: Solve the inequality: 2( x - 4 ) ≥ 10. Show your working.

Answer: x ≥ 9

Question 3: Plot the graph of y > 2x + 1 on the grid.

Answer: Student draws appropriate line and shading

Question 4: Construct a triangle with sides that satisfy the inequality: side1 + side2 < 15. Use the grid for drawing.

Answer: Student draws triangle with sides summing less than 15

Question 5: A toy costs less than £30. The price p is related by the inequality p < 30. If you buy 2 toys, what is the maximum total cost? Show your reasoning.

Answer: Maximum total cost is less than £60 (since 2 × 30)

Question 6: Solve for y: 5y - 3 > 2y + 4. Show your working.

Answer: y > 7/3 or y > 2.33

Question 7: A runner completes a race in less than 50 minutes. The time t in minutes satisfies t < 50. If the runner improves and runs 5 minutes faster, what is the new maximum time? Show your reasoning.

Answer: Maximum new time is less than 45 minutes

Question 8: Incorrect solution: Solve 4x + 2 ≤ 10 assuming x = 2. Is this correct? If not, explain and correct it.

Answer: Incorrect — x=2 gives 4(2)+2=10, which equals 10, not less than. Correct inequality: 4x + 2 ≤ 10, x ≤ 2.5

Question 9: Solve the inequality: -2x + 6 > 10. Show your working.

Answer: x < -2

Question 10: A store sells items at a discount such that the final price p satisfies p ≥ 5. If the original price before discount is x, and the discount is 20%, write an inequality for x.

Answer: x ≥ p / 0.8

Question 11: A student scores more than 85 on a test. The score s satisfies s > 85. If the student scored 3 points less in the retake, what is the maximum original score? Explain your reasoning.

Answer: Maximum original score is less than 88 (since 85+3=88)