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0580/31 Oct/Nov 2024, Question 8: Quadratic Graphs and the Parabola

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 12 marks

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The question, in short

From a net of six rectangles, identify the solid, work out volumes with x = 4 and in terms of x, solve for x at volume 360 cm³, then complete a table and graph for y = 2x² + x and solve 2x² + x = 30.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

State the mathematical name of the 3D shape formed by folding the given net.

  1. 1Six rectangular faces: cuboid

AnswerCuboid

Part (aii) · 2 marks

Calculate the solid's volume using x = 4, with the net's 10 cm and x cm labels.

  1. 1The net folds into a cuboid x cm by x cm by 10 cm.
  2. 2Volume = length × width × height
  3. 3With x = 4: 4 × 4 × 10 = 160 cm³

Answer160

Part (aiii) · 1 mark

Give a formula for the volume of the solid involving x.

  1. 1x × x × 10 = 10x²

Answer10x²

Part (aiv) · 2 marks

Determine x when the solid's volume equals 360 cm³.

  1. 110x² = 360
  2. 2x² = 36
  3. 3x = 6

Answer6

Part (bi) · 2 marks

Fill in the missing y values in the table for y = 2x² + x at x = 3, 4, 5.

  1. 1x = 3: 2 × 9 + 3 = 21
  2. 2x = 4: 2 × 16 + 4 = 36
  3. 3x = 5: 2 × 25 + 5 = 55

Answer21, 36, 55

Part (bii) · 3 marks

Plot the curve y = 2x² + x on the axes for x from 0 to 5.

  1. 1Plot (0, 0), (1, 3), (2, 10), (3, 21), (4, 36), (5, 55)
  2. 2Join with a smooth curve

AnswerCorrect smooth curve

Part (biii) · 1 mark

Read off the x value where the drawn curve meets y = 30.

  1. 1Draw the line y = 30 and read x where it meets the curve
  2. 22x² + x − 30 = 0 gives x = (−1 + √241)/4 = 3.63…
  3. 3x ≈ 3.6

Answer3.5 to 3.7

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Also searched as: 0580/31/O/N/24 · 0580_w24_qp_31 · 0580 w24 31 · question 8.
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