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0580/33 May/Jun 2024, Question 9: Recognising and Sketching Graph Shapes

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Given a line with gradient 4 through (0, 3), find its equation; use y = 2 − 6x to find a when y = 5; complete a table for y = x² − 6, plot it, then find its symmetry line and a positive root of x² − 6 = 0.

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

Part (a) · 1 mark

State the equation of the line with gradient 4 passing through (0, 3) as y = mx + c.

  1. 1m = 4 and c = 3
  2. 2y = 4x + 3

Answery = 4x + 3

Part (b) · 3 marks

Given that the line y = 2 − 6x contains (a, 5), determine a.

  1. 15 = 2 − 6a
  2. 26a = 2 − 5 = −3
  3. 3a = −1/2

Answer−1/2

Part (ci) · 2 marks

Fill the missing y-values in the table for y = x² − 6 at x = −3, 0 and 3.

  1. 1x = −3: y = 9 − 6 = 3
  2. 2x = 0: y = 0 − 6 = −6
  3. 3x = 3: y = 9 − 6 = 3

Answer| x | −3 | 0 | 3 | | y | 3 | −6 | 3 |

Part (cii) · 4 marks

Plot y = x² − 6 on the grid for x values from −4 to 4.

  1. 1Plot (−4, 10), (−3, 3), (−2, −2), (−1, −5), (0, −6), (1, −5), (2, −2), (3, 3), (4, 10)
  2. 2Join with a smooth U-shaped curve, lowest point (0, −6)

Answercorrect curve

Part (ciii) · 1 mark

Give the equation of the mirror line of the curve y = x² − 6.

  1. 1The curve is symmetrical about the y-axis: x = 0

Answerx = 0

Part (civ) · 1 mark

Using your graph, find the positive x-value where x² − 6 equals 0.

  1. 1Read where the curve crosses the x-axis (y = 0) for x > 0
  2. 2(Check: x = √6 = 2.449…)
  3. 3x ≈ 2.45

Answer2.3 to 2.6

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Also searched as: 0580/33/M/J/24 · 0580_s24_qp_33 · 0580 s24 33 · question 9.
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