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4024/21 May/Jun 2020, Question 6: Plotting Curves from a Table of Values

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 12 marks

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The question, in short

Complete a table for y = x³/4 − x + 1, plot its graph on the grid for −3 ≤ x ≤ 3, add the line y = 1/3 x + 1, read off intersection x-values, and find integers A and B in Ax³ = Bx; then match three given quadratic equations to three sketches.

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

Part (ai) · 1 mark

Use the rule y = x³/4 − x + 1 to work out the missing y-value when x = 3.

  1. 1x = 3: y = 27/4 − 3 + 1
  2. 2= 6.75 − 2 = 4.75

Answer4.75

Part (aii) · 3 marks

Plot the completed points and draw a smooth curve for y = x³/4 − x + 1 between x = −3 and x = 3.

  1. 1Plot (−3, −2.75), (−2, 1), (−1, 1.75), (0, 1), (1, 0.25), (2, 1), (3, 4.75)
  2. 2Join with a smooth cubic curve through all seven points (maximum near x = −1, minimum near x = 1)

AnswerCorrect curve

Part (aiiia) · 2 marks

  1. 1y-intercept is 1, gradient 1/3
  2. 2Points: (−3, 0), (0, 1), (3, 2)
  3. 3Rule a straight line through them

AnswerRuled line through (0, 1), gradient 1/3

Part (aiiib) · 2 marks

From your graphs, state every x-value where the straight line meets the cubic curve.

  1. 1Read off the x-coordinates where the line meets the curve
  2. 2x ≈ −2.3, x = 0, x ≈ 2.3

Answer−2.5 to −2.1, 0, 2.1 to 2.5

Part (aiiic) · 2 marks

Rearrange the intersection condition to the form Ax³ = Bx and give the integer values of A and B.

  1. 11/3 x + 1 = x³/4 − x + 1
  2. 2x³/4 = x + 1/3 x = 4/3 x
  3. 3Multiply by 12: 3x³ = 16x
  4. 4A = 3, B = 16

AnswerA = 3, B = 16

Part (b) · 2 marks

Match each of the three U-shaped sketches to the correct equation from the four listed, writing it beneath the graph.

  1. 1Minimum at O: y = 2x²
  2. 2Symmetrical with y-intercept below O: y = 2x² − 2
  3. 3Through O with roots 0 and 2 (minimum to the right): y = x² − 2x

Answery = 2x², y = 2x² − 2, y = x² − 2x

Stuck on a step? Read the free lesson: Plotting Curves from a Table of Values

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Also searched as: 4024/21/M/J/20 · 4024_s20_qp_21 · 4024 s20 21 · question 6.
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