UniGeniusGCSE Maths · Edexcel 1MA1

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Quadratic formula and rearranged quadratics

3 exam-style questions. Answers and the mark for each step are on the last page.

  1. Question 1Calculator · 3 marks

    Solve 2x2+5x−4=02x^2 + 5x - 4 = 0. Give each solution correct to 2 decimal places.

    (a) Write down the larger solution. (2)

    (b) Write down the smaller solution. (1)

  2. Question 2Calculator · 5 marks

    A rectangle has width x cm and length (2x+3)(2x+3) cm. Its area is 6 cm².

    (a) Find the width to 3 significant figures. (3)

    (b) Find the length to 3 significant figures. (2)

  3. Question 3Non-calculator · 4 marks

    Solve x+1x=3x−2\dfrac{x + 1}{x} = 3x - 2. Give your solutions in exact form.

    (a) Solve the equation. You must show your working. (4)

Answers and marks

Question 1

(a) 0.640.64

  • M1 Substituting correctly into the formula, including b2−4ac=25+32b^2 - 4ac = 25 + 32.
  • A1 The correct answer, 0.640.64.

(b) −3.14-3.14

  • B1 The correct answer, −3.14-3.14.

Question 2

(a) 1.141.14 cm

  • P1 Form the area equation and bring all terms to one side.
  • P1 Use the quadratic formula with the positive root for a length.
  • A1 Correct answer: 1.141.14 cm

(b) 5.275.27 cm

  • P1 Substitute the unrounded width into the length expression.
  • A1 Correct answer: 5.275.27 cm

Question 3

(a) x=3±216x = \dfrac{3 \pm \sqrt{21}}{6}

  • M1 Multiplying through by xx: x+1=3x2−2xx + 1 = 3x^2 - 2x.
  • M1 Rearranging to 3x2−3x−1=03x^2 - 3x - 1 = 0.
  • M1 Substituting into the formula with b2−4ac=9+12=21b^2 - 4ac = 9 + 12 = 21.
  • A1 3±216\frac{3 \pm \sqrt{21}}{6}.

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Quadratic formula and rearranged quadratics

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