UniGeniusGCSE Maths · Edexcel 1MA1

Worksheets · Foundation

Foundation algebra and graph clinic

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

  1. Question 1Non-calculator · 4 marks

    Answer each part.

    (a) Expand and simplify 3(x+4)−2(x−1)3(x + 4) - 2(x - 1) (2)

    (b) Solve 3(x+4)−2(x−1)=203(x + 4) - 2(x - 1) = 20 (2)

  2. Question 2Non-calculator · 4 marks

    −10<2x+1≤25-10<2x+1\le 25, where x is an integer.

    (a) Write all possible values of x. (2)

    (b) Find the sum of all these values. (2)

  3. Question 3Non-calculator · 4 marks

    Answer each part. Show clear algebraic working.

    (a) Solve the simultaneous equations 2x+y=112x + y = 11 and x−y=1x - y = 1. Give your answer as (x,y)(x, y). You must show your working. (2)

    (b) Solve x2+x−12=0x^2 + x - 12 = 0. You must show your working. (2)

Answers and marks

Question 1

(a) x+14x + 14

  • M1 Expanding both brackets correctly: 3x+123x + 12 and −2x+2-2x + 2.
  • A1 The correct answer, x+14x + 14.

(b) x=6x = 6

  • M1 Writing x+14=20x + 14 = 20 (or their simplified expression =20= 20).
  • A1 The correct answer, x=6x = 6.

Question 2

(a) −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

  • M1 Subtract 1 from all three expressions and divide by 2.
  • A1 Correct answer: −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

(b) 6363

  • M1 Add the finite arithmetic list using its average and count.
  • A1 Correct answer: 6363

Question 3

(a) x=4x = 4, y=3y = 3

  • M1 Eliminating yy: 3x=123x = 12.
  • A1 x=4x = 4 and y=3y = 3.

(b) x=3x = 3 or x=−4x = -4

  • M1 Factorising to (x+4)(x−3)(x + 4)(x - 3).
  • A1 x=3x = 3 and x=−4x = -4.

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Foundation algebra and graph clinic

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