UniGeniusGCSE Maths · Edexcel 1MA1

Worksheets · Foundation and Higher

Forming equations from situations

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

  1. Question 1Non-calculator · 3 marks

    Zara thinks of a number. She doubles it and then adds 7. Her answer is 31.

    (a) Form an equation and solve it to find Zara's number. You must show your working. (3)

  2. Question 2Calculator · 3 marks

    (a) A rectangular garden is 24 m long and 18 m wide. A path of uniform width is made inside all four edges. The remaining central rectangle has area 280 m2.m^{2}. Work out the width of the path. (3)

  3. Question 3Calculator · 4 marks

    (a) A small auditorium has 330 seats arranged in rows. Each row has 3 more seats than the row immediately in front. The back row has three times as many seats as the front row. Work out the number of rows. You may use: sum of an arithmetic sequence = 12\frac{1}{2} ×\times number of terms ×\times (first term + last term). (4)

Answers and marks

Question 1

(a) 1212

  • M1 Forming 2n+7=312n + 7 = 31.
  • M1 Reaching 2n=242n = 24.
  • A1 The correct answer, 1212.

Question 2

(a) 22 m

  • P1 Establishing (24−2w)(18−2w)=280(24-2w)(18-2w)=280 or an equivalent valid method.
  • P1 Establishing (w−2)(w−19)=0(w-2)(w-19)=0 or an equivalent valid method.
  • A1 Correct answer: 22 m

Question 3

(a) 1111 rows

  • P1 Establishing 2a=3(n−1)2a=3(n-1) or an equivalent valid method.
  • P1 Establishing 2an=3302an=330 or an equivalent valid method.
  • P1 Establishing (n−11)(n+10)=0(n-11)(n+10)=0 or an equivalent valid method.
  • A1 Correct answer: 1111 rows

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Forming equations from situations

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