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A22Inequalities

Edexcel GCSE Maths (1MA1), Higher tier · Algebra

Practise Inequalities. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.

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Sample questions

Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.

Question 1Easy2 marks
Solve \(6(x - 1) \gt 48\)[2]
Show the answer and mark scheme
Answer: \(x \gt 9\)
  • M1 for \(6x - 6 \gt 48\) or \(x - 1 \gt 8\)
  • A1 for \(x \gt 9\) oe

Worked solution: \(x - 1 \gt 8\), so \(x \gt 9\)

Question 2Medium4 marks
Two taxi firms charge for a journey of \(d\) miles.
Firm A: a fixed charge of £3 plus £1.40 per mile.
Firm B: £1.80 per mile, with no fixed charge.
(a) Write down an inequality, in terms of \(d\), for the journeys where Firm A is cheaper than Firm B.
Solve your inequality.[3]
(b) Kim says, 'Firm B has no fixed charge, so it is always cheaper. I will use Firm B for my 9-mile journey.'
Is Kim correct? Give a reason for your answer.[1]
Show the answer and mark scheme
(a) Answer: \(d \gt 7.5\)
  • M1 for \(3 + 1.4d \lt 1.8d\) oe
  • M1 for \(3 \lt 0.4d\) oe
  • A1 for \(d \gt 7.5\)

Worked solution: \(3 + 1.4d \lt 1.8d\)
\(3 \lt 0.4d\)
\(d \gt 7.5\)

(b) Answer: No: 9 > 7.5, so Firm A is cheaper (A £15.60, B £16.20).
  • C1 for 'no' with a correct reason, e.g. 9 > 7.5, or A costs £15.60 and B costs £16.20

Worked solution: Firm A: \(3 + 1.4 \times 9 = 15.60\). Firm B: \(1.8 \times 9 = 16.20\). Firm A is cheaper for 9 miles, so Kim is wrong.

Question 3Hard4 marks
(a) Solve \(1 \le \frac{2 - 3x}{2} \lt 7\)
You must show all your working.[3]
(b) Write down all the integer values of \(x\) that satisfy \(1 \le \frac{2 - 3x}{2} \lt 7\)[1]
Show the answer and mark scheme
(a) Answer: \(-4 \lt x \le 0\)
  • M1 for multiplying every part by \(2\): \(2 \le 2 - 3x \lt 14\)
  • M1 for subtracting \(2\) from every part and dividing every part by \(-3\), reversing the inequality signs
  • A1 for \(-4 \lt x \le 0\) oe

Worked solution: Multiply every part by \(2\): \(2 \le 2 - 3x \lt 14\)
Subtract \(2\) from every part: \(0 \le -3x \lt 12\)
Divide every part by \(-3\), which reverses the signs: \(0 \ge x \gt -4\), i.e. \(-4 \lt x \le 0\)

(b) Answer: \(-3, -2, -1, 0\)
  • B1 for \(-3, -2, -1, 0\) (ft their answer to part (a))

Worked solution: \(-3, -2, -1, 0\)

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