Printable · GCSE Higher · ages 14-16
Algebra worksheet — GCSE Higher
Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
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Algebra worksheet — GCSE Higher
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- 1.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.
- 2.f(x) = (x + 1)/2. Find f⁻¹(x).
- 3.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.
- 4.When a number is added to its square the result is 30. Work out the possible values of the number.
- 5.The equation x² = 5x − 3 is to be solved using iteration. Work out which of these iterative formulas comes from a correct rearrangement of the equation.
- 6.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.
- 7.Make x the subject of the formula y = 2x − 9.y = 2x − 9
- 8.Which of these is a formula, rather than an expression, an equation, or an identity?
- 9.Solve the simultaneous equations x + y = 1 and 2x + y = 5.
- 10.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
- 11.Simplify (5x² + 3x − 2) − (2x² − x + 5)
- 12.Solve x² + 7x = 0.
- 13.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.
- 14.Solve the inequality 5x − 3 > 2x + 9.
- 15.f(x) = 2x² + 1 and g(x) = x − 1. Work out fg(x), giving your answer in expanded form.y = 2x² + 1
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