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.Factorise 6x² − 7x − 3.
- 2.Which expression means 'triple c, then add double d'?
- 3.x = 5. Work out the value of 3x² − 4.
- 4.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.
- 5.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
- 6.Solve the inequality 5 − x ≤ 2.
- 7.Work out the coordinates of the reflection of (6, −3) in the y-axis.
- 8.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?
- 9.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).y = x² − 1
- 10.Solve x² + 3x − 10 = 0.
- 11.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
- 12.A circle has centre (0, 0) and passes through the point (7, 24). Work out the equation of the circle.
- 13.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.
- 14.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
- 15.Expand and simplify (x + 1)(x + 2)(x + 3).
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