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 proof that (n + 3)² − (n − 3)² is always a multiple of a certain number begins: Line 1: (n + 3)² − (n − 3)² = (n² + 6n + 9) − (n² − 6n + 9). Which expression correctly completes Line 2?
- 2.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.
- 3.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 4.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.
- 5.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.
- 6.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.
- 7.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
- 8.Which expression is equivalent to 0.5(4x + 6) − x?
- 9.Which expression is equivalent to 7x − 3(2x − 6)?
- 10.Work out the coordinates of the reflection of (6, −3) in the y-axis.
- 11.A circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.
- 12.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.
- 13.Work out the value of 3x² − 4x when x = −2.
- 14.Which expression means 'triple c, then add double d'?
- 15.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
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