Printable · GCSE Foundation · ages 14-16
Algebra worksheet — GCSE Foundation
Fifteen questions across the algebra statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Non-calculator
Algebra worksheet — GCSE Foundation
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- 1.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.
- 2.Work out the distance of the point (−6, 4) from the x-axis.
- 3.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?
- 4.Factorise fully 12x² + 18x.
- 5.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.
- 6.y = 3x − 2. Work out the value of y when x = 4.y = 3x − 2
- 7.Work out the value of a² − 2b when a = −3 and b = 4.
- 8.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).
- 9.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
- 10.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.
- 11.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
- 12.Which of these statements is an equation with exactly one solution?
- 13.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
- 14.Work out the value of 3n − 2 when n = 1
- 15.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
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