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.

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Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.
(a)x = −8
(b)x = 1
(c)x = 8
(d)x = 5
2.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)
3.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
(a)y = −2x + 7
(b)y = −2x − 5
(c)y = 2x + 7
(d)y = −2x + 1
4.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.
(a)25
(b)20
(c)18
(d)21
5.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
(a)An equation, because solving it gives the value of n
(b)An identity, because it is true for many values of n
(c)A formula, because it works out n from 9
(d)An inequality, because ≤ compares the two sides
6.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?
(a)Yes, but only when x is a whole number.
(b)No, since 6(x − 1) means 6x − 1.
(c)No, brackets always change an expression's value.
(d)Yes, since expanding 6(x − 1) gives 6x − 6.
7.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.
(a)5
(b)4
(c)6
(d)−5
8.Work out the y-intercept of the graph of y = x² + 3x − 10.
y = x² + 3x − 10
(a)(−10, 0)
(b)(0, 3)
(c)(0, 10)
(d)(0, −10)
9.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.
(a)16
(b)24
(c)84
(d)50
10.Write down the expression that means the same as w ÷ 6.
(a)6w
(b)6/w
(c)w/6
(d)w − 6
11.Solve the inequality x − 10 < −3.
(a)x < 13
(b)x > 7
(c)x < −13
(d)x < 7
12.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
(a)12
(b)4
(c)8
(d)16
13.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?
(a)(2, 3)
(b)(2, 5)
(c)(2, 6)
(d)(3, 2)
14.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
15.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.
(a)(0, 16)
(b)(0, −2)
(c)(−8, −2)
(d)(5, 3)

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