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.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?
(a)A formula, relating two quantities
(b)An identity, true for all values of x
(c)An expression, with x terms and numbers
(d)An equation, true for one value of x
2.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7
3.Which of these points lies in the first quadrant?
(a)(−1, −4)
(b)(4, −1)
(c)(−2, 3)
(d)(3, 5)
4.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
5.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
6.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
7.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.
y = x
(a)(0, 4)
(b)(4, 0)
(c)(0, 0)
(d)(0, −4)
8.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11
9.Solve x² − x − 12 = 0.
(a)x = 4 or x = −3
(b)x = −4 or x = 3
(c)x = 12 or x = −1
(d)x = 4 or x = 3
10.Work out the value of n² − n when n = −3
(a)6
(b)−3
(c)−6
(d)12
11.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6
12.Which expression is equivalent to 3(2x − 5) + 4x?
(a)10x + 15
(b)6x − 15
(c)10x − 15
(d)10x − 5
13.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.
(a)25
(b)28
(c)27
(d)31
14.The point B has coordinates (−2, −2). In which quadrant is B?
(a)the fourth quadrant
(b)the second quadrant
(c)the first quadrant
(d)the third quadrant
15.Expand and simplify 2(a + 6) − 2(a − 7)
(a)13
(b)4a − 2
(c)−2
(d)26

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