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 · 15 questions

MathsUKwww.geekhero.co.uk

1.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
2.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.
(a)S = PC
(b)S = P − C
(c)S = P + C
(d)S = C − P
3.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
(a)10
(b)16
(c)12
(d)13
4.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.
(a)4n + 1
(b)4n + 5
(c)4n − 3
(d)n + 4
5.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
6.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?
(a)1.76
(b)0
(c)10
(d)6
7.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.
(a)(1, 3)
(b)(−1, 3)
(c)(9, 4)
(d)(−1, 4)
8.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.
(a)36 km/h
(b)14.4 km/h
(c)6.25 km/h
(d)0.6 km/h
9.The graph of y = (x − 4)(x + 1) crosses the x-axis. Which pair gives the correct roots and reasoning?
(a)x = −4 and x = −1, because the roots are always the negative of the numbers shown in the brackets.
(b)x = 4 and x = 1, because both brackets must be positive at the roots.
(c)x = 4 and x = −1, because the graph crosses the x-axis where x − 4 = 0 or x + 1 = 0.
(d)x = −4 and x = 1, because the signs inside the brackets must be reversed to solve them.
10.Which expression is equivalent to 0.5(4x + 6) − x?
(a)3x + 3
(b)2x + 3
(c)x + 3
(d)x + 6
11.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.
y = 4x − 5
(a)4
(b)−4
(c)5
(d)−5
12.y = x + 4. Work out the value of y when x = 3.
y = x + 4
(a)7
(b)1
(c)12
(d)4
13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.
(a)0.25
(b)4
(c)9
(d)36
14.Solve 4x² − 9 = 0.
(a)x = 3/2 or x = −3/2
(b)x = 3/2 only
(c)x = 3 or x = −3
(d)x = 9/4 or x = −9/4
15.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).
(a)y = (x − 3)(x − 5)
(b)y = (x − 3)(x + 5)
(c)y = (x + 3)(x + 5)
(d)y = (x + 3)(x − 5)

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