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.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.
(a)x = 2, y = 5
(b)x = 3, y = 2
(c)x = 2, y = 3
(d)x = −2, y = 11
2.Which expression means 'triple c, then add double d'?
(a)6cd
(b)2c + 3d
(c)3c + 2d
(d)5(c + d)
3.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.
(a)−7
(b)4
(c)−5
(d)7
4.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
5.Expand and simplify 2(a + 6) − 2(a − 7)
(a)13
(b)4a − 2
(c)−2
(d)26
6.Write down the expression that means the same as (x + 7) ÷ 4.
(a)4(x + 7)
(b)4/(x + 7)
(c)(x + 7)/4
(d)(x + 7) − 4
7.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.
(a)h = Vlw
(b)h = V − lw
(c)h = V / (lw)
(d)h = lw / V
8.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.
(a)0.05
(b)20
(c)100
(d)25
9.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.
y = 2x − 7
(a)(0, 7)
(b)(−7, 0)
(c)(2, −7)
(d)(0, −7)
10.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
11.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?
(a)Isla is wrong, because 5 − 1 = 4
(b)Isla is wrong, because 5 × 1 = 5
(c)Isla is right, because the machine adds 1 to its output
(d)Isla is right, because 5 + 1 = 6
12.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.
(a)y = 3x − 2
(b)y = x + 4
(c)y = 3x + 2
(d)y = 2x + 3
13.y = 3x − 2. Work out the value of y when x = 4.
y = 3x − 2
(a)6
(b)14
(c)10
(d)12
14.p = 4. Work out the value of 2p³.
(a)512
(b)24
(c)64
(d)128
15.Make p the subject of the formula n = p/3.
(a)p = n/3
(b)p = 3n
(c)p = 3/n
(d)p = n − 3

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