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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Algebra worksheet — GCSE Foundation

Maths · GCSE Foundation · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.
(a)(n − 5)/2
(b)n/2 − 5
(c)2(n − 5)
(d)(5 − n)/2
2.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
3.A number machine adds 5 to its input. Work out the output when the input is 0.
(a)5
(b)−5
(c)0
(d)6
4.Work out the value of 2x² when x = −3
(a)18
(b)36
(c)−18
(d)−12
5.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.
(a)20
(b)32
(c)16
(d)24
6.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.
(a)s/f
(b)sf
(c)f/s
(d)s − f
7.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
8.Write down the gradient of the line with equation y = −x + 3.
y = −x + 3
(a)−3
(b)−1
(c)3
(d)1
9.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
10.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.
(a)(−4, 3)
(b)(4, −9)
(c)(3, 4)
(d)(4, 3)
11.A school trip costs a £15 deposit plus £9 per student for the coach. The total cost for a class is £186. Work out how many students went on the trip.
(a)22.33
(b)20.67
(c)19
(d)11.8
12.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
(a)9
(b)7
(c)1
(d)11
13.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
(a)(2, 7)
(b)(4, 14)
(c)(5, 2)
(d)(2, 9)
14.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.
(a)−7
(b)4
(c)−5
(d)7

Build your own mix at the worksheet builder.