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.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
2.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.
(a)P = 100I / (RT)
(b)P = 100I/R
(c)P = 100RT/I
(d)P = IRT/100
3.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.
(a)0, 3, 6, 9
(b)3, 6, 9, 12
(c)4, 5, 6, 7
(d)3, 9, 27, 81
4.Which expression means 'y squared, multiplied by 3'?
(a)3y²
(b)y³
(c)(3y)²
(d)3 + y²
5.Which of these statements is an identity?
(a)x + 4 = 2x
(b)2(x + 4) = 20
(c)2(x + 4) ≡ 2x + 8
(d)2(x + 4) = 2x + 4
6.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.
(a)7.4
(b)6.2
(c)3.2
(d)5
7.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.
(a)(2, −5)
(b)(−2, 5)
(c)(2, 5)
(d)(−2, −5)
8.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.
(a)y = x + 3
(b)y = 3x − 1
(c)y = 3x + 1
(d)y = 3x + 4
9.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.
(a)40
(b)11
(c)20
(d)80
10.Expand 2(x + 12)
(a)2x + 24
(b)2x + 14
(c)24x
(d)2x + 12
11.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
12.A number machine adds 6 to its input. Work out the output when the input is −4.
(a)10
(b)−10
(c)2
(d)−24
13.Make b the subject of the formula a = 5b.
(a)b = 5/a
(b)b = a/5
(c)b = 5a
(d)b = a − 5
14.Work out the gradient of the straight line with equation 3y = 12 − 6x.
(a)2
(b)4
(c)−2
(d)−6
15.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.
(a)(−3.5, 3.5)
(b)(5, 3)
(c)(4, 5)
(d)(4, 8)

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