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

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1.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.
(a)16
(b)9
(c)8
(d)12
2.Work out the gradient of the straight line with equation 2x + y = 8.
(a)−1/2
(b)8
(c)2
(d)−2
3.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
4.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.
(a)8
(b)3
(c)11
(d)−8
5.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
(a)30
(b)27
(c)28
(d)20
6.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
7.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.
(a)x ≥ 30
(b)x ≤ 50
(c)x ≤ 90
(d)x ≤ 30
8.Work out the y-intercept of the graph of y = x² + 3x − 10.
y = x² + 3x − 10
(a)(−10, 0)
(b)(0, 3)
(c)(0, 10)
(d)(0, −10)
9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
10.Write down the expression that means the same as 3 × y × y.
(a)3y²
(b)3 + y²
(c)y³
(d)(3y)²
11.Work out the value of 3n − 2 when n = 1
(a)5
(b)1
(c)3
(d)−1
12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.
(a)(3, −4)
(b)(−4, 3)
(c)(8, 3)
(d)(−4, −5)
13.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?
(a) $y = 2 x + 1$
(b) $y = - 2 x - 1$
(c) $y = x - 1$
(d) $y = 2 x - 1$
14.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.
(a)y = 3x + 9
(b)y = 12x
(c)y = 9x + 3
(d)y = 9x
15.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18

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