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.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
2.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.
y = x²
(a)x = −1 and x = 2
(b)x = −3 and x = 4
(c)x = 0 and x = 1
(d)x = −2 and x = 3
3.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.
(a)−4.5
(b)50
(c)29.5
(d)8
4.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.
(a)(1, 6)
(b)(−1, 6)
(c)(−1, −6)
(d)(6, −1)
5.Expand 7(a + 8)
(a)a + 56
(b)7a + 15
(c)7a + 8
(d)7a + 56
6.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?
(a)The equation has one solution; the inequality has many.
(b)Both have exactly one solution.
(c)Both have many solutions.
(d)The equation has many solutions; the inequality has one.
7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
8.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.
(a)27
(b)22.5
(c)18
(d)36
9.Which expression is equivalent to 3(x + 4) − 2(x − 1)?
(a)x + 14
(b)x + 10
(c)5x + 10
(d)x + 13
10.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
(a)−2 and 2
(b)0 and 2
(c)−4 and 4
(d)−2 and 3
11.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
12.A square has sides of length y cm. Write down an expression for the perimeter of the square.
(a)2y
(b)y + 4
(c)y²
(d)4y
13.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.
(a)s = P − 4
(b)s = P + 4
(c)s = P / 4
(d)s = 4P
14.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.
(a)28 km/h
(b)24 km/h
(c)16 km/h
(d)20 km/h
15.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

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