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.Two expressions are 4(x + 3) and 4x + 3. A student checks whether they are equivalent by substituting x = 2. Which statement correctly interprets the result?
(a)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, because the bracket means the 3 must be added before multiplying by 4.
(b)4(x + 3) = 11 and 4x + 3 = 11 when x = 2, since the bracket has no effect on the multiplication, so the two expressions are equivalent.
(c)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, but the two expressions are equivalent because both involve the same terms, 4x and 3.
(d)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, but they would become equal for some larger value of x.
2.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.
(a)y + 1
(b)y − 4
(c)y − 9
(d)y + 9
3.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
4.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
5.Solve 2(x + 3) = 10
(a)x = 3.5
(b)x = 8
(c)x = 5
(d)x = 2
6.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
(a)The graph has only one branch, in quadrant 1
(b)The graph passes through the origin, (0, 0)
(c)The graph crosses the y-axis but never the x-axis
(d)The graph never crosses either axis
7.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
8.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.
(a)0
(b)8
(c)3
(d)1
9.Which of these equations describes a vertical line?
(a)y = 5x
(b)x = y
(c)x = 5
(d)y = 5
10.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.
(a)t + 1
(b)t − 1
(c)1 − t
(d)t
11.Simplify 2a + 3b − a + 2b − b
(a)a + 4b
(b)a + 6b
(c)5ab
(d)3a + 4b
12.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.
(a)12a + 8
(b)8a + 6
(c)8a + 2
(d)5a
13.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.
(a)4.6
(b)7.4
(c)90
(d)6
14.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.
(a)11
(b)4
(c)7.5
(d)22
15.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.
(a)4, 12, 15, 18
(b)4, 12, 36, 108
(c)4, 7, 10, 13
(d)12, 36, 108, 324

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