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.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?
(a)The total cost for a job lasting 1 hour.
(b)The hourly rate the plumber charges.
(c)The number of hours worked before charging starts.
(d)The fixed call-out fee, charged before the hourly rate.
2.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.
(a)405
(b)1215
(c)2187
(d)3645
3.Which expression means the same as a × a × a?
(a)a²
(b)3a
(c)a³
(d)3 + a
4.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.
(a)x = 2, y = 5
(b)x = 3, y = 2
(c)x = 2, y = 3
(d)x = −2, y = 11
5.Which of these is an identity?
(a)2(3x + 1) = 6x + 2
(b)5x + 1 = 5(x + 1)
(c)7 − x = x − 7
(d)4x − 3 = 3x + 5
6.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.
(a)100/3
(b)25
(c)24
(d)50/3
7.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.
(a)5/L − 3
(b)(L − 3)/5
(c)L/5 − 3
(d)L − 3/5
8.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
9.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)
10.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
11.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
12.Solve 2x + 1 = 9
(a)x = 8
(b)x = 16
(c)x = 4
(d)x = 5
13.Write down the gradient of the line with equation y = 7x − 2.
y = 7x − 2
(a)−7
(b)7
(c)2
(d)−2
14.Work out the value of 5a + 2 when a = 3
(a)17
(b)10
(c)15
(d)25
15.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36

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