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.a = 2 and b = 5. Work out the value of ab².
(a)50
(b)10
(c)20
(d)100
2.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?
(a)5x − 3 = 4x + 9
(b)6x − 3 = 4x + 9
(c)6x − 1 = 4x + 9
(d)6x − 4 = 4x + 9
3.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
4.The diagram shows two curves drawn on the same grid. Curve A is the graph of $y = x^{2}$ . Which equation could represent curve B?
(a) $y = (x - 3)^{2}$
(b) $y = x^{2} - 3$
(c) $y = x^{2} + 3 x$
(d) $y = x^{2} + 3$
5.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
6.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)
7.A graph shows the total monthly cost of a mobile phone tariff against the number of minutes of calls. The line starts at £12 and stays level until 200 minutes, then rises by 5p for each further minute of calls. Use the graph to work out the total cost of a month in which 250 minutes of calls are made.
(a)£14.50
(b)£13.50
(c)£12.50
(d)£24.50
8.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.
(a)18.67
(b)12
(c)15.33
(d)4.3
9.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
(a)y = −2x + 7
(b)y = −2x − 5
(c)y = 2x + 7
(d)y = −2x + 1
10.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.
(a)216
(b)36
(c)180
(d)250
11.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
12.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.
(a)£24
(b)£14
(c)£12
(d)£8
13.Expand 7(a + 8)
(a)a + 56
(b)7a + 15
(c)7a + 8
(d)7a + 56
14.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.
y = 2x − 6
(a)(−3, 0)
(b)(6, 0)
(c)(0, −6)
(d)(3, 0)
15.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.
(a)r = C / (2π)
(b)r = C / π
(c)r = 2πC
(d)r = C − 2π

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