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 · 15 questions

MathsUKwww.geekhero.co.uk

1.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.
(a)h = Vlw
(b)h = V − lw
(c)h = V / (lw)
(d)h = lw / V
2.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
3.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.
(a)6 s
(b)8 s
(c)32 s
(d)12 s
4.Solve 4x − (2x − 6) = 18
(a)x = 6
(b)x = 3
(c)x = 12
(d)x = 24
5.A number machine multiplies its input by 3. The output is 15. Work out the input.
(a)45
(b)12
(c)18
(d)5
6.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
7.The point A is at (5, −3). In which quadrant does A lie?
(a)the first quadrant
(b)the third quadrant
(c)the fourth quadrant
(d)the second quadrant
8.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?
(a)3(w − 5) ≥ 16
(b)3w − 5 ≥ 16
(c)3w − 5 > 16
(d)3w − 5 ≤ 16
9.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.
(a)0, 3, 6, 9
(b)3, 6, 9, 12
(c)4, 5, 6, 7
(d)3, 9, 27, 81
10.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.
(a)3
(b)40
(c)−3
(d)13
11.Solve 6x + 4 = 28
(a)x = 4
(b)x = 144
(c)x = 24
(d)x = 18
12.Solve the inequality 3x − 1 ≤ 11.
(a)x ≥ 4
(b)x ≤ 4
(c)x ≤ 12
(d)x ≤ 10/3
13.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
(a)−6
(b)−3
(c)−1/3
(d)3
14.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
15.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.

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