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 charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.
(a)24 days
(b)30 days
(c)27 days
(d)33 days
2.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?
(a)Line 1
(b)Line 2
(c)Line 4
(d)Line 3
3.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.
(a)£65, and C = 40 + 25h is an expression
(b)£115, and C = 40 + 25h is a formula
(c)£195, and C = 40 + 25h is a formula
(d)£115, and C = 40 + 25h is an expression
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.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?
(a)an equation
(b)an identity
(c)a formula
(d)an expression
6.A student says that 5(x + 2) is equivalent to 5x + 2. Which statement explains why the student is wrong?
(a)Addition must always be done before multiplication, so 5(x + 2) equals 5x + 10 only when x = 0.
(b)The bracket must be worked out first using a value of x, so the two expressions can only be compared once x is known.
(c)The 5 must multiply both terms inside the bracket, so 5(x + 2) expands to 5x + 10, which is never equal to 5x + 2 for any value of x.
(d)5(x + 2) means 5 × x + 2, so the student's answer of 5x + 2 is actually correct.
7.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?
(a)1.76
(b)0
(c)10
(d)6
8.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.
(a)(−3.5, 3.5)
(b)(5, 3)
(c)(4, 5)
(d)(4, 8)
9.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.
(a)0
(b)12.5
(c)12
(d)6.25
10.n = 3. Work out the value of (2n)².
(a)12
(b)9
(c)18
(d)36
11.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.
(a)s = t / d
(b)s = d / t
(c)s = d − t
(d)s = dt
12.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.
(a)−3
(b)−2
(c)3
(d)6
13.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
14.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.
(a)£165
(b)£105
(c)£75
(d)£90
15.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.

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