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

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1.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
2.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
(a)t = 4
(b)t = 8
(c)t = 10
(d)t = 5
3.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
(a)y = −3x − 5
(b)y = 3x − 11
(c)y = −3x + 5
(d)y = −3x + 11
4.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.
(a)£26.67
(b)£40
(c)£6.67
(d)£20
5.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
6.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
7.The point B has coordinates (−2, −2). In which quadrant is B?
(a)the fourth quadrant
(b)the second quadrant
(c)the first quadrant
(d)the third quadrant
8.Make x the subject of the formula y = 3(x + 2).
(a)x = (y − 2)/3
(b)x = y/3 − 2
(c)x = 3y − 2
(d)x = y/3 + 2
9.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?
(a)y = x² + 2
(b)y = 2x + 2
(c)y = 2/x
(d)y = x³ + 2
10.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.
(a)5x ≥ 30
(b)x + 5 ≤ 30
(c)5x < 30
(d)5x ≤ 30
11.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
(a)No: the 8th term is 50 − 8 × 6 = 2, which is positive.
(b)Yes, but the 8th term is 50 − 8 × 8 = −14.
(c)No: repeated subtraction from 50 can never go negative.
(d)Yes: the 8th term is 50 − 8 × 7 = −6, which is negative.
12.Solve 2(x + 3) = 10
(a)x = 3.5
(b)x = 8
(c)x = 5
(d)x = 2
13.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
(a)68, and it is an equation
(b)36, and it is a formula
(c)52, and it is a formula
(d)68, and it is a formula
14.Which expression is equivalent to 2(x + 6)?
(a)2x + 8
(b)x + 12
(c)2x + 12
(d)2x + 6
15.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.
(a)16
(b)24
(c)84
(d)50

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