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.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.
(a)R
(b)Q
(c)P
(d)S
2.A number machine adds 6 to its input. Work out the output when the input is −4.
(a)10
(b)−10
(c)2
(d)−24
3.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?
(a)The cost, in pounds, for each extra 2 gigabytes of data used
(b)The fixed monthly fee, in pounds
(c)The cost, in pounds, for each extra gigabyte of data used
(d)The total number of gigabytes included in the plan
4.Expand and simplify (x − 3)²
(a)x² + 6x + 9
(b)x² − 9
(c)x² − 3x + 9
(d)x² − 6x + 9
5.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
6.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.
(a)4
(b)1/5
(c)5
(d)13
7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
8.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.
(a)38
(b)40
(c)32
(d)39
9.Work out the value of 5y + 9 when y = 0
(a)45
(b)0
(c)9
(d)14
10.A number machine multiplies its input by 5. Work out the output when the input is −1.
(a)−5
(b)5
(c)4
(d)−6
11.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km
12.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?
(a)The two roots must both be positive.
(b)The graph has no roots at all.
(c)The graph must touch the x-axis at exactly one point.
(d)If the graph has two real roots, they are equal and opposite in value, so they sum to zero.
13.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.
14.Simplify 5x + 3y − 2x + y.
(a)3x + 2y
(b)7x + 4y
(c)3x + 4y
(d)6xy
15.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.
(a)2b
(b)b + 2
(c)2b + 2
(d)b/2

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