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 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
2.Solve the inequality 6x ≥ 18.
(a)x ≥ 12
(b)x ≤ 12
(c)x ≥ 3
(d)x ≤ 3
3.Solve x² − 2x − 24 = 0.
(a)x = 6 or x = −4
(b)x = −6 or x = 4
(c)x = −8 or x = 3
(d)x = −6 or x = −4
4.y = 3x − 2. Work out the value of y when x = 4.
y = 3x − 2
(a)6
(b)14
(c)10
(d)12
5.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.
(a)8/3
(b)−3
(c)3
(d)1/3
6.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.
(a)S = PC
(b)S = P − C
(c)S = P + C
(d)S = C − P
7.Solve the inequality x + 5 < 12.
(a)x < 7
(b)x < 17
(c)x > 7
(d)x < −7
8.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.
y = 4x − 5
(a)4
(b)−4
(c)5
(d)−5
9.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.
(a)11
(b)−11
(c)1
(d)8
10.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
(a)23
(b)27
(c)24
(d)20
11.A graph has equation y = −2x² + 5. Which statement about its shape is correct?
y = -2x² + 5
(a)It is U-shaped, since x² is always positive.
(b)It is a straight line, because of the constant term +5.
(c)It repeatedly rises and falls, like a wave shape.
(d)It is n-shaped, since the x² coefficient is negative.
12.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.
(a)7.4
(b)6.2
(c)3.2
(d)5
13.Which of these is a formula?
(a)4s + 7
(b)P = 4s
(c)4s > 20
(d)4s = 20
14.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.
(a)2 + 3m
(b)3 + 2m
(c)5 + m
(d)5m
15.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

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