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Expressions, equations, formulae, identities and inequalities worksheet — GCSE Higher

Fifteen questions on "expressions, equations, formulae, identities and inequalities" — DfE statement A3. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Expressions, equations, formulae, identities and inequalities worksheet — GCSE Higher

Maths · GCSE Higher · A3 · Expressions, equations, formulae, identities and inequalities · Non-calculator · 15 questions

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1.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.
(a)11 — 6 and (4x + 3) are correct factors of 24x + 18.
(b)66 — 6 and (4x + 3) are not correct factors of 24x + 18.
(c)84 — 6 and (4x + 3) are correct factors of 24x + 18.
(d)66 — 6 and (4x + 3) are correct factors of 24x + 18.
2.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
(a)An equation, since it has an equals sign and unknown x.
(b)An identity, since both sides are equal for every x.
(c)A formula, since it relates two different quantities.
(d)An inequality, since the sides are equal sometimes.
3.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.
(a)£47, and T=15+8h is an equation (solved for h).
(b)£47, and T=15+8h is a formula (relates T and h).
(c)£27, and T=15+8h is a formula (relates T and h).
(d)£32, and T=15+8h is a formula (relates T and h).
4.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
5.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
6.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
(a)An equation, because solving it gives the value of n
(b)An identity, because it is true for many values of n
(c)A formula, because it works out n from 9
(d)An inequality, because ≤ compares the two sides
7.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
8.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
9.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
10.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.
(a)1
(b)3
(c)2
(d)5
11.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
(a)w < 630
(b)w ≥ 630
(c)w > 630
(d)w ≤ 630
12.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
13.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
14.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?
(a)The equation has one solution; the inequality has many.
(b)Both have exactly one solution.
(c)Both have many solutions.
(d)The equation has many solutions; the inequality has one.
15.Which of these statements is an identity?
(a)x + 4 = 2x
(b)2(x + 4) = 20
(c)2(x + 4) ≡ 2x + 8
(d)2(x + 4) = 2x + 4

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