Printable · GCSE Foundation · ages 14-16

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

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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

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

Maths · GCSE Foundation · A3 · Expressions, equations, formulae, identities and inequalities · 15 questions

MathsUKwww.geekhero.co.uk

1.Which of these is a term, rather than a whole expression, an equation, or a formula?
(a)A = 5x²
(b)5x² + 3x
(c)5x² = 20
(d)5x²
2.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
(a)An identity, because it is true for every value of x
(b)An identity, because the brackets can be expanded
(c)An equation, because solving it gives x = 3
(d)A formula, because it works out 4x + 12 from x
3.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
4.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
5.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
6.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
7.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
8.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?
(a)a formula
(b)an expression
(c)an identity
(d)an equation
9.Which of these is an equation, rather than an expression, a formula or an identity?
(a)3x + 5
(b)A = πr²
(c)3x + 5 = 17
(d)3(x + 5) ≡ 3x + 15
10.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).
11.Which of these is a formula?
(a)4s + 7
(b)P = 4s
(c)4s > 20
(d)4s = 20
12.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
13.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.
14.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.
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

Build your own mix at the worksheet builder.