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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.

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

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

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1.Which of these is an expression?
(a)P = 5y − 2
(b)5y − 2 > 8
(c)5y − 2
(d)5y − 2 = 8
2.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
3.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
4.In the expression 5x² − 3x + 7, which of these is a single term of the expression?
(a)5x² − 3x
(b)5x² − 3x + 7
(c)5x²
(d)−3x + 7
5.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
6.Write down the coefficient of p in the expression 7 − 4p + 9q.
(a)7
(b)4
(c)9
(d)−4
7.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.
8.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
9.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).
10.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
11.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
12.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
13.Which of these is an inequality?
(a)P = 2n + 7
(b)2n + 7 = 15
(c)2n + 7
(d)2n + 7 > 15
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.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

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