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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 · 15 questions

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1.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
2.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
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.Write down the number of terms in the expression 4x² − 7x + 3.
(a)2
(b)5
(c)4
(d)3
5.Which of these is an inequality?
(a)P = 2n + 7
(b)2n + 7 = 15
(c)2n + 7
(d)2n + 7 > 15
6.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
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.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
9.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
10.Which of these is a formula, rather than an expression, an equation, or an identity?
(a)lwh
(b)lwh = 60
(c)2(l + w) ≡ 2l + 2w
(d)V = lwh
11.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
12.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.
13.Write down the coefficient of p in the expression 7 − 4p + 9q.
(a)7
(b)4
(c)9
(d)−4
14.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
15.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

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