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.

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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.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
2.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
3.Which of these is an inequality?
(a)P = 2n + 7
(b)2n + 7 = 15
(c)2n + 7
(d)2n + 7 > 15
4.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
5.Which of these is an expression?
(a)P = 5y − 2
(b)5y − 2 > 8
(c)5y − 2
(d)5y − 2 = 8
6.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
7.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
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 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.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
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.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
13.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
14.Which of these is a formula?
(a)4s + 7
(b)P = 4s
(c)4s > 20
(d)4s = 20
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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