Printable · GCSE Higher · ages 14-16
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
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- 1.Which of these statements is an equation with exactly one solution?
- 2.Which of these is a formula, rather than an expression, an equation, or an identity?
- 3.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.
- 4.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.
- 5.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.
- 6.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?
- 7.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.
- 8.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?
- 9.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
- 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.
- 11.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
- 12.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.
- 13.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?
- 14.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.
- 15.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?
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