Worksheets · Foundation and Higher
Monic quadratics and difference of squares
3 exam-style questions. Answers and the mark for each step are on the last page.
Question 1Non-calculator · 4 marks
Factorise each expression.
(a) Factorise x2+7x+12 (2)
(b) Factorise x2−5x+6 (2)
Question 2Non-calculator · 4 marks
Consider x2−2x−24.
(a) Factorise x2−2x−24. (2)
(b) Hence solve x2−2x−24=0. (2)
Question 3Non-calculator · 4 marks
(a) Use factorisation to work out 10032−9972. You must show your working. (2)
(b) n is a positive whole number. Prove that n2+5n+6 is never a prime number. (2)
Answers and marks
Question 1
(a) (x+3)(x+4)
- M1 Brackets of the form (x±a)(x±b) with ab=12 or a+b=7.
- A1 (x+3)(x+4).
(b) (x−2)(x−3)
- M1 Brackets with ab=6 or a+b=−5.
- A1 (x−2)(x−3).
Question 2
(a) (x−6)(x+4)
- M1 Find two numbers with product -24 and sum -2.
- A1 Correct answer: (x−6)(x+4)
(b) 6,−4
- M1 Set each factor equal to zero.
- A1 Correct answer: 6,−4
Question 3
(a) 12000
- M1 Writing (1003+997)(1003−997).
- A1 The correct answer, 12000.
(b) n2+5n+6=(n+2)(n+3), a product of two whole numbers greater than 1.
- M1 Factorising to (n+2)(n+3).
- C1 Stating that both factors are greater than 1 for positive n, so the number is not prime.
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Monic quadratics and difference of squares
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