Worksheets · Foundation and Higher

Solving monic quadratics by factorisation

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 3 marks
Solve each equation.
(a) Solve $x^2 + 5x + 6 = 0$ (2)
(b) Solve $x^2 - 16 = 0$ (1)
Question 2Non-calculator · 4 marks
A square lawn has side 10 m. A path x m wide is laid along two adjacent sides, so that the lawn and the path together form a square of side (10 + x) m. The area of the path is 44 m².
(a) Show that $x^2 + 20x - 44 = 0$ . (2)
(b) Find the width of the path. (2)
Question 3Calculator · 3 marks
(a) The two roots of $x^{2}$ $-$ 6x + c = 0 are positive. One root is three times the other. Find c. (3)

Answers and marks

(a) $x = -2$ or $x = -3$

(b) $x = 4$ or $x = -4$

(a) (10 + x)^2 - 100 = 44, so x^2 + 20x + 100 - 100 - 44 = 0, which gives x^2 + 20x - 44 = 0.

P1 Subtract the lawn area from the large square.
C1 Correct conclusion with supporting reasoning: (10 + x)^2 - 100 = 44, so x^2 + 20x + 100 - 100 - 44 = 0, which gives x^2 + 20x - 44 = 0.

(b) $2$ m

(a) $\frac{27}{4}$

Solving monic quadratics by factorisation

Type your working online and see every mark you earned and lost.