Word Problems with Quadratics (Grade 11) — Worksheet & Memo

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Grade 11 · Equations and Inequalities

Word Problems with Quadratics (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 24

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
The product of two consecutive positive integers is 132. Determine the integers.
(4)
x² + x − 132 = 0 → (x + 12)(x − 11) = 0 → reject x = −12 → 11 and 12✓✓✓✓ (4)
2
A rectangle is 3 m longer than it is wide and has an area of 40 m². Determine its dimensions.
(4)
x(x + 3) = 40 → x = 5 (reject −8) → 5 m by 8 m✓✓✓✓ (4)
3
The sum of a number and its square is 56. Determine the number if it is positive.
(3)
x + x² = 56 → (x + 8)(x − 7) = 0 → 7 (reject −8)✓✓✓ (3)
4
A cyclist rides 60 km. Riding 5 km/h faster would take 1 hour less. Determine her speed.
(4)
60/x − 60/(x + 5) = 1 → x² + 5x − 300 = 0 → 15 km/h✓✓✓✓ (4)
5
Two consecutive POSITIVE even numbers have a product of 168. Determine them.
(3)
x(x + 2) = 168 → x² + 2x − 168 = 0 → (x + 14)(x − 12) = 0 → 12 and 14✓✓✓ (3)
6
Why must you write down a line rejecting one of the two answers?
(2)
Because a length, speed or count cannot be negative — the rejection line is worth a mark.✓✓ (2)
7
A rectangle's length is twice its width. Its area is 72 m². Determine the width.
(3)
2x² = 72 → x² = 36 → 6 m (reject −6)✓✓✓ (3)
8
What is the first line you should write in any word problem?
(1)
A definition of the variable, e.g. 'Let x be the width in metres'.✓ (1)

TOTAL: 24 marks