The Tangent Ratio

Worksheet Answers

Worksheet 1: Programme Questions

1. opposite/adjacent
2. 1m
3. Inverse tan or tan^-1, or arctan
4. A clinometer
5. 20m
6. Angle BAC
7. 3 significant figures
8. Yellow
9. 1.6m
10. The adjacent

Worksheet 2: Tick or Trash

Question 1

Student B is correct. Student A has calculated 3 ¸ tan 8.

Question 2

Student B is correct. Student A has calculated DB, not CD.

Worksheet 3: Exam Practice Questions (Edexcel)

This is a selection of past exam questions from Edexcel, targeted at the middle ability range. You can use the sequence as it stands or select individual questions to suit your needs.

Below is the mark scheme for each question, which may help you to see how marks are allocated and what the examiner is especially looking for. The mark schemes use the following abbreviations:

oe or equivalent
cao correct answer only
ft follow-through marks
dep dependent
ind independent
M method marks
A accuracy marks
B benefit-of-doubt mark
SC special case

Question 1

(a) 32² - 15²

= 28.3km

(b) cos W = 15 ¸ 32
W = 62.0
Bearing = 360 - 'W'
= 298º

Notes:
(a) M1 for 32^{2 - 15}2
M1 (dep) for
A1 cao for 28.3 or better
(b) M1 for cos W = 15/32, sin W = 'a'/32, etc
M1 (dep) for inv cos, inv sin etc
A1 cao for 62º or better
B1 ft on angle for bearing 360 - 'W'
SC: 306±2º B1
SC: finding angle at B and identified gets M1, M1 max

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Question 2

(a) = 622km
(b) Tan 20º = x ¸ 440
x = 440 Tan 20º = 160
Distance = 440 + 160 = 600km

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Question 3

(a) Isosceles
(b) ½ x 28.6 x (19.7 - 11.3) = 120.12m2
(c) 8.42 + 14.32

= 16.6m

(d) tan x =	8.4	= 0.5874 = 30.4º
	14.3
cos x =	14.3	= 0.8614 = 30.4º
	16.6
sin x =	8.4	= 0.5060 = 30.4º
	16.6

Notes:
(a) B1 cao (recognisable)

(b) M1 for ½ x 28.6 x (19.7 - 11.3) or ½ x 28.6 x 8.4
A1 cao for 120.1, 120.12; A0 for 120

(c) M1 squaring and adding 'height' and 'base'
M1 (dep on M1) finding the square root
A1 cao anything rounding to 16.6

(d) M1 tan =	'8.4'	(oe)
	'14.3'

M1 (dep) finding tan^-1
A1 cao anything rounding to 30.4

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Question 4

(a) 5.3² + '0.9'² = 5.38

(b) tan angle =	'0.9'	; angle = 9.6º
	5.3

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Question 5

½ x 12sin55 x 12cos55 x 2 = 67.7cm²