Instructions

Use black ink or ball-point pen.

If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).

Fill in the boxes at the top of this page with your name, centre number and candidate number.

Answer all the questions and ensure that your answers to parts of questions are clearly labelled.

Answer the questions in the spaces provided – there may be more space than you need.

You should show sufficient working to make your methods clear. Answers without working may not gain full credit.

Inexact answers should be given to three significant figures unless otherwise stated.

Information

A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.

There are 6 questions in this question paper. The total mark for this paper is 49.

The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.

Advice

Read each question carefully before you start to answer it.

Try to answer every question.

Check your answers if you have time at the end.

If you change your mind about an answer, cross it out and put your new answer and any working underneath.

1.	Solve, for 0 x < 180°

cos (3x − 10°) = −0.4

giving your answers to 1 decimal place. You should show each step in your working.

(Total 7 marks)

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2.	(a)	Show that the equation

cos2 x = 8sin2 x – 6sin x

can be written in the form

(3sin x – 1)2 = 2

(3)

(b)	Hence solve, for 0 ⩽ x < 360°,

cos2x = 8sin2x – 6sin x

giving your answers to 2 decimal places.

(5)

(Total 8 marks)

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3.	(a)	Show that the equation

tan 2x = 5 sin 2x

can be written in the form

(1 – 5 cos 2x) sin 2x = 0

(2)

(b)	Hence solve, for 0 x 180°

tan 2x = 5 sin 2x

giving your answers to 1 decimal place where appropriate.

You must show clearly how you obtained your answers.

(5)

(Total 7 marks)

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4.	(a)	Show that the equation

3 sin2 x + 7 sin x = cos2 x − 4

can be written in the form

4 sin2 x + 7 sin x + 3 = 0

(2)

(b)	Hence solve, for 0 x < 360°

3 sin2 x + 7 sin x = cos2 x − 4

giving your answers to 1 decimal place where appropriate.

(5)

(Total 7 marks)

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5.	(i)	Solve, for 0 ≤ < 360°, the equation 9 sin ( + 60°) = 4, giving your answers to 1 decimal place. You must show each step of your working.

(4)

(ii)	Solve, for – ≤ x < , the equation 2 tan x – 3 sin x = 0, giving your answers to 2 decimal places where appropriate.

[Solutions based entirely on graphical or numerical methods are not acceptable.]

(5)

(Total 11 marks)

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6.	(i)	Solve, for –180° x < 180°,

tan(x – 40) = 1.5,

giving your answers to 1 decimal place.

(3)

(ii)	(a)	Show that the equation

sin tan = 3 co s + 2

can be written in the form

4 cos2 + 2 cos – 1 = 0.

(3)

(b)	Hence solve, for 0 < 360°,

sin tan = 3 cos + 2,

showing each stage of your working.

(5)

(Total 11 marks)

TOTAL FOR PAPER: 49 MARKS