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CAIE IGCSE Additional Mathematics Geometry and Trigonometry Question Bank

CAIE IGCSE Additional Mathematics Geometry and Trigonometry Question Bank
Cambridge IGCSE Additional Mathematics 0606 syllabus for exams in 2028, 2029 and 2030Exams 2028-2030

Practise straight-line and circle geometry, radians, sector measures and trigonometric graphs, identities and equations across coordinate and diagram-based problems.

Covered syllabus points

7. Straight-line graphs8. Coordinate geometry of the circle9. Circular measure10. Trigonometry

Question 1

Question 1(a)

(a)

A straight line passes through the points (4,23) and (-8,29). Find the point of intersection, P, of this line with the line y=2x+5.

[ 5 ]

Question 1(b)

(b)

Find the distance of P from the origin.

[ 2 ]

Question 1

Question 1(a)

(a)

Write down the amplitude and period of 3cos⁡2x−13 \cos 2 x-1.

Amplitude =
Period =

[ 2 ]

Question 1(b)

(b)

Sketch the graph of y=3cos⁡2x−1y=3 \cos 2 x-1 for 0∘⩽x⩽360∘0^{\circ} \leqslant x \leqslant 360^{\circ}.

Figure for Question 1(b) — CAIE IGCSE Additional Math
[ 3 ]

Question 3

[Maximum number: 8]

A circle with centre C has the equation x2+y2−10x−4y+24=0x^{2}+y^{2}-10 x-4 y+24=0.

Question 3(a)

(a)

Show that the line y=2 x-3 is a tangent to this circle.

[ 3 ]

Question 3(b)

(b)

Given that this tangent touches the circle at the point P, find the coordinates of P.

[ 2 ]

Question 3(c)

(c)

Find the equation of the circle which has its centre at P and passes through the origin.

[ 3 ]

Question 3

[Maximum number: 6]

Point A has coordinates (3,-1).
A circle has equation (x−4)2+(y+3)2=5(x-4)^{2}+(y+3)^{2}=5.

Question 3(a)

(a)

Show that A lies on the circumference of the circle.

[ 1 ]

Question 3(b)

(b)

Given that AB is a diameter of the circle, find the coordinates of B.

[ 2 ]

Question 3(c)

(c)

Find the equation of the tangent to the circle at A.

[ 3 ]

Question 4

[Maximum number: 7]

4 The coordinates of points A, B, C and D are as follows.

The line L has equation y=11 x-75 .

The perpendicular bisector of the line A B meets L at the point E .

Find the area of triangle C D E .

Question 5

[Maximum number: 4]

In this question, all angles are in radians.

Question 5(a)

(a)

Write down the period of 5tan⁡(x4)+15 \tan \left(\frac{x}{4}\right)+1.

[ 1 ]

Question 5(b)

(b)

On the axes, sketch the graph of y=5tan⁡(x4)+1y=5 \tan \left(\frac{x}{4}\right)+1 for −2π⩽x⩽4π-2 \pi \leqslant x \leqslant 4 \pi.

State the intercept with the y-axis.
Show clearly the positions of any asymptotes.

Figure for Question 5(b) — CAIE IGCSE Additional Math
[ 3 ]

Question 5

[Maximum number: 5]

Solutions to this question by accurate drawing will not be accepted.
A circle has centre (4,2) and meets the x-axis at (-2,0).

Question 5(a)

(a)

Find the equation of the circle.

[ 2 ]

Question 5(b)

(b)

Find, in exact form, the coordinates of the points where the circle meets the y-axis.

[ 3 ]

Question 6

Question 6(a)

(a)
Figure for Question 6(a) — CAIE IGCSE Additional Math

The diagram shows an equilateral triangle ABC with side a.
M is the midpoint of AC and angle AMB=90∘AMB=90^\circ.
Use the diagram to find sec⁡30∘\sec 30^\circ.

[ 3 ]

Question 6(b)

(b)

Show that 1sec⁡x−1+1sec⁡x+1\frac{1}{\sec x-1}+\frac{1}{\sec x+1} can be written as 2cosec⁡xcot⁡x2\operatorname{cosec}x\cot x.

[ 4 ]

Question 11

[Maximum number: 10]

The coordinates of points A and B are (-5,6) and (4,-6) respectively. The point C lies on the line AB, between A and B, such that ACCB=12\frac{AC}{CB}=\frac12.

Question 11(b)

(a)

The line CD is perpendicular to AB. Find the equation of CD in the form y=mx+c.

[ 4 ]

Question 11(c)

(b)

The length of BD is 125\sqrt{125}. Find the coordinates of the two possible positions of point D.

[ 6 ]

Question 8

[Maximum number: 8]

In this question the units are metres.

Figure for Question 8 — CAIE IGCSE Additional Math

The diagram shows a circle, centre O and radius 2.
The chord AB has length 232\sqrt3.
The point Q lies on the circle such that AQ=BQ.
The arc APB is part of a circle, centre Q.

Question 8(a)

(a)

Find the exact value of angle AQB in radians.

[ 2 ]

Question 8(b)

(b)

Hence find the area of the shaded region. Give your answer in terms of π\pi.

[ 6 ]