IGCSEFurther MathsEdexcelExam QuestionsGeometry & TrigonometryRadians

Radians (Edexcel IGCSE Further Pure Maths): Exam Questions

Exam code: 4PM1

38 mins6 questions
1
3 marks
Triangle AOB and sector BOC. OA is 10 cm, OB and OC are 6 cm each, and arc BC is π cm. Centred at O, labelled as Figure 1.

Figure 1 shows a shape A B C spacein which A O B is a triangle, A O C is a straight line and O B C is a sector of a circle with centre O.

A O space equals space 10 spacecm comma space O C space equals space O B space equals space 6 spacecm and the length of arc B C space equals space pi cm.

Find, to 3 significant figures, the area of the shape space A B C.

How did you do?

2a
2 marks
Circle inscribed in a triangle with vertices A, B, O; radius r, angle θ rad, and side AO is 3r cm. Diagram not to scale, labelled Figure 1.

Figure 1 shows the sector A O B of a circle with centre O and radius 3 r cm

A circle with radius r cm touches O A and O B and the arc A B

Angle A O B spaceis theta radians, where 0 space less than space theta space less than straight pi over 2

Find the exact value of theta

How did you do?

2b
4 marks

The area of the region shown shaded in Figure 1 is 8 pi cm2

Find the value of r

How did you do?

3a
2 marks
A sector ROS with angle θ rad, radius 2 cm. Points R, S on arc, O as centre. Note: Diagram not accurately drawn. Underneath is the label "Figure 1".

Figure 1 shows sector R O S of a circle with centre O and radius 2 cm
The size of angle R O S is theta radians.

The area of sector R O S is straight pi over 2 cm squared. Find the exact value of theta

How did you do?

3b
3 marks
A sector with centre O and radius 2 cm is shown. Angle θ rad is between radii OR and OS. Note: Diagram not accurately drawn.

Figure 1 shows sector R O S of a circle with centre O and radius 2 cm
The size of angle R O S is theta radians.

The perimeter of sector R O S is P cm. Find the exact value of P

How did you do?

4
6 marks
Diagram of a circle with centre O, radius r cm. Sector AOB shaded. Angle θ rad at centre. Labelled points: P on perimeter, A and B on circle edge. Diagram not to scale.

Figure 1 shows a circle, centre O, with radius r cm.

The points A, P and B lie on the circle.

The obtuse angle A O B equals theta radians.

The area of the sector A P B O, shown shaded, is 372.4 cm2 and the length of the arc A P B is 53.2cm.

Find, to 3 significant figures where appropriate, the value of

(i) r

(ii) theta

How did you do?

5a
7 marks
Geometric diagram with a semicircle ABCD of diameter 2x cm. Triangle OAB is above with OB and OA being x cm. Point E is inside the semicircle.

A logo, A E B C D, is shown shaded in Figure 2.

The straight line A B C is the diameter of the semicircle A D C
A E B is an arc of a circle with centre O
All angles are measured in radians.

  • B C equals 2 x space cm

  • O A equals O B equals x space cm

  • length space of space arc space A E B italic equals 1.8 x space cm

The perimeter of the logo is P

Show that P equals a x space left parenthesis pi plus pi space sin space 0.9 plus b right parenthesis where a and b are constants to be found.

How did you do?

5b
6 marks

Given that x equals 10 space cm,

find, in cm2 to 3 significant figures, the area of the logo.

How did you do?

6
5 marks
Grey sector diagram with angle 0.5 rad at centre D, labelled vertices A to G, dimensions x and y cm, and note: "Diagram NOT accurately drawn."

Figure 1 shows a badge, shown shaded, made from two identical rectangles, A B C D and D E F G, and a sector D C G of a circle with centre D.

Each rectangle measures x cm by y cm.
The radius of the sector is x cm and the angle C D G is 0.5 radians.

The area of the badge is 50 cm2
The perimeter of the badge is P cm.

Show that

P equals 2 x plus 100 over x

How did you do?