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1. The coordinates of the end points of the diameter of a circle are and .
Calculate

(a) the coordinates of the centre of the circle,

(b) the length of the diameter of the circle.

Answer (a) ……………………………… [2]

(b) ……………………………… [2]

2. The size of each interior angle of a regular polygon is Calculate the number of
sides of the polygon.

Answer ………………………. [3]

3. The point lies on the circumference of the circle, centre .

(a) If KM is the diameter of the circle, calculate the coordinates of M.

(b) Calculate the length of the diameter of the circle.

Answer (a) ……………………. [2]

Answer (b) ……………………. [2]

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4. The diagram below shows a right-angled triangle PQR in which and

. It is given that , and
R

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P Q

Using as much of the information as necessary, calculate the length of RQ.

Answer………………… [2]

5. The diagram below shows triangle P.

On the same diagram, draw the image of triangle P, after a translation

using vector [2]

6. The diagram shows vector and a point R.

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P
.
R

(a) Express as a column vector.

(b) .
On the grid above represent the vector by a line segment. [1]

(c) Work out .

(d) Calculate the magnitude of .

y Answer (a) ……………………….. [1]

4 (c) ………………………. [2]

E 3 (d)
F ………………………. [2]

1 R S

-2 -1 0 1 2 3 4 5 6 x
7. The diagram below-1shows square EFGH and square RSTU.
U T
-2

H -3 G
3
-4
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A transformation maps square EFGH onto square RSTU.

Describe the transformation fully.

Answer ……………………...

………………………………………………………………………………… [3]

8. The size of each exterior angle of a regular polygon is 15°.

Calculate the number of sides of the polygon.

Answer ………………. [2]

9. The coordinates of the end points of the diameter of a circle are ( 3, 1 ) and ( -1, 4 ).

Calculate

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(a) the coordinates of the centre of the circle,

(b) the length of the diameter of the circle.

Answer (a) …………….. [2]

(b) …………….. [2]

10. The diagram below shows a circle with centre O.

The length of the chord AB = 24 cm.
The perpendicular distance of the chord from the centre is 9 cm.

.O
9
A B
24

Calculate the radius of the circle.

Answer………………………… [2]

11. Given that

and ,

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(a) express as a column vector,

(b) calculate the magnitude of .

Answer (a) …………………. [2]

(b) …………………. [2]

12. The diagram below shows the positions of two villages A and B.
B is 150 km away from A on a bearing of 053°.
North

North B

150

53°
A

(a) Calculate the bearing of A from B.

(b) Another village, C, is due east of A and also 90 km due south of B.

Calculate the distance from A to C.

Answer (a) …………………….. [2]

(b) ……………………. [2]

13. The diagram below shows triangle U and triangle V.

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A transformation maps triangle U onto triangle V.

Describe the transformation fully.

Answer ………………………

………………………………………………………………………………. [2]

14. A straight line, l , passes through the points A ( 9,-2 ) and B ( 3, 6).

(a) Calculate the distance between A and B

Answer (a) ………………………… [2]

(b) Find the coordinates of midpoint of the line segment AB.

A 8
Answer (b) …………………………
B [2]
15. The diagram below shows the points A, B and C on the circumference of a circle,
centre O. AB = 8 cm and BC = 6 cm.

6
O
.

7 C
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(a) State, with a reason, the size of

(b) Calculate the length of the diameter, AC, of the circle.

Answer (a) ……………………………………………………………….. [2]

(b) .................................... cm [2]

16. The diagram below shows a parallelogram ABCD with .

The point E is such that and

A B
70° 30°

E 54°
8

D C
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Calculate

(a) ,

(b) .

Answer (a) …………………….. [1]

(b) ……………………. [2]

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S
17. The diagram below shows a triangle S5and a triangle T.

4
T
3

1
9
x
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
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Describe fully a transformation that maps triangle T onto triangle S.

Answer ………………………………

……………………………………………………………………………………… [2]

18. (a) Using the point A marked on the grid below, represent by line segment the
following vectors

, .
[2]

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.A

(b)Write as a column vector.

Answer (b)……………………… [2]

(c)Calculate the magnitude of

Answer (c)………………………… [2]

19. Describe fully the symmetry of the parallelogram below.

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Answer …………………………………………………………………………….. [2]

20. Given that p = and q = ,

(a) express p + 2q as a column vector,

(b) calculate the magnitude of p.

Answer (a) …………………………….. [2]

(b) …………………………….. [2]

21. A table top is in the form of a regular pentagon.

Calculate the size of each interior angle of the table top.

Answer ……………………………….. [2]

22. An isosceles triangle JKL is such that JK = 11cm, and LJ = LK.

(a) In the space provided below, construct triangle JKL. [2]

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(b) Measure and write down the length of LK.

Answer (b) ……………………….. cm [1]

A
23. In the diagram, O is the centre of the circle with radius 15 cm.
AB is a line segment 9 cm from the centre of the circle.

O 15
.
9

13

B
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(a) Write down the geometrical name for the line AB.

(b) Calculate the length of AB.

Answer (a) …………………………… [1]

(b) ………………………… cm [3]

.A

24. The diagram below shows a triangle P and a point A.

Draw the image of P under an enlargement of scale factor , with centre A.

P

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25. Triangle ABC is such that AB = 7 cm, BC = 4 cm and .

(a) Showing all construction lines, construct triangle ABC. [2]

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(b) Measure and write down the length of AC.

(c) Showing all construction lines, construct, on the same diagram,

the angle bisector of . [2]

Answer (b) …………………………… [1]

26. The diagram shows the logo of a Maths club at a college.

The logo consists of a triangle ABC with its vertices on the circumference of a circle.
The circle has centre O and radius 3.5 cm.
COA is a straight line and angle BAC is 300.
MATHS
B A
300
.O
C 3.5
16CLUB
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(a) Why is angle ABC = 900?

(b) Using as much of the given information as is necessary, calculate the

length of AB.

Answer (a) ……………………………………………………………………..

………………………………………………………………………………… [1]

(b) ………………………………… cm [2]

27. A company uses thin metal sheets to make triangular earrings with sides measuring
5 cm, 6 cm and 7 cm.

(a) Using a ruler and a pair of compasses, construct the triangle representing
an earring. [2]

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(b) The company wants to alter the earring by cutting through the middle of, and
perpendicular to, the longest side.
Showing all construction lines, on the same diagram, construct a line along
which the company has to cut. [2]

28. In the diagram,

K lines KL and NM are parallel. L
Angle KLN = 433800 and angle MKL = 430. 380

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p
N M
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(a) State with a reason the size of angle p.

(b) Calculate angle q.

Answer (a) …………………………………………………………………..

…………………………………………………………………… [1]

Answer (b) ………………………….. [2]

29. In the diagram, O is the centre of a circle and LM is a chord such that
and LM = 32 cm.

.O

300
L 19 M
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Using as much of the given information as necessary, calculate the distance of LM

from the centre of the circle.

Answer …………………………… cm [3]

30. The vector B

is represented by a line segment on the grid below.

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(a) On the same grid, draw another line segment from B to represent

.
[1]

(b) Write down as a column vector.

Answer (b) …………………………… [1]

31. The points O and Q are on a plane. O is the origin and .

(a) What are the coordinates of the point Q?

(b) Calculate the magnitude of .

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Answer (a) ……………………………. [1]

(b) ……………………………. [2]

32. (a) Use the line AB below to construct a triangle ABC such that AC = 6.4 cm and
BC =7.1 cm. [2]

A 6 B

A 5
(b) Construct a perpendicular bisector of line AB. [2]
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33. The diagram below shows kite A and kite B. 1

x
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5
-1

-2
B
-3

-4
22
-5
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Describe fully a single transformation that maps kite A onto kite B.

Answer ……………………………………………………………… [2]

34. The coordinates of the point P are (-3, 4), the point Q are (2, -5) and .

(a) What are the coordinates of the point R?

(b) Write down as column vector.

(c) Calculate the magnitude of .

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Answer (a) ……………………………. [2]

(b) ……………………………. [2]

(c) …………………................. [2]

35. The diagram below shows two similar triangles ACD and ABE. AE = 10 cm,
EB = 4 cm and DC = 9 cm. DC and EB are parallel.
9 C
D

4 B
E

10

Calculate the length of AD.

Answer ……………………………... cm [2]

36. The size of an exterior angle of a regular polygon is 30o.

Calculate the

(a) number of sides of the polygon,

(b) size of each interior angle.

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Answer (a) ………………………… [2]

(b) …………………………. [2]

37. The diagram below shows the positions of three villages; Makhubu, Mabe and
Letlhare. Mabe is 12 km due South of Letlhare and 5 km due East of Makhubu.

Letlhare

12

Makhubu Mabe
5

Calculate the distance between Makhubu and Letlhare.

Answer …………………………… km [2]

38. The coordinates of the point G are (1, 2) and the coordinates of point H are (7, -6).

Calculate

(a) the coordinates of the midpoint of the line segment GH,

(b) the length of the line segment GH.

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Answer (a) ( , ) [2]

(b) …………………. units [2]

39. The diagram below shows a triangle S and a triangle T.

y

3
S T
2

x
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Describe fully a transformation that maps triangle T onto triangle S.

Answer ………………………………

……………………………………………………………………………………… [2]
40. In the diagram, lines AB and CD are parallel.
Angle BAD = 380 and angle ABC = 430.

A B
380 430

p
C D

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State, with a geometrical reason, the size of angle p.

Answer …………………………………………………………………..

…………………………………………………………………… [2]

41. A straight line passes through the points and .

(a) Find the equation of the line KL.

Answer (a) ……………………………. [2]

(b) Calculate the coordinates of the midpoint of the line KL.

Answer (b) ……………………………. [2]

.

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42. Calculate the size of an exterior angle of a regular 15 sided polygon.

Answer ………………………………… [2]

43. The interior angles of a regular polygon are each 1600.

Calculate

(a) the size of each exterior angle,

Answer (a) …………………………….. [2]

(b) the number of sides of the polygon.

Answer (b) …………………………….. [2]

44. The coordinates of point P are and .

What are the coordinates of the point R?

Answer ………………………………… [2]

45. The size of each exterior angle of a regular polygon is 24°.

Calculate the size of each interior angle of the polygon.

Answer ………………………………… [2]

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