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Math 0010: Geometry And Vector Question Paper

Math 0010: Geometry And Vector

Course:Certificate Of Bridging

Institution: Chuka University question papers

Exam Year:2012

1
CHUKA UNIVERSITY
COLLEGE
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF CERTIFICATE
BRIDGING COURSE IN MATHEMATICS
MATH 0010: GEOMETRY AND VECTORS
STREAM: CERT (BRIDGING MATHS) TIME: 2 HOURS
DAY/DATE: FRIDAY 10/12/2010 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:
(i) Answer all Questions in Section A and any three Questions in Section B.
(ii) All working must be clearly and neatly shown.
(iii) Adhere to all instructions on your answer booklet.
SECTION A (30 MARKS)
1. State the x and y-intercepts given the equation y – 12x – 4 = 0. [2 marks]
2. A point T divides a line AB internally in the ratio 5:2. Given A (-4, 10) and
B (10, 3) Find the co-ordinate of T. [3 marks]
3. In a triangle ABC, D is the midpoint of AB and E is a point on BC such that
BE =
3
2
BC. If AD = p and AC = q express EC in terms of p and q. [3 marks]
4. The gradient of a curve at any point (x y) is 3x
2
. Given that the curve passes
through point (-2 3) find its equation and a perpendicular line through point
(-2 3). [4 marks]
5. Given Sin x =
30
20
state Cos x and tan x without using tables or calculator.
[3 marks]
6. Find the angle subtended at the centre of a circle by an arc of 11cm if the
diameter of the circle is 21cm
(take
)
7
22
? ?
. [2 marks]
2
7. A metal bar 14cm long and 5cm in diameter is melted down and cast into
circular washers. Each washer has an external diameter of 4 cm and an
internal diameter of
2
3
cm and is 0.3cm thick. Calculate the number of
complete washers obtained. [4 marks]
8. Two pairs of trousers and three shirts cost a total of Sh.390. Five such pairs of
trousers and two shirts cost a total of Sh.700. Find the price of a pair of
trousers and a shirt. [3 marks]
9. State and prove Sine Rule. [3 marks]
10. Given that Sin (x + 30°) = Cos 2x° Find the value of x and Cos
2
3x.
[3 marks]
SECTION B (30 MARKS)
Answer any three Questions from this Section.
11. Given that
, 2
~
k j i a ? ? ? k j i b 2
~
? ? ?
and
k j i c 4 5
~
? ? ?
Calculate
(i)
c b a ? ? 2
[3 marks]
(ii) Angle between
a
~
and
b
~
. [3 marks]
(iii) Express vector
b
~
as a linear combination of
a
~
and
c
~
.
[4 marks]
12. (a) Solve for x in the Equation
5Sin (3x + 20°) = 1½ - 2 Sin (3x + 20°). [3 marks]
(b) Universities X, Y and Z are such that Y is 120km South of X and Z is
150km from X. Z is on the bearing 330° from Y. Find the bearing of Z
from X. [3 marks]
(c) Given
XY
AND
PZ
are parallel chords of a circle 2cm apart, if
PZ
= 10cm and
XY
= 8cm, find the radius of the circle. [4 marks]
3
13. (a) From the top of a watch tower 20m high the angle of depression of Boat A
is 60° and that of Boat B is 30°, Find possible distances between the two
Boats. [4 marks]
(b) State the value of the angles X°, Y° and Z° in the figure below given that
angle ABC = 130° and 0 is the centre of the circle. [3 marks]
A
C
B
(c) A right pyramid OABCD has a square base of side 40cm and its slant
height is 29cm. Find its surface Area and its volume. [3 marks]
14. (a) (i) State the co-ordinate of the centre of the circle given by the
equation 2x
2
+ 2y
2
+ 8x + 12y – 24 = 0.
(ii) Identify four major points on the circumference of this circle.
[6 marks]
(b) A living tent in the shape of a cone and its diameter 14ft and 24ft high.
Find its total surface Area and its volume. [4 marks]
Z°
O
x°
130°
4
15. In the figure below OA =
a
~
, OB =
b
~
point P and T divide OB and AB internally
in the ratio 2:3 and 1:3 respectively. Line OT and AP meet at Q.
A
T
Q
O P B
Find in terms of
a
~
and
b
~
, OT, OP, AP, OQ and state the ratios OQ:QT and
PQ:QA. [10 marks]
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Math 0010: Geometry And Vector Question Paper

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