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Math 0010: Geometry And Vectors Question Paper
Math 0010: Geometry And Vectors
Course:Bridging Certificate In Mathematics
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF CERTIFICATE IN BRIDGING COURSE IN MATHEMATICS
MATH 0010: GEOMETRY AND VECTORS
STREAMS: TIME: 2 HOURS
DAY/DATE: WEDNESDAY 17/4/2013 11.30 AM – 1.30PM
INSTRUCTIONS:
Answer all questions in section A and any other three (3) in section B.
All working must be clearly and neatly shown
Do not write on the question paper at all
Follow all instructions on the answer booklet.
SECTION A (30 MARKS) ANSWER ALL QUESTIONS IN THIS SECTION.
1. Find the equation of a line which is perpendicular to the line 2y + 3x = 5 passing through point (3 -1). [3 Marks]
2. Find the distance between the point p (-1 -3) and the midpoint of the line joining A and B where A (3 2) and B (5 -4.) [3 Marks]
3. The position vectors of A and B are 3i-j-4k and 8i-6j+6k respectively. If a point R divides AB in the ratio 2:3 state the position vector of R. [3 Marks]
4. Determine the angle between the vectors =2i+j-2k and B ~=i-2j+2k
[3 Marks]
5. Solve the equation 2 cos??3?-1=0?. [3 Marks]
6. Given tan???=3/4 state cos??? and sin?? ? ? without using tables or calculator. [3 Marks]
7. The length of a hollow cylindrical pipe is 6 metres. If its external diameter is 11 cm and has a thickness of 1 cm, calculate the volume in cm3 of the material used to make the pipe. [3 Marks]
8. Find the value of angles x°,y° and Z° in the figure below, given that point O is the centre of the circle and angle ABD =35°. [3 Marks]
B
C
A
D
E
9. In the diagram, O is the centre of a circle of radius 6 cm and sector AOB has an area of
4p?cm?^2 Calculate the size of the angle ACB. [3 Marks]
C
A ----- 8888
B
10. Given vectors a ~=3i+j
b ~=i-2j and c ~=2i-5j
Determine |a-b-3c| [3 Marks]
SECTION B (30 MARKS)
11. (a) Find the co-ordinates of a point. M(x y) which divides the line segment AB in the
ratio 2:5 given A(-3 2) and B (11,-5) plot the line segment Am and calculate its length. [4 Marks]
(b) Find the angle subtended at the centre of a circle by an arc of 11 cm if the diameter of the circle is 21cm. [3 Marks]
(c) Proof that points A(1 2) B (3 5) and C(7 11) are collinear. [3 Marks]
12. (a) Find the equation of a perpendicular bisector of the line segment joining the points A (3 5) and B (-3 7). [4 Marks]
(b) (i) State the co-ordinate of the centre of the circle given by the equation ? x?^2+y^2+4x+6y-12=0
(ii) Identify the radius and the co-ordinates of the four major points on the
circumference of the circle in b(i). [6 Marks]
13. (a) O
a ~
b ~
A
A P B Q
In the diagram OA = a ~, OB=b ~, P lies on AB such that AP:PB=1:2 and Q lies on AB produced so that AQ=3AB.
Determine OQ and PQ in terms of a ~ and b ~. [4 Marks]
(b) (i) Given a ~=i+2j-3k, b ~=-i-j+3k ,c ~=i+4j-3k
Express c ~ as a linear combination of a ~ and b ~. [4 Marks]
(ii) Obtain |a+b+c| [2 Marks]
14. (a) From the top of a cliff 20m high the angle of depression of boat A is 60° and that
of boat B is 30°, state possible distances between boat A and B. [4 Marks]
(b) A right pyramid OABCD has a square base of side 40cm and its slant height is
29cm, find its volume and surface area. [3 Marks]
(c) Solve the equation 5-5 cos???=3? sin?^2 ?? [3 Marks]
15. (a) A living tent is in the shape of a cone and its diameter in 14 ft and its height is
24ft. find its volume and its total surface area. [4 Marks]
(b) State and prove Sine Rule. [3 Marks]
(c) Prove that ?cos?^2 ?=(1+cos?2?)/2 [3 Marks]
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