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Math 0010: Geometry And Vectors Resit Examination Question Paper

Math 0010: Geometry And Vectors Resit Examination

Course:Certificate In Mathematics Bridging Course

Institution: Chuka University question papers

Exam Year:2013

CHUKA UNIVERSITY

UNIVERSITY EXAMINATIONS
EXAMINATION FOR THE AWARD OF CERTIFICATE IN
MATHEMATICS BRIDGING COURSE

MATH 0010: GEOMETRY AND VECTORS RESIT EXAMINATION
STREAM: BRIDGING TIME: 2 HOURS
DAY/DATE: THURSDAY 17/1/2013 11.30 A.M. – 1.30 P.M
INSTRUCTIONS:

Do not write on the question paper.
Answer all questions in this paper.
All working must be clearly and neatly shown.

SECTION A (40 MARKS)

1. Find the equation of the line through point P(-1,-2) and parallel to the line 2y+x-1=0 [4 Marks]

2. Prove that the angle at the centre of a circle is twice the angle at the circumference if subtended by the same chord. [4 Marks]

3. The perpendicular distance between a chord of length 42cm and the centre of a circle is 20cm. Calculate the area of the circle. [4 Marks]

4. Find the value of x given sin??(3x+15)=cos??30°? ? [4 Marks]

5. Given that x and y are complementary angles and tan?x=2.4. Find? cos??x ?,sin??x,tan?y.
[4 Marks]

6. Given P (0, 5) Q (4, 3) and R (2, 1) are three points in a plane.

Find the column vectors PQ and PR

(ii) If PQ = kPR determine the value of k. [4 Marks]

7. Given that ?a=2i+3j-2k and ?b=-3i-2j+3k obtain |3?a+2?b | [4Marks]

8. A prism has a triangular base 5cm by 3cm by 4cm. If it is 30cm long calculate the surface area and its volume. [4 Marks]

9. A ladder 13m ling leans against a vertical wall such that it reaches 12m up the wall. The foot of the ladder slips away from its original position. Calculate how up the wall the ladder now reaches. [4 Marks]

10. Prove that ?cos?^2 ?=1/2+1/2 cos?2? [4 Marks]

SECTION B (20 MARKS)

11. (a) (i) Find the total surface area of a right pyramid whose slanting edge is 12cm
and has rectangular base of 6 cm and 8 cm. [4 Marks]

(ii) Calculate the volume of this pyramid. [2 Marks]

(b) The base area of a cone is three fifths that of its curved surface. Find the radius of
the base if the height is 16 cm. [4 Marks]

12. (a) Given ?(a )=-i+j-k ?b=2i-j+2k and ?c=i+j+k, express ?c as a
linear combination of ?(a ) and ?(b ). [4 Marks]

(b) Solve the equation 3 cos?(3x-20°)=2-cos?(3x-20°) [4 Marks]

(c) Find the angle between ?p=2i-j+k amd ?(q )=-i+j+3k. [2 Marks]

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Math 0010: Geometry And Vectors Resit Examination Question Paper

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