Get premium membership and access revision papers, questions with answers as well as video lessons.
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
BRIDGING CERTIFICATE IN MATHEMATICS
MATH 0010: GEOMETRY AND VECTORS
STREAMS: BRIDGING TIME: 2 HOURS
DAY/DATE: TUESDAY 6/8/2013 11.30 AM- 1.30 PM
INSTRUCTIONS:
Answer All Questions in Section A and any Three Questions from Section B
All Working Must be Clearly and Neatly Shown
Adhere to the Instructions on Your Answer Booklet.
Do Not Write on the Question Paper.
Section A (30 Marks): Answer All Questions in this Section
1. Given the equation y-12x-4=0 state
(i) Y – intercept
(ii) X – intercept
(iii) Equation of a perpendicular line at (0,4). [4 marks]
2. Given sin???=2/3? state cos?? and tan?? without using tablets or calculator. [2 marks]
3. (i) Express b ~ as a linear combination of a ~ and c ~ given that a ~=2i+j-k, b ~,
b ~=i-2j+k and c ~=7i-4j+k.
(ii) Calculate the angle between a ~ and b ~. [3 marks]
4. An open right circular cone has a base radius of 5 cm and a perpendicular height of 12 cm. calculate the surface area and volume of the cone. [3 marks]
5. A cylinder of radius 14 cm contains water. A metal solid cone of base radius 7 cm and height 18 cm if submerged into the water. Find the change in height of the water level in the cylinder. [3 marks]
6. (i) State the equation of a circle centre (2,-3) and radius 4cm.
(ii) State he co-ordinate of four major points on the circumference of this circle.
[3 marks]
7. Solve the equation 8 ?sin?^2 x+2cosx-5=0 [3 marks]
8. A triangular plot ABC is such that AB=36m,BC=40m and AC=42m
Calculate
(i) The area of the plot
(ii) Acute angle between AB and BC. [3 marks]
9. Calculate the length of line AB given that B is the midpoint of AC when A(-2-3) and C(6 ,7) [3 marks]
10. Given that the radius of a circle is 6cm, calculate the area and the arc length subtended by
30° at the centre of the circle. [3 marks]
Section B: Answer Any Three Questions in this Section
11. (a) A point A is directly below a window, another point B is 15m from A and at the same horizontal level. From B the angle of elevation of bottom of the window is 30° and the angle of elevation of the top of the window is 35°. Calculate
(i) The vertical distance from A to the top of the window. [2 marks]
(ii) Distance from A to the bottom of the window. [2 marks]
(iii) The length of the window. [2 marks]
(b) An object in the shape of a prism has a triangular base of 6cm, if its length is 12 cm calculate its total surface area and volume. [4 marks]
12. C 3 a ~ B
c ~
O a ~ A
(a) Given S in a point on AC such that AX:XC=1:2 state in terms of a ~ and c ~
(i) A ~C
(ii) O ¯X
(iii) A ¯B [6 marks]
(b) Show that O ¯X is parallel to A ¯B. [2 marks]
(c) O ¯X produced cuts CB at Z, find the ratio (OX) ¯:XZ [2 marks]
13. (a) Prove that the triangle whose vertices are A(-12,1),B(9 3) and C(11 -18) is a right angled triangle. [3 marks]
(b) Prove that ?sin?^2 ?=(1-cos2?)/2. [3 marks]
(c) State and prove Sine Rule [4 marks]
E D
14. (a)
A
C
B
(i) State angle x, y and Z given that angle ADC =750. [3 marks]
(ii) Calculate the length of minor arc AC. [3 marks]
(b) The position vectors of A and B are 3i-j-4k and 8i-6j+6k respectively. A point P divides AB in the ration 2:3. Find the position vector of point P and modulus of AB. [4 marks]
15. (a) The length of a hollow cylindrical pipe is 6 metres. If its diameter is 11 cm and has a thickness of 1 cm calculate the volume in cm3 of the material used to make the pipe. [4 marks]
(b) A line with the gradient of (-3) passes through points (3k) and (k,8) find the value of k and state the equation of that line. [3 marks]
(c) Determine the angle ? between the vectors A ~=2i+3j and B=5i+j
[3 marks]
______________________________________________________________________________
More Question Papers
Popular Exams
Return to Question Papers