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Mathematics (Alt.1) Question Paper

Mathematics (Alt.1)

Course:Secondary Level

Exam Year:2012

121/1
MATHEMATICS (Alt. 1)
Time: 21/2 hours
Paper 1
July / August 2012
Instruction to candidate.
Answer ALL questions in section I and only five questions in section II.
All answers and working must be written on the question paper in the spaces provided below each question.
Show all the steps in your calculations, giving your answer at each stage in the spaces below each question.
Marks may be given for correct working even if the answer is wrong.
Non – programmable silent electronic calculators and KNEC mathematical tables may be used where stated otherwise.
SECTION I
Answer all questions in this section in the spaces provided.
Without using a calculate evaluate:
(-8÷2+12×9-4×6)/(6-48÷6×7) (3 marks)
A regular polygon with 3n sides has interior angle 40o greater than those of one with n sides. What is the value of n? (3 marks)

Simplify:
(5(2a-1))/6 - (3(4a+1))/8 + 11/12 (3 marks)
Given that sin (90o-XO) =12/37 where x is the acute angle. Find without using mathematical tables the value of Tan x. (2 marks)

A matatu is supposed to start a journey at 11.58 a.m and to reach its destination at 1.49 p.m. If it starts 4 minutes late and arrives 18 minutes late, how long does it take to make the journey? (3 marks)

Solve for x in the equation

125 x +53x – 75 = 175 (3 marks)
A right circular closed cylinder of height 4cm has a total surface area of 165cm. Find the radius of the base. (Take p= 22/7) (3 marks)

Given that DBC = 60o and angle BAD = 25o.

Find:
Angle AED. (1 mark)

x (1 mark)

y (1 mark)

z (1 mark)

PQRS is a parallelogram where P(-1, 2) , Q(0, 5) and R(-3, 4)
Find:
Column vector QP (1 mark)

Coordinate of s (2 mark)

Magnitude of PR (1 mark)

A train leaves Kikuyu Town at 7.00 a.m a towards Nairobi full of passengers. After this no one boards but people alight. The train makes 25 stops and the number of alighting passengers is noted.
How many people got at the train station? (2 marks)

Find the average number of passengers alighting at each stop. (2 marks)

The line 3x – 2y + n =0 passes through Q (4, 2) and is parallel to the line mx – 2y + 9 =0. Find the value of m and n.
Line LM is 8cm long. Point P divides line LM in the ratio LP:PM =3:4

By construction determine the position of P. Measure LP. (4 marks)
Simplify the equation
(2m(n-3)- n(n-3))/(10m-5n-2m^2+nm) (3 marks)
Twenty four 8 tonnes lorries shift a dump of clay of mass 1384 tonnes in 15 days. How long will it take eighteen 10 tonnes lorries to shift 1903 tonnes.
The length of an enlarged photograph is (2x +2) cm, whilst that of the original is ½ (x + 1)cm. Find the width of the original if the enlarged photograph is 16cm wide. (3 marks)
Give the range of values which will satisfy the inequality and plot on a number line
4x>3x – 2 = 4x – 2 (3 marks)
SECTION II (50 marks)
Answer any five questions in this section in the spaces provided.
Mr. Maina earns a salary of Ksh. 446,712 p.a and receives free housing from his employer. He pays insurance premiums of Ksh. 12000 p.m. He is entitled to a personal relief. Income tax for all the income earned was charged at the rates shown below.
Reliefs
Insurance = 15% of the premium up to a maximum of Ksh. 3000 p.m
Personal = Ksh. 1096 p.m
Calculate his monthly salary. (2 marks)
Calculate his P.A.Y.E
How much does Mr. Maina pay slip has at the end of the month.
18 (a) Plot a trapezium ABCD with coordinates A (1, 0) B (4, 0) C (3, 2) D (1, 2) (2 marks)
(b) Plot the image of AIBICIDI of ABCD when reflected in the line y = -x (2 marks)
(c) Plot the image AIIBIICIIDII of AIBICIDI under translation (6¦6) (2 marks)
(d) Describe a single transformation that will map AIIBIICIIDII on to ABCD
19. The figure below shows a circle with centre O and radius 14cm. Angle YOZ = 120O. The diameter WOX is an axis of symmetry.
Using p =22/7, Find to 2 decimal places the length of:
YZ (2 marks)
YN (2 marks)
The area of triangle WYZ (2 marks)
The area of segment YXZN (2 marks)
The area of WYXZ (2 marks)
20. Given that -3i + 4j -3i + -4j, 4i – 3j and the position vector of X, Y and Z respectively. O is the origin of these vectors
(i) If OT = OX + OZ, express OT as a column vector (2 marks)
(ii) If OH = OY + OT, express OH as a column vector. (2 marks)
If OG = 1/3(OX + OY +OZ), find OG as a column vector. (2 marks)
Find the coordinates of T, H and G (2 marks)
Show that points O, G and H lie in a straight line. (2 marks)
21. (a) Below is a velocity – time graph representing the motion of an object which travels for 5 seconds at a constant velocity of 56 m/s before decelerating uniformly for 4 seconds and coming to rest

Calculate:
the total distance travelled by the object (2 marks)
the velocity of the object at t = 7 seconds (3 marks)
the average velocity of the object throughout the 9 seconds of motion shown on the graph (2 marks)
(b) If the velocity time graph below the phase of acceleration lasts one – quarter of time in deceleration. Given that the total distance m the motion is 800m. Calculate the total time taken. (3 marks)
21. Three women, Mary, Janet and Alice decided to invest in a farming project. They decided to buy 15 acres of land which was costing Ksh. 2,800,000. The owner agreed that the three women could pay a deposit of 60% of the money and the money and the rest to be paid within one year. Mary, Janet and Alice raised the deposit in the ratio 3:2:5 respectively. The balance was to be paid to the owner of the farm from the proceeds of farming in the same ratio as the deposits. During the year the farm realized the farm realized Ksh. 2,080,000.
(a) How much of the deposit did Janet contribute? (2 marks)
(b) How much of the remaining amount did Alice pay at the end of the year? (2 marks)
(c) After paying the remaining amount, at the end of the year, how much money was Mary left with? (4 marks)
(d) Mary decided to sell her share of land to Janet at a value of Ksh. 200,000 per acre. Given that they shared the land in the same ratio as the initial deposit, how much did Janet pay her? (2 marks)
23. Given the curve
Y = 2x2 + 3x – 7
Find:
the gradient of the curve at point (3,17) (3 marks)
the equation of the tangent to the curve at point (3,17) (2 marks)
the angle the tangent at (3,17) makes the x – axis (2 marks)
Determine the equation of the Normal to the curve at point (3,17) (3 marks)
24. A crane is made in the shape shown in the figure below. QR is horizontal.PQ=PR=27m, PS=RS=30m and angle PQR=650

Calculate:
Length of QR (2 marks)
Angle PRS (2 marks)
Angle of elevation of S from R (2 marks)
The vertical height of S above R (2 marks)
The horizontal distance of S from Q (2 marks)

Mathematics (Alt.1) Question Paper

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