**MAT-OP1-001**

**MATHEMATICS **

**PAPER 121/1 K.C.S.E 2000**

**QUESTIONS**

**Duration 2hrs**

**SECTION 1 (52 Marks)**

*Answer all the questions in this section*

* *

1) Evaluate

2) Simplify the expression

3) In the figure below ABCD is a rectangular pentagon and M is the midpoint of AB. DM intersects EB at N.

Find the size of:

a) <BAE

b) < BED

c) < BNM

4) The table below shows heights of 50 students

Height (cm) Frequency 140 – 144 3 145 – 149 15 150- 154 19 155- 159 11 160-164 2

(a) State the modal class

(b) Calculate the median height

5) Find the value of x that satisfies the equation

Log (x + 5) = log 4 – log ( x + 2)

6) The enclosed region shown in the figure below represents a ranch drawn to scale. The actual area of the ranch is 1075 hectares.

a) Estimate the area of the enclosed region in square centimeters

b) Calculate the linear scale used

7) Given that sin θ = ^{2}/_{3} and is an acute angle find:

a) Tan θ giving your answer in surd form

b) Sec^{2}θ

8) Shopping centers X, Y and Z are such that Y is 12 km south of X and Z is 15 km from X.Z is on a bearing of 330^{0} from Y.

9) The figure below shows an octagon obtained by cutting off four congruent triangles from rectangle measuring 19.5 by 16.5 cm

Calculate the area of the octagon

10) The length and breath of a rectangular paper were measured to be the nearest centimeter and found to be 18cm and 12 cm respectively.

Find the percentage error in its perimeter.

11) A pyramid VABCD has a rectangular horizontal base ABCD with AB= 12 cm and BC = 9cm. The vertex V is vertically above A and VA = 6cm. Calculate the volume of the pyramid.

12) A tailor intends to buy a sewing machine costs Kshs. 48,000. He borrows the money from a bank the loan has to be repaid at the end of the second year. The bank charges an interest at the rate of 24% per annum compounded half – yearly. Calculate the total amount payable to the bank.

13) On the figure below lines ABC and DC are tangents to the circle at B and D respectively < ACD = 40^{0} and <ABE = 60^{0}<

Giving reasons find the size of:

a) < CBD

b) <CDE

14) The acceleration a m/s^{2} of a particle moving in a straight line is given by a = 18t – 4, where t is time in seconds. The initial velocity of the particle is 2 m/s

a) Find the expression for velocity in terms of t

b) Determine the time when the velocity is again 2m/s

15) Three people Korir, Wangare and Hassan contributed money to start a business. Korir contributed a quarter of the total amount and Wangare two fifths of the remainder. Hassan’s contribution was one and a half times that of Korir. They borrowed the rest of the money from the bank which was Kshs 60, 000 less than Hassan’s contribution, find the total amount required to start the business.

16) Karani bought 4 pencils and 6 biro-pens for Kshs 66b and Tachora bought 2 pencils and 5 biro- pens for Kshs 51.

a) Find the price of each item

b) Musoma spent Kshs. 228 to buy the same type of pencils and biro pens. If the number of biro- pens he bought were 4 more than the number of pencils, find the number of pencils bought.

**SECTION II (48 Marks) **

*Answer any six questions from this section*

17) A triangular plot ABC is such that AB = 36m, BC = 40m and AC = 42 m

a) Calculate the:

i) Area of the plot in square metres

ii) Acute angle between the edges AB and BCb) A water tap is to be installed inside the plot such that the tap is equidistant from each of the vertices A, B and C. Calculate the distance of the tap

18) In form 1 class there are 22 girls and boys. The probability of a girl completing the secondary education course is 3 whereas that of a boy is ^{2}/_{3 }

a) A student is picked at random from class. Find the possibility that,

i) The student picked is a boy and will complete the course

ii) The student picked will complete the courseb) Two students are picked at random. Find the possibility that they are a boy and a girl and that both will not complete the course.

19) a) Complete the table below for the equation

y = 2x^{3} + 5x^{2} – x -6

x -4 -3 -2 -1 0 1 2 2x ^{3}^{-128}^{-54}^{0}^{2}^{16}^{5×3}^{80}^{45}^{20}^{5}^{0}^{5}^{20}^{-x}^{4}^{3}^{0}^{-1}^{-6}^{-6}^{-6}^{-6}^{-6}^{-6}^{-6}^{-6}^{y}^{-50}^{2}^{-6}^{0}

b) On the grid provided draw the graph y = 2x^{3} + 5x^{2} –x -6 for -4 ≤ x ≤ 2

c) By drawing a suitable line use the graph in (b) to solve the equation 2x

^{3}+ 5x^{2}+ x – 4 = 0

20) A solid made up of a conical frustrum and a hemisphere top as shown in the figure below. The dimensions are as indicated in the figure.

a) Find the area of

i) The circular base

ii) The curved surface of the frustrum

iii) The hemisphere surface

b) A similar solid has a total area of 81.51 cm

^{2}. Determine the radius of its base.

21) The figure below shows triangle OAB in which M divides OA in the ratio 2: 3 and N divides OB in the ratio 4:1 AN and BM intersect at X

a) Given that OA = a and OB = b, express in terms of a and b:

- AN
- BM
b) If AX = s AN and BX = tBM, where s and t are constants, write two expressions for OX in terms of a,b s and t.

i) Find the value of s

ii) Hence write OX in terms of a and b

22) A plane leaves an airport A (38.5^{0}, 37.05^{0}W) and flies dues North to a point B on latitude 52^{0}N.

(a) Find the distance covered by the plane

(b) The plane then flies due east to a point C, 2400km from B. Determine the position of C

Take the value ∏ of as ^{22}/_{7} and radius of the earth as 6370 km

23) Matrix p is given by

Find P

^{-1}

24) Two institutions, Elimu and Somo, purchase beans at Kshs. B per bag and maize at Kshs M per bag. Elimu purchased 8 bags of beans and 14 bags of maize for Kshs 47,600. Somo purchased 10 bags of beans and 16 of maize for Kshs. 57,400.

a) Find the values of B and M

b) The price of beans later went up by 5% and that of maize remained constant. Elimu bought the same quantity of beans but spent the same total amount of money as before on the two items. State the new ratio of beans to maize.

25) a) Complete the table for the equation

Y = 2 sin (3x + 30^{0})

X 0 ^{0}^{100}^{200}^{300}^{400}^{500}^{600}^{700}^{800}^{900}^{3x + 300}^{30}^{60}^{90}^{120}^{150}^{180}^{210}^{240}^{270}^{300}^{Y=2 sin (3x + 300}^{1}^{1.73}^{2}^{0}^{-2}^{-1.73}

b) Using the grid provided, draw the graph of y = 2 sin ( 3x + 30

^{0}) for 0 ≤ x ≤ 90^{0 }. Take 1 cm to represent 50 on the x- axis and 2 cm to represent I unit on the y- axis

c) Use the graph in (b) to find the range of x that satisfy the inequality y

^{3}1.6