**Time: 3 Hours Tuesday 14th, July 2020 a.m
**

**Instructions
**

1.This paper consist of section A, and B with total of fourteen (14) questions

2. Answer ALL questions in both sections.

3. NECTA mathematical tables may be used

4. Write your Examination Number on every page of your answer sheet(s)

**SECTION A (60 MARKS)
**

Answer **ALL** questions in this section.

1. (a) Four bells ring at an internal of 20 seconds, 30 seconds, 40 seconds and 50 seconds

respectively. At what time will all bells ring together?

(b) Express1. 4 In the form of where

2. (a) If = 4, find value of – 1

(b) given that find without using tables

(i) (ii)

3. (a) given a universal set µ and two set A and B such that µ=, A=

and B=. Find i) AUB ii) A﮲ꓵB﮲

(b) There are 30 farmers in the village. 15 farmers grow coffee and 21 grow banana. How

many farmers grow a single crop if only two (2) grow neither coffee nor banana?

4. (a) Find the equation of a line which passes through point A which is parallel

to the line 3x +4y -15=0

(b) The vectors. =16-3 and =-4+7 and position on vectors, Find the vector =+ and

its magnitude.

5. (a) Given that triangle ABC is similar to triangular PQR =8cm, = 10cm , =36cm and

angle PQR is 60°. Find the area of triangle PQR.

(b) In the figure below ABCD is a square AQ =. Prove that R is the midpoint of

D Q R C

A B

6. (a) The number of surface tiles needed to a surface of floor of hall varies inversely as the

square of the length of a sides of the tiles used. If 2016 tiles of side of 0.4m would be

needed to surfaces the floor of a certain hall, how many tiles of 0.3m would be required?

(b) Mr.Ongongo from Kenya visited Tanzania. He had 15000 Kenya shillings (Ksh) and wanted

to change the money into US dollar. If 1 US dollar was equivalent to 2400 Tanzania

shillings ( Tshs) and 1 Ksh was equivalent to 25 Tshs, how much US dollar did he get?

7. (a) Mr Ngwalla commenced business on January 1st 2020 with capital 2,500,000/= with

following transactions.

January 3rd bought goods for cash 2, 300, 0000/=

January 5th paid rent for cash 200,000/=

January 8th bought furniture for cash 550,000/=

January 10th cash sales 3,000,000/=

January 15th bought shelves for cash 350,000/=

January 20th paid salary for cash 250,000/=

January 25th paid wages for cash 100,000/=

Prepare cash book account and hence extract trial balance of Mr. Ngwalla

(b) If a: b=4:10 and b: c=14:18, Find a: c

8. (a) The first term of AP is 2 and common difference is 0.4. How many terms would be

required to give a total of 170?

(b) The third term of a geometric progression is equal to the square of its first term. If the

second term is 8 determine the sixth term.

9. (a) If and A is an acute angle, find without using tables the value of

29sin A +19cosA

(b) A ladder reaches the top of wall 10m high, when the other end is 6m from the foot of the

wall. Find

(i) The length of ladder ( ii) The angle that the ladder makes with the ground.

10. (a) Given that that=² find **m** and** r
**

**
**(b) The products of two consecutive odd numbers are 143. Find the two numbers

**SECTION B (Marks 40)
**

Answer **ALL **questions in this section

11. A table below shows the number of 116 men in various age groups with the some form of paid employment in the village of Somanda.

Age in Years | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 |

Frequency | 12 | 14 | 26 | X | 23 | 5 | 1 |

- Find the value of X ?
- Use the assumed mean method to find the mean.( use A=45.5)
- Calculate i) The median ii) The modes
- Sketch the Histogram

12. (a) Define the following terms as used in mathematics

(i) Nautical miles

(ii) Knot

(b) A ship sails from point A to at 20 knot, leaves point A at 12:00

mid night on Monday. When will it arrives at point B? Use Rᴇ=6370km and.

(c) Prove that the two tangents from an external point are equal

13. (a) If B= and . Find 3B²-2BI

(b) Given that , find

(C) From the result obtain in (b) above solve simultaneous equation

(d) Find the image of point after rotated 180° clockwise about the origin.

14. (a) The manager of Butcher goes to the market to buy a number of cows and a number of

goats. He has a capital of shillings 2,000,000/= but he has space for only 40 animals .The

average markets price for cows is shs 80,000/= each and for goats is shs 20,000/= each.

If the profit per cow is shilling 10,000/= and per goat is 3,000/=

(i) How many cows and goat must be bought to get a maximum profit

(ii) Using (a) find the maximum profit

(b) Given

(i) Sketch the graph of

(ii) From the graph find domain and range

(iii) Find the value of and .