**INSTRUCTIONS TO CANDIDATES**

This assessment requires you to demonstrate competence against unit of competency:

In this assessment, you will be required to answer written questions.

i. The paper consists of three sections: A, B and C

ii. You are allocated Two (2) hours to attempt all the questions.

iii. You are provided with a separate answer booklet.

iv. Do not write on the question paper

v. Scientific calculator can be used

vi. Marks for each question are indicated in the brackets [ ]

### SECTION A – 20 MARKS

**1. What is the amount left over when a number can’t be divided equally?**

A. Whole number

B. Remainder

C. Odd Number

D. Divisor

**2. Choose the fraction equivalent to the decimal 0.09**

A. 9/10

B. 90/10

C. 90/100

D. 9/100

**3. On a real number line, what is the midpoint of -4 and 18?**

A. 8

B. 11

C. 7

D. 4

**4. How many right angles does a square have?**

A. 4

B. 1

C. 24

D. 26

**5. Determine the value of 13-2×3+14+(2+5)**

A. 13

B. 9

C. 15

D. 6

**6. The sum of the measures of two complementary angles is**

A. 180°

B. 60⁰

C. 450

D. 90⁰

**7. A teacher is organizing an inter-school sport day. There are 8 teams in the competition. Each team must play one game against each of the other teams. What is the total number of games played?**

A. 8

B. 28

C. 64

D. 54

**8. A straight line on a d-t graph represents**

A. Slowing down

B. Constant speed

C. Speeding up

D. No movement

**9. If a transversal intersects two parallel lines then the interior angles on the same side of the transversal are**

A. vertically opposite angles

B. supplementary angles

C. complementary angles

D. alternate angles

**10. Which of the following are arranged from smallest unit to largest unit?**

A. Mm, m, cm, km

B. Km, m, cm, mm

C. Cm, mm, m, km

D. Mm, cm, m, km

**11. What is an object measured in three dimensions of length, width, and height?**

A. One-dimensional

B. Five-dimensional

C. Three-dimensional

D. Two-dimensional

**12. What is the next number in the pattern 2, 6, 12, 20, 30….?**

A. 36

B. 40

C. 42

D. 50

**13. What is the square root of the number obtained when 196 is multiplied by 4?**

A. 28

B. 56

C. 392

D. 784

**14. Two shelves are to be joined to provide space for bigger file storage. If the first shelf length measure 4meters 56cm and 6mm, while the second shelf measure 3 meters48cm and 4mm. what will be the new length of the joined shelf?**

A. 8.5m

B. 8 meters 5 cm

C. 8.41 meters

D. 8meters, 4cm and Imm

**15. On a map of scale 1:100,000 a rectangular plot of land measures 7em by 4cm. what are the actual lengths of the plot in kilometres?**

A. 70,000 by 40,000

B. 700 by 400

C. 70 by 40

D. 7 by 4

**16. A company sold 2.5 tonnes of rice in 2kg packets. How many packets were sold?**

A. 125

B. 1250

C. 2500

D. 5000

**17. When 55 is added to a certain number and the sum is divided by 3, the result is 4 times the original number. What is the original number?**

A. 5

B. 6

C. 7

D. 4

**18. What is the gradient of line that passes through the points (3,2) and (2,0)?**

A. -2

B. -1

C. 2

D. 0

**19. Which of the following is not a solid?**

A. cone

B. frustrum

C. cuboid

D. rectangle.

### SECTION B – 40 MARKS

20. Given that a:b = 1:2 and b:c = 3:4. Find a:b:c (4marks)

21. Three bells ring at intervals 30mins, 35mins and 50 mins. If they ring together at 11:25 p.m on Monday at what time and day will they next ring together? (4marks)

### SECTION C – 40 MARKS

**Answer any 2 questions **

30. A rectangular plot measures 100m by 200m. Determine:

a. Its perimeter in km. (4mks)

b. Its area in m2. (4mks)

c. Its area in ha. (4mks)

d. Square tiles of 100cm by 100cm are used to cover the floor. How many tiles are used? (4mks)

e. If the cost of 1 tile is sh. 25. How much money will be spent on tiles. (4mks)

31. a) Using a ruler and pair of compasses only construct a triangle ABC in which AB = 6cm BC= 7cm and angle B = 112.50 and measure AC. (6mks)

b) Drop a perpendicular line from point B to cut AC at N and measure NB. (4mks)

c) using AC as base and height NB find the area of the triangle ABC (4mks)

d) construct triangle ABC in which BC = 6.8 cm angle B = 65 and angle A = 45. (4mks)

32. The table below shows the distribution of marks scored by 40 students in an examination.

(a) Find the value of x (2mark)

(b) State the modal class (2 mark)

(c) Calculate the mean mark correct to 2 d.p (8 marks)

(d) Calculate the median mark (8 marks)

33. Four towns A, B, C and D are such that B is 84km direct to the north of A and C is on a bearing of N65oW from A at a distance of 60km. D is on a bearing of 340o from C at a distance of 30km. Using a scale of 1 cm rep 10km

a) Make an accurate scale drawing showing the relative positions of the towns (10marks)

b) Find the distance and bearing of B from C (4marks)

c) Find the distance and bearing of D from B (4marks)

d) Find the bearing of A from D (2mark)

34. Construct a cube of side 4 cm (20 marks)

35. Find the volume and surface area of the frustrum below. (20 marks)