**PRESIDENT’S OFFICE
**

**REGIONAL ADMINISTRATION AND LOCAL GOVERNMENT
**

**MARY WILSON GIRLS’ SECONDARY SCHOOL
**

**BASIC MATHEMATICS TERMINAL EXAMINATIONS
**

**FORM 4 -2019
**

**Duration: 02:30 Hours Friday , 14 ^{th} June, 2019
**

INSTRUCTIONS

- This paper consists of section
**A**and**B.**

- Answer
**all**questions in section A and any**four (4)**questions from section B.

**Mathematical**tables and**Geographical**instruments may be used whenever it is necessary.

- Whenever it is necessary use π = 3.14 and R= 6370 km

**SECTION A: (60 Marks)
**

**Answer all questions in this section
**

- (a) Use mathematical table to evaluate , give your answer to the

nearest whole number.

(b) Express 3.2121… in the form a/b where a and b are integers and b 0

- a) Evaluate 2

b) Solve for x if (9

^{-1})

c) Calculate the value of x in the equation (

^{½}^{ }

- (a) The universal set has n() = 23 and its two subsets A and B has n(A) = 17 and

n(B) = 8. If n(AB) = 3, determine n (A B)^{/}

(b) The Venn diagram below shows the Universal set

and its two subsets P and Q

- 7 3 0

2 8

3 9 4 10

**
**

P Q

List down the elements of

(i) P⋃Q (ii)

Q

(iii) P

Q

(iv) P

Q

- a) Find the equation of a straight line passing through (-4, 2) and which is perpendicular

to the line whose equation is x + 2y – 4 = 0

b) Given vectors V = 3i + j and U = 6i + 8j, evaluate

–⋃ (ii) ││ ││

- a) i) Prove that triangle is similar to triangle in the figure below.

**B** **D**

**C**

**E
**

**A
**

ii) If EC = 20cm, calculate the value of

b) Find the area of a regular polygon of sides, inscribed in a circle of radius 4cm

- a) A sales man bought goods from South Africa for 30, 000/= rands. When he

arrived in Tanzania he was charged a tax of How much Tanzania shillings did he pay as tax? (Assume that 1 South Africa rand 100 Tsh).

b) The variable varies directly as square of

*Y*and inversely as Find the value of when and, given that and when

- (a) Bakari sold a phone at a price of 400Tsh and made a profit of Determine the buying price of a phone.

(b) Find a simple interest on Tsh. 50, 000/= invested for 18 Months at the rate of 15% per annum.

- (a)If a sequence x, 5 , 1 – 4x is an Arithmetic sequence. Calculate the value of

(b) Find the first term and the common ratio of a geometric progression whose third term is and the 8

^{th}term is – 96.

- (a) Given that SinA

and CosB

where A is obtuse angle while B is acute angle. Find the value of Cos (A + B)

b) Find in the triangle below.

** A
**

^{0}

^{0}

B** C
**

- (a) Factorize the expression x
^{2}+ 5x + 6

b) Given the right angled triangle below. Calculate the length of hypotenuse side.

A

(2x + 1) cm

2x cm

**
**C (x – 1) cm B

**SECTION B (40MARKS)
**

**Answer any four (4) questions.
**

11. A factory needs to employ new workers. It employ skilled and unskilled workers. The conditions are; there cannot be more than workers. There are must be at least skilled workers. Each skilled worke is paid per day and each unskilled worker is paid per day. The total wages cannot be more than

- Write down inequalities in and for the above conditions.
- Illustrate these inequalities, shading out the unwanted region.

- Each skilled worker produces items per day and each unskilled worker produces items. Use the graph to find how many workers of each type should be hired to maximize production.

12. The table below shows the test scores of a certain class in mathematics at Juhudi Secondary School.

21 | 21 | 21 | 22 |

22 | 22 | 22 | 23 |

23 | 24 | 24 | 24 |

21 | 24 | 24 | 25 |

26 | 27 | 27 | 27 |

- Construct a frequency distribution table showing scores (X) and frequency (f)

- By using a frequency distribution table in (a) above, calculate

- Median score

- Mean score

- Mode score

- Draw the Histogram to present the data.

13. a) By using the figure below, show that = if O is the centre of the circle and

= ^{0}

** O
**

** X Y
**

** N
**

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b) If O is the centre of a circle, and and

Prove that =

**
**

** T N Q
**

** O
**

** K
**

c) Calculate the distance between (^{0}, ^{0}) and (^{0}, ^{0}). Give your answer in nautical miles (nm)

- Tabiseni traders started business on 1
^{st}April 2014 with capital in cash 3 263 000/=

April 2: purchases for cash 234 000/=

2: purchases goods for cash 1 400 000/=

3: bought furniture for cash 203 000/=

3: sold goods for cash 402 000/=

4: purchases shelves for cash 150 000/=

5:sold goods for cash 1 600 000/=

9:Paid wages for cash 32 000/=

20: paid rent for cash 72 000/=

21:cash sales 375 000/=

22:bought goods for cash 314 000/=

26:paid salaries for cash 52 000/=

29:paid electricity 41 000/=

Required

- Prepare cash account

- Prepare the trading and profit and loss account as at 31
^{st}2014

15. a) The matrix is singular. What is the value of k?

b) Given A = find:

i)

ii) Use your answer in (i) to solve equation

c) Find the image of the line y = – x under reflection in the

16. a) A card is chosen at random from a park of cards numbered

What is the probability that it is:

- Multiple of 3?

- Multiple of 8?

- Multiple of 3 and 8?

- Multiple of 3 or 8?

b) A function is defined as = x^{2} + 3

i) Find

ii) Write down the domain and range of

iii) Calculate the Axis of Symmetry of

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