🌊PAPER 17-Qns

 

MARKAZ ISLAMIC SEMINARY

FORM THREE MID-TERM TEST

041-BASIC MATHEMATICS

April, 2024-Time: 3:00

INSTRUCTIONS

1. This paper consists of sections A and B with a total of fourteen (14)questions.

2. Answer all questions.

3. Each question in section A carries six (6) marks while each question in

4. section B carries ten (10) marks.

5. All necessary working and answers for each question must be shown clearly.

6. NECTA mathematical tables and non-programmable calculators may be used.

7. All communication devices and any unauthorized materials are not allowed in the examination room.

8. Write your Full name on every page of your answer sheet.

SECTION A (60% Marks)

1. (a) Given that 𝑝𝑝 = 0.13̇ 𝑎nd 𝑞𝑞^̇ = 1. 5̇3, calculate the value of p × q

   2. Square tiles are used to build the floor 910cm long and 780cm wide. find the greatest size of each tile .

2. (a) Solve for x and y,

   2. Rationalize the denominator

   3. Calculate log₃ 2187 − log₂ 64

3. (a) There are 100 people at the party , 56 are eating goat meat,52 are eating chicken meat and 10 are eating both meat

1. How many people are eating either goat or chicken meat?

2. How many people are eating neither goat nor chicken meat?

2. Given P = {Prime numbers less than 12} and

Q = {Odd numbers less than 13}

Find n(𝑃𝑃∪𝑄𝑄) −𝑎𝑎(𝑃𝑃∩𝑄𝑄)

4. (a) Find the equation of the line at x- intercept -2 and y – intercept 3 (b) Calculate the slope, y - intercept and x – intercept of 12𝑥𝑥− 5𝑦𝑦− 15 = 0

5. (b) The interior angle of a regular polygon is 1 times the exterior angle.

Find the number of sides of the polygon

2. What is the area of a square whose one diagonal is 84cm long,

6. (a) The power (P) used in an electric circuit is directly proportional to the square of current (I) . When the current is 8 Ampere, the power used is 640 Watts

1. Write down the equation relating the power (P) and the current (I)

2. Calculate the current when the circuit uses 360 watts (b) Shumayra planted trees on both sides of the road to her house. the road km long and the trees are 2.5m apart . How many trees are there?

7. (a) A man and a woman share a prize of Tsh 8,000,000,000 between them the ratio 1:3. The woman shares her part between herself, her mother and her son in the ratio 2:1:2. How much does she receive?

2. Answer the questions that follows after the balances sheet below

BALANCE SHEET AS AT 31st DECEMBER 2009

Liability	Amount	Assets	Amount
Capital	330,000	Equipment	60,000
Creditors	100,000	Furniture	90,000
Bank Overdraft	60,000	Premises	30.000
		Machines	70,000
		Stock	100,000
		Debtors	40,000
		Cash in bank	60,000
		Cash in hand	40,000
	490,000		490,000

Calculate;

i. Working capital

ii. Current ratio

8. (a) A small business sells products worth Tsh 1,000,000 during its first year. The owner of the business has set a goal of increasing annual sales by Tsh 750,000 each year. Find the his total salary during the ten years of the operation

   2. Find the compound interest on sh 1000000 invested for 3 years at 7 % semi annually.

9. (a) An eagle on a tree 20m high views a chick with an angle of depression of 23⁰ .Calculate the distance from the chick to the foot of the tree

   2. In the figure below 𝐴𝐴𝐴𝐴 = 13 𝑐𝑐𝑐𝑐, 𝐴𝐴𝑃𝑃 = 5 𝑐𝑐𝑐𝑐 𝑎𝑎𝑎𝑎𝑎𝑎 𝐴𝐴𝐴𝐴 = 15 𝑐𝑐𝑐𝑐

Calculate the lengths of 𝐴𝐴𝑃𝑃 𝑎𝑎𝑎𝑎𝑎𝑎 𝐴𝐴𝑃𝑃

10. (a) Solve for x , 3𝑥𝑥²− 2𝑥𝑥− 1 = 0

    2. A rectangle has length 8cm and width 6cm, what length added to the shorter side and reduced to the longer side to make a result of an area of 45cm²

SECTION B (40% Marks)

11. The table shows the ages in tears of 48 people who attended a conference

Age in years	30 – 39	40 - 49	50 – 59	60 -69	70 -79	80 -89	90 - 99
Number of people	2	9	11	8	12	6	2

1. Find the mean by using assumed mean method

2. State the modal class and find mode

3. Find the median class and median

11. (a) A figure below shows a rectangular prism in which 𝑀𝑀𝑀𝑀 = 12 𝑐𝑐𝑐𝑐

NP = 5 cm and PT = 8 cm.

Calculate

1. The length 𝑀𝑀𝑀𝑀

2. The volume and surface area.

2. Work out the volume of a sphere whose radius is 21cm

11. (a) A translation takes the point (3,2) to (-4,5). Find where it takes (-2,-7)

    2. Find the image of; the line P(3,-4) under reflection in the y -axis,

11. The cost of 3 cups of coffee and 2 queen cakes is Tsh 60 while the cost of two cups of coffee and a queen cake is Tsh 35. By graphically method , find the cost of a cup of coffee and a queen cake.

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