PROSHABO ONLINE SCHOOL

BASIC MATHEMATICS EXAMINATION

FORM 1 – SERIES 1

TIME: 2:30 HRS                                                                                                                                                             25 October 2020

INSTRUCTIONS:

1. This paper consists of two (2) compulsory questions.
2. Show clearly all the working and answers.
3. All writing must be in blue or black ink except drawings which must be in pencil.
4. Geometric instruments and graph papers may be used where necessary.
5. All communication devices, calculators, and any unauthorized materials are not allowed in the examination room.
6. Write your PROSHABO Examination Number at the top right-hand corner of every page

SECTION A (100 Marks)

(Answer all question in this section)

1. (a) Define the following terms:

(i). number

(ii). Natural number

(iii). Rational numbers

(iv). Integers 

(b) Write the following numbers in words

i). 3,003,003,003

(ii). 10,010,010

(c) Approximate 0.00065703 to:

(i) One decimal place)

(ii) One significant figure

(iii) Four decimal places

(iv) Four significant figures

(d) Evaluate the following expressions:

(i)

(ii)

(e) The L.C.M and G.C.F of the four numbers are 21600 and 6 respectively. If the three numbers are 96, 108, and 120. find the fourth number.

(f) Express the following repeating decimals as a ratio of two integers (Make sure you simplify your answer to the end).

(i)

(ii)

(g). If the ratio of two numbers that differs by 12 is 8:9. Find the product of these numbers.

(h). A black smith has two types of gold alloys. The first contains 90% of gold and the second type contains 40% of gold. He wants to make 500g of 80% of gold alloy; how much of each alloy must he use?

(i). Find x and y such that:

(j). Find the smallest number which when divided by 77 or 101 or 305 leave a remainder of 5 in each case.

(l). A rectangular tank of base 2.4m by 2.8m and height of 3m contains 3,600 litres of water initially. Water flows into the tank at the rate of 0.5 litres per second. Calculate the time in hours and minutes required to fill the tank.

(m). A manufacture sells a bottle of fruit juice to a trader at a profit of 40%. The trader sells it for sh.84 at a profit of 20%. Find:
(i) The traders buying price.
(ii). The cost of manufacture of one bottle.

(n). A man spent 1/9 of his salary on food and 1/4 of the remainder on electricity and water bills. After that he spent Tsh.2000 on drinks, he saved Tsh.5350. Calculate his total monthly earning.

2. (a) Divide the following and give your answer in meter (23 km 74 dam 80 dm) ÷ 6

(b). The distance between the market and the church is 100km. Anna can walk at the speed of 10km/h while Justine can walk at the speed of 15km/h. One day Justine and Anna started walking together from church to the market, due to his high speed, John was the first one to arrive at the market. Then he discovered that he forgot to give Anna her phone, so he returns back and he met Anna on the way. Find the distance from the market where Justine and Anna met each other. (NOTE: assume John and Anna maintains their speed and they never stop walking).

(c) Find the equation of the line passing through the points A (3,1) and (3, 7). Then represent this line graphically.

(d) Find the coordinates of the points at which a line passing through points (-2, 7) and (2.3, 4.5) cuts the coordinate axes.

(e) In the figure below, m<RTS = 80⁰ and TP bisects <QPS, TP = PS. Find degree measure of angle m<PSR (i.e. x) and m<PRS (i.e. y).

(f). The cost of cultivating one hectare of land (100m x 100m) using a tractor is Tsh 50,000. Flora farm is 90 wide and 110 m long. If the tractor drivers charge her Tsh 50,000 is it fair to her? What is the exact cost of cultivating her farm?

(g). The profit on an item costing Tsh 8,000 is decreased by Tsh 480 when its sales price is reduced by 5%. Find the sales price and the percentage profit before reduction.

(h). In a class of 50 students, five times the number of girls exceeds twice the number of boys by five. Find the number of girls in the class.

(i). Solve the inequality |5a – 14 – 3a x 15 + 7| > 10, and then represent your answers on the number line. 

(j). Find the area of the triangle ABC if the equation of the line AB is

(k). Asha deposited 1,500,000 in the bank which gives a simple interest of 12% per year. After 3 years she withdrew all the money from her account and spent 70% of it, then she deposited again the remaining balance at the same bank for 7 years. After that period she withdrew all the money in her bank account and gave it to her mother. How much did Asha give her mother? 

(l). Find the number of sides of a regular polygon whose interior angle is 179.9⁰.

(m). The area of the shaded region is 1512 cm². Find the radius of the circle and its area.