FORM TWO POST MOCK KILIMANJARO MATHEMATICS EXAMINATION

1. (a) Describe how does mathematics relates with physics, chemistry and Agriculture.




(b) At KAWAWA village, the ratio of men, women and children living there is 6:7:3.If there are 4200 women, find how many;
(i) Children living in the village.


(ii) People altogether living in the village.


2. (a) A dealer sells mattresses whose cost price(c) is directly proportional
to the selling price (s).If the selling price and cost price of one

mattress are Tsh 20,000 and Tsh 18,000 respectively.
(i) Find the constant of proportionality


(ii) By using the answer obtained in part (a) (i) above; determine the equation that relates the cost price and the selling price.


(b) Mr Njoroge from Nakuru Kenya visited Tanzania. He had 5000 Kenya shillings (Kshs) and wanted to change the money into US dollar. If 1US dollar was equivalent to 2500 Tanzanian shillings(Tshs) and 1Kshs was equivalent to 20Tshs, how much US dollar did he get?



3. (a) SHABIBY LUXUARY COACH travels 2 of the total distance to its
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destination at a speed of 30km/h and then travels the remaining distance at a speed of 40km/h. If the bus took 4 hours for the whole journey, what is the total distance of the journey? Express your answer as a repeating decimal.


(b) (i) In an experiment for determining the values of pi (π),the following values were obtained; 3.142, 3.1578, 3.099867, 3.14103 and 3.15009. Calculate an average value of pi (π) correct to 3 significant figures.



(ii) Estimate the value of 3.485×√35.82
351.25

correct to 1 decimal place.


4. (a) From the rectangle JKLM given below.
(i) Name the two triangles which are congruent.


(ii) Prove your answer in part (i) above



(b) Given the following diagram,𝐾𝐿// 𝑀𝑁, 𝐵𝐾 = 15cm, 𝐾𝐿 = 12cm, 𝑀𝑁 = 30 cm

Find the value of y






5. (a) (i) The distance of the Earth from the sun is approximately 1494000000000 kilometres.Write this distance in form of 𝐴 × 10𝑛, where 1≤ A< 10 and state the value of A and n.





(ii) Evaluate the expression 4848×10−5 giving your answer in standard notation.
20×10


(b) Show that log10(0.01 × 100000) = 3

6. (a) Solve for 𝑥 and 𝑦 using the equation.
53𝑥−4 × 33𝑦 = 675.



(b) The area of a rectangular Manila sheet is (4+2√3 )𝑚2.If one side of the manila sheet is (3+2√3 )m, find the length of the other side leave your answer in surd form.


7. (a) In a certain situation,a company uses a special calculation formula defined by 𝑈∆𝑉 = √𝑈𝑉 to determine the production efficiency of a company.
𝑉
Find the value of 9∆4.


(b) A local farmer wants to calculate the exact difference in the area between two fields, one measuring 10082 square metres and the other measuring 9922 square metres.Find the difference between the areas of the two fields.


8. (a) If A and B are two sets such that n(A∩B) = 4, n(A∪B) = 6 and n(A) = 4.
(i) How many elements are there in B?


(ii) Between A and B, which set is a subset of the other?



(b) There are 24 men at a meeting, 12 are farmers, 18 are soldiers and 8 are both farmers and soldiers, by using a Venn diagram find;
(i) How many men are either farmers or soldiers?



(ii) How many men are neither farmers nor soldiers?



9. (a) A straight line has a gradient of 3 and passes through the point (−1,2).
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Find;
(i) Its equation in the form of 𝑦 = 𝑚𝑥 + 𝑐




(ii) The 𝑥 and 𝑦-intercepts