FORM FOUR POST MOCK KILIMANJARO BASIC MATHEMATICS EXAMINATION

SECTION A (60 Marks)
1. (a). (i) Equal squares as large as possible are drawn on a rectangular board measuring 54 cm by 80 cm
Find the size of the square.
(ii) Evaluate 284243÷ 26 to 2 significant figures
(b). A radio is sold at Tsh, 40,500/= . This price includes 20% Value Added Tax (V.A.T.) Calculate the amount of V.A. T

2. (a). Solve for x if 4x – 6(2x ) + 8 = 0
(b). (i) Given that log2 = 0.30103, log3 = 0.47712 and log 5 = 0.69897 Find the value of log 90
(ii) Determine the value of x if log3 x + log3 x + log3 (x+1) = log3 12

3 . (a). In a group of 29 tourists from different countries, 17 went to Manyara National Park, 13 went to Mikumi National Park and 8 went to neither Mikumi nor Manyara National Park.
How many tourists went to both places?
(b) In a class of 40 students 24 take chemistry and 8 take Biology Find the Probability that a student selected at random will either chemistry or Biology.

4. (a). If a = (4,3), b = (-4 ,1) and c = (2,5), determine which of the vectors a +2b and 3a + c is longer than the other.
(b). If a line passing through the point (4,2) is perpendicular to another line whose equation is 2x +3y+14, find the equation of the line.

5. (a) The perimeter of a regular hexagon inscribed in a circle is 72cm . Find the radius of the circle.
(b) Tringle ABC is an isosceles triangle in which AB and AC are equal . If D is the mid-point of BC, Prove that ABD ACD

6 . (a) John walks 48 km every day. Find in metres , the distance he walks in 2 days.
(b) . The surface area of a circular object varies directly as the square of its radius. If its surface area is 78.5cm2 , when the radius is 5cm , find the surface area of the circular object when the radius is 7cm .

7. (a) A damaged chair that costs Tshs 20,000 was sold at a loss of 15%. Find the loss made and the selling price .
(b) The following list represents the assets and liabilities of Mwajuma’s business as on 31st December 2018:
Creditors Tsh 100,000 Bank overdraft Tsh 50,000 Stock Tsh 85,000
Premises Tsh 250,000
Debtors Tsh 150,000 Cash in hand Tsh 15,000 Furniture Tsh 42,000
Capital Tsh 392,000
Use this information to find
i. Total Current assets
ii. Total current liabilities
iii. Working capital
8. (a) . If the nth term of A.P is Given by 12- 4n Find (i).The first term
(ii).The common difference

(b) . The second, fifth and eleventh terms of an A.P are in G.P, and the seventh tern of A.P is 4.
Find (i) Common difference of A.P
(ii). Common ratio of G.P
9.(a).(i) Verify that sin 900 = 2 sin 45o cos 45o
(ii) Without using tables or Calculator , find the value of cos 1050

(b) An electric pole casts a shadow 5.5m long . If the angle of elevation of the sun is 550 , find the height of the pole.

10 (a) Find two consecutives even numbers whose product is 80
(b) Solve x2 +5x-14 =0 by completing the square

SECTION B (40 Marks)
Answer all questions in this section
11. (a). In a competition , 30 children had to pick up as many paper clips as possible in one minute. The results were as follows:
3, 17, 8,11,26,23,18,28,33,38,12,38,22,50,5,35,39,30,31,43,27,34,9,25,39,14,27,16,39,49.
Construct a frequency distribution table using intervals 1-10, 11-20, 21-30 and so on . Hence, determine the mode
(b) . Prove that the exterior angle of a Cyclic quadrilateral is equal to interior opposite angle when extended.

12. (a) Define the following terms.
(i) Nautical mile. ( ii) Knots.

(b) . (i) P and Q are two points on latitude 50°.The distance between P and Q measure along the parallel of latitude is 1429 km, find the difference between the longitude.

13. (a) Find the values of x, y, z, and w in the following matrix equation. =
(b). Find the image of the point (3,4) after a reflection in the line y = x
(c). A translation takes the point (3,2) to (-4, -5) . Find where it takes the point (5,5).
14. (a) If f (x) is defined as follows; f ( x) = -2 if x ≤ 0
{ 0 if x = 0
2 if x ≥ 0

i. Find f (-8)
ii. Find f (7)
iii. Find the domain and range of f(x)
(b) A technical school is planning to buy two types of machines. A lather machine needs 3m2 of floor space and a drill machine requires 2m2 of floor space. The total space available is 30m2.The cost of one lather machine is 250,000 shillings, a drill machine costs 300,000 shillings, and the school can spend no more than 3,000,000 shillings. Find the greatest number of machines the school can buy.