1. (a) Three bells ring together at a certain starting point of time t, then they ring at intervals of 20, 25, and 50 minutes respectively. If they ring together at 9.05 a.m, when will they ring together again?
(b) if x=0.21 and (b) y=0.8 find the rational numbers of the following:
(i) x+y.
(ii) x.
y
2. (a) Solve for x: 25x+1+52x=130
(b) Solve: log x+y =0
2 log x = log y+1
3. (a) In a class of 20 pupils, the number of pupils who study English but not History is 6 times the number of pupils who study both English and History. 4 pupils study only History and only 2 study neither English nor History. How many pupils study History?
Use a Venn diagram
(b) A box contains 40 identical discs, some of them being white and the rest are blue. If a
disc is drawn at random. The probability that it is white is 4, then:
5
(i) How many blue discs are in the box?
(ii) After removing two white and three blue discs from the box, what is the probability of drawing a white disc?
4. (a) A line has an equation ax+ a−2 y+2a=0
(i) Re write the equation in the form of y=mx+c.
(ii) If the line passes through point 0,2 find the value of a
(b) Find the vector v whose magnitude is 5 and whose sum of the components in the i
and j direction is 7.
5. (a)Prove that the area A of an equilateral triangle inscribed in a circle with radius
r is A=
r2 . Use the result to find the area of an equilateral triangle inscribed in a
circle with diameter 4 cm.
(b) Given that XY∥BC , where AX:BX=3:5:
(i) Prove that ∆ AXY~∆ABC
(ii) Calculate segment BC, if segment XY=18 cm
6. (a) 60 people working 8 hours a day take 2 days to cultivate a maize farm. How long will it take 20 people to cultivate the same farm if they work 16 hours a day?.
(b) At the height of h m above the sea level, the distance, dm to the horizon is proportional to the square root of h. From the top of a 25 m mast, the horizon is 12 300 m away
(i) Find the equation connecting d and h
(ii) How far can you see from the top of a 49 m mast?
7. (a) The ratio of the number of girls to that of boys in a school is 7:12. If the number of boys is 120, find the following:
(i) The number of girls.
(ii) The total number of all students.
(b) On January 1 st 2015 MTL group started a business with capital in cash 2 000 000/= January 2: purchased goods on cash 1 400 000/=
January 9 : sold goods or cash 1 000 000/= January: 20 purchased goods for cash 60 000/= January : 21 paid rent for cash 220 000/= January :28 sold goods for cash 620 000/= Prepare the cash account and balance it.
8. (a) The first, third, and eleventh terms of arithmetic progression form the first three terms of geometric progression. It is further given that the sum of the first 13 terms of the arithmetic proregression is 390, find
(i) The first term and the common difference of the arithmetic progression.
(ii) The common ratio of the geometric progression.
(b) The difference between the fourth and the seventh terms of an increasing arithmetic progression is 12. Calculate the sum of the first 10 terms of arithmetic progression if the first term is 5.
9. (a) Lona walked 1 km up the side of the hill. If she climbed a vertical distance of 600 m, find the horizontal distance through which she travelled.
(b) If tan 165° =−2+ 3, find the value of tan 105°.
10. (a)A certain company devised a cost saving tool expressed as x2--y2. Data on cost saving among individual were collected and expressed as 9832−172. Use the cost saving tool to find how much the company saved on a bulk purchase discount?
(b) Leon wants to design a garden and needs to create a rectangular flower bed with dimensions that fit a specific area. The area of the bed can be modelled by the quadratic expression 3y2−11y + 10 m2. Determine the possible length and width of the flower garden.
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