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The velocity, v m/s of a particle after t seconds is given by v = t2 – 2t + 4.
a)i) Using the mid- coordinate rule with six strips, estimate the distance covered by the particle between t = 1 and t =13 seconds.
ii) Find the exact distance the particle covered between t =1 and t = 13 seconds.
b)Calculate the percentage error arising from the estimate in (a) above.
Date posted:
October 12, 2019
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Point R divides line PQ externally in the ratio 4:3. The position vectors of P and Q are 2i + j – 3k and i – 2j + k respectively. Find the position vector, of R.
Date posted:
October 12, 2019
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The probability of a team losing a game is 1/5. The team plays the game until it wins. Find the probability that the team wins in the fourth round.
Date posted:
October 12, 2019
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The figure below represents a hollow cylinder. The internal and external radii are estimated to be 6cm and 8cm respectively, to the nearest whole number. The height of the cylinder is exactly 14cm.
a)Determine the exact values for the internal and external radii which will give maximum volume of the material.
b)Calculate the maximum possible volume of the material
Date posted:
October 12, 2019
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The current price of a vehicle is ksh. 500,000. The value of the vehicle depreciates at a rate of 15% p.a for the first two years and at 20% p.a thereafter. Find the number of years it will take for its value to reduce to ksh. 147,968.
Date posted:
October 12, 2019
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The figure below shows a triangular prism ABCDEF
a)Draw the net of the prism
b)A fly walks from A to D along the diagonals of rectangular faces:
i)On your net show the locus of the fly.
ii)Measure the distance covered by the fly, one way.
iii)The fly takes 15 seconds to reach D one way. Calculate its’ speed in, km/h.
Date posted:
October 12, 2019
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A bus left Mombasa at 7.45 am towards Nairobi at an average speed of 60km/h. A saloon car left Mombasa at 9.15 am on the same day along the same road at an average of 120km/h. the distance between Mombasa and Nairobi is 360km.
a)Determine the time of day when the salon car overtook the bus.
b)Both vehicles contained towards Nairobi at their original speed. How long had the saloon car waited in Nairobi before the bus arrived.
Date posted:
October 12, 2019
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Water and alcohol are mixed in the ratio 1:4. If the density of water and alcohol are 1g/cm3 and 0.8g/cm3 respectively. Find the density of the mixture.
Date posted:
October 11, 2019
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Two fair dice one a regular tetrahedron (4 faces) and the other a cube are thrown. The scores are added together. show all possible outcomes.
a)Find the probability that:
i) The sum is 6.
ii) The sum is an odd number.
iii)The sum is 6 or 9.
b)If a player wins a game by throwing a sum of 6 or 9, draw a tree diagram and use it to find
probability that he wins at least once when the dice are thrown twice
Date posted:
October 9, 2019
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The above diagram represents a wooden prism. ABCD is a rectangle. Points E and F are directly below C and B respectively. M is the midpoint of CD. AB = 8cm, BC = 10cm and CE = 4.5cm.
a)The size of angle CDE.
b) Calculate:
i) Length of AC.
ii) The angle CAE makes with the plane ADEF.
c) Find the:
i) Length of MB.
ii) Angle CBM.
Date posted:
October 9, 2019
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Make P the subject of the formula XYP = QPX
Date posted:
October 9, 2019
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A straight line passes through points (8, -2) and (4, -4)
a)Write its equation in the form ax + by + c = 0 where a, b and c are integers.
b)If the line in (a) above cuts the x axis at point P, determine the coordinates of P.
c)Another line which is perpendicular to the line in (a) above passes through point P and cuts the
Y axis at the point Q. Determine the co-ordinates of point Q.
d)Find the length of QP.
Date posted:
October 9, 2019
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A passenger noticed that he had forgotten his bag in a bus 12 minutes after the bus had left. To catch up with the bus, he immediately took a taxi which travelled 95km/h. The bus maintained an average speed of 75km/h.
Determine:
a)The distance covered by the bus in 12 minutes.
b)The distance covered by the taxi to catch up with the bus.
Date posted:
October 9, 2019
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A seven sided figure has three of its angles equal to x and the other angles are (2x - 30), (x + 28), 3(x - 4) and (126 -x). Find the value of x.
Date posted:
October 9, 2019
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Given that Cos A = 5/13 and Angle A is acute, find the value of 2tan A + 3 Sin A.
Date posted:
October 9, 2019
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A point (-3, 2) is the image of a point (7,4) after a reflection. Find the mirror line.
Date posted:
October 9, 2019
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In the figure below AB is parallel to DE. Find the value of x and y.
Date posted:
October 9, 2019
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a) Complete the table below, for the function y =2x2 + 4x - 3.
b) On the grid provided, draw the graph of y=2x2 + 4x - 3 for -4<= x<= 2 and use the graph to estimate the roots of the equation to 1 decimal place.
c) In order to solve graphically 2x2 + x – 5 = 0, a straight line must be drawn to intersect the curve y = 2x2 + 4x – 3. Determine the equation of the straight line and draw it, hence obtain the roots of the equation 2x2 + x - 5 = 0 to 1 decimal place.
Date posted:
October 8, 2019
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A youth group decided to raise Kshs. 480,000 to buy a piece of land costing Kshs. 80,000 per hectare. Before the actual payment was made, four of the members pulled out and each of those remaining had to pay an additional Kshs. 20,000.
a)If the original number of the group members was x write down
i)An expression of how much each was to contribute originally
ii)An expression of how much the remaining members were to contribute after four pulled out.
b)Determine the number of members who actually contributed towards the purchase of the land
c)Calculate the ratio of the supposed original contribution to the new contribution
d)If the land was sub-divided equally , find the size of land each member got
Date posted:
October 7, 2019
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Samatha and Meshi entered into a business partnership in which they contributed Kshs. 120,000 and Kshs. 150,000 every year respectively. After one year Fuki joined the business and contributed Kshs. 90,000
a)Calculate the ratio of their investment after 3 years of business
b)It was agreed that 30% of the profits after 3 years be used to cater for the cost of running the business, while the remaining would be shared proportionally. Calculate each persons share if the profit made after three years was Kshs, 187,000.
c)If each of them invested their shares in the business, find their new individual investments at the beginning of the fourth year.
Date posted:
October 7, 2019
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Mrs. Wekesa paid Kshs. 12500 for a wrist watch after the shopkeeper gave her a discount of 2%. If the shopkeeper made a profit of 20% calculate the price the shopkeeper bought from the manufacturer.
Date posted:
October 7, 2019
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Solve for x in
(4/9)x x (8)1-x = 486
Date posted:
October 7, 2019
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Use the exchange rates below to answer this question
Buying selling
1 US dollar 63.00 63.20
1 UK£ 125.30 125.95
A tourist arriving in Kenya from Britain had 9600 UK sterling pounds (£). He converted the pounds to Kenya shillings at a commission of 5%. While in Kenya he spent ¾ of this money. He changed the balance to US dollars after his stay. If he was not charged any commission for this last transaction, calculate to the nearest US dollars the amount he received.
Date posted:
October 7, 2019
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The scale of a map is given as 1:50,000
Find the actual area in hectares of a region represented by a triangle of sides 6cm by 7cm by 8cm (give your answer to the nearest whole number).
Date posted:
October 7, 2019
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3 pens and 5 exercise books cost Shs. 111. 4 pens and 3 exercise books cost Kshs 18 less.
Determine the cost of each item
Date posted:
October 7, 2019
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Evaluate 5 ½ -1 1/7 (1 1/5 + 9/10 ) + 1/3 of(2/3 ÷5/6)
Date posted:
October 7, 2019
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Complete the table below for y=2 sin x and y= cos ½ x
Date posted:
September 30, 2019
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A group of people planned to contribute sh.2000 000 to start a business. However before the contributions were made the group disintegrated and 40 members pulled out. A a result each of the remaining members were to contribute sh. 2500 more/
(a) Find the original number of members in the group.
(b) After each member contributing half of the expected amount the members opted to get a bank
That would offset ¼ of the remaining amount. How much would each member contribute after
he bank loan.
(c) Twenty new members joined the group just before the business started. As a result the old
Members were to be refunded some money. How much was the refund?
Date posted:
September 30, 2019
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Hellen’s earnings are as follows:
Basic salary sh. 38000 per month
House allowance sh. 14000 per months
Travelling allowance sh.8500 per month and
Medical allowance Ksh.3300 per month.
She is given a personal relief of Ksh. 12672
The table for payable tax is shown below
Income in K£ p.a Payable tax rate in Kshs per K£
0-6000 2
6001-12000 3
12001-18000 4
18001 -24000 5
24001-30000 6
30001-36000 7
36001-42000 8
42001-48000 9
Over 48000 10
Calculate
(a) (i) Hellen’s taxable income in K£ p.a
(ii) Her P.A.Y.E
(b) Hellen is deducted the following items per month
NHIF Ksh.320
Cooperative shares Ksh.2000
Loan repayment Ksh5000
Determine her net salary per month
Date posted:
September 30, 2019
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Position vectors A and B are 3i+2j+k and –i+3j+4k respectively. Determine the magnitude of AB.
Date posted:
September 30, 2019