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KCSE 2018 Mathematics Paper 1 Video Questions and Answers
Given that $6^{2n-3}=7776$, find the value of n.
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1.
Without using a calculator, evaluate: $\frac{2\frac{1}{3}-1\frac{1}{5}\,of\,2}{\frac{1}{4}-\bigl(\begin{smallmatrix} -\frac{1}{2} \end{smallmatrix}\bigr)^{3}} $
2.
Given that $6^{2n-3}=7776$, find the value of n.
3.
The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid.
4.
In the figure below ABCDEF is a uniform cross section of a solid. Given that FG is one of the visible edges of the solid, complete the sketch showing the hidden edges with broken lines.
5.
The lengths of three wires were 30 m, 36 m and 84 m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained.
6.
A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number.
7.
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle. (2 marks) (b)The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. (2 marks)
8.
Given that OA =$\binom{2}{3}$ and OB = $\binom{-4}{5}$. Find the midpoint M of AB
9.
Two towns R and S are 245 km apart. A bus travelling at an average speed of 60 km/h left town R for town S at 8.00 a.m. A truck left town S for town R at 9.00 a.m and met with the bus c 11.00 a.m. Determine the average speed of the truck.
10.
In the parallelogram WXYZ below, WX = 10 cm, XY = 5 cm and WXY = 150
o
. Calculate the area of the parallelogram. (3 marks)
11.
Without using mathematical tables or a calculator, evaluate $\frac{sin\,30^{0}-sin\,60^{0}}{tan\,60^{0}}$
12.
Use matrix method to solve: 5x + 3y = 35, 3x — 4y =-8 (3 marks)
13.
Expand and simplify. (2x + 1)
2
+ (x - 1) (x - 3). (2 marks)
14.
Use mathematical tables to find the reciprocal of 0.0247, hence evaluate $\frac{\sqrt[3]{3.025}}{0.0247}$ Correct to 2 decimal places. (3 marks)
15.
A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. (3 marks)
16.
A photograph print measuring 24cm by 15 cm is enclosed in a frame .A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space is 270cm
2
, find the value of x. (3 marks)
17.
A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively. (a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (4 marks) (b) Find the capacity of the tank, in litres, correct to the nearest litre. (3 marks) (c) On a certain day, the tank was filled with water.
18.
Two vertices of a triangle ABC are A (3,6) and B (7,12). (a) Find the equation of line AB. (3 marks) (b) Find the equation of the perpendicular bisector of line AB. (4 marks) (c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the co-ordinates of C. (3 marks)
19.
The distance covered by a moving particle through point O is given by the equation, s = t
3
- 15t
2
+ 63t — 10. Find: (a) Distance covered when t= 2; (2 marks) (b) The distance covered during the 3
rd
second ;( 3 marks) (c) The time when the particle is momentarily At rest ;( 3 marks) (d) The acceleration when t =5. (2 marks)
20.
The diagram below shows triangle ABC with vertices A (-1, -3), B (1, -1) and C (0, 0), and line M.
21.
The figure below shows two triangles, ABC and BCD with a common base BC = 3.4 cm. AC = 7.2 cm, CD = 7.5 cm and ABC = 90
o
. The area of triangle ABC = Area of triangle ?BCD.
22.
(a) On the grid provided, draw the graph of $y=4-\frac{1}{4}x^{2}$ for -4 $\le\,x\le4$(2 marks)
23.
Three business partners Abila, Bwire and Chirchir contributed Ksh 120 000, Ksh 180 000 and Ksh 240 000 respectively, to boost their business.They agreed to put 20% of the profit accrued back into the business and to use 35% of the profits for running the business (official operations).
24.
The equation of a curve is given as $y=\frac{1}{3}x^{2}-4x+5$ Determine: (a) The value of y when x = 3; (2 marks) (b) The gradient of the curve at x = 3; (3 marks) (c) The turning points of the curve and their nature. (5 marks)
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