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SECTION I (50 Marks)Answer all the questions in this section
Using logarithms correct to 4 decimal places, evaluate;-
Make Y the subject of the formula;-
By correcting each number to one significant figure, approximate the value of 788 x 0.006 hence calculate the percentage error arising from this approximation.
Find the equation of the line which passes through the point of intersection of lines y+2x=8 and 2y-x =6 and the point (4,3)
Without using a calculator or mathematical tables, simplify;-
In the figure below, R,T and S are points on a circle centre O. PQ is a tangent to the circle at T, PQR is a straight line and angle QPR=200
Find the size of angle RST
Given thatis a unit vector, find the value of q.
The points with co-ordinates (5,5) and (-3,-1) are the ends of a diameter of a circle centre A. Determine;-
a) The co-ordinates of A (1mk)
b) The equation of the circle expressing it in the form , where a, b and c are constants. (3mks)
The size of an interior angle of a regular polygon is times that of its exterior angle. Determine the number of sides of the polygon.
The table below is part of tax table for monthly income of a certain year;-
In this particular year, the tax on Nyongesa’s monthly income was Ksh.1,916. Calculate his monthly income. (3mks)
State the amplitude and the period of the function;-
Nanjala bought five exercise books and three geometrical sets for sh.725. If she had bought four similar exercise books and five geometrical sets, she would have paid sh.375 more. How much would she pay for two exercise books and six geometrical sets?
Expandand use your expansion to find the value of
Without using tables or calculators, simplify;-
An object of density 12kg/m3 is dropped into a cylindrical tank of diameter 3m. If the water level rises by 0.75m, calculate the mass of the metal.
The figure below shows a circle centre O and radius 10cm. The tangent to the circle at A meets OB at T. Given that the area of triangle OAT is 60cm2, calculate the area of the sector OAB.
SECTION II (50 Marks)Answer only FIVE questions in this section
a) A certain amount of money is deposited in a bank that pays simple interest at a certain rate. After 3 years, the total amount of money in the account is Sh.358, 400. The interest earned each year is sh.12 800. Calculate;-
i) The amount of money which was deposited (2mks)
ii) The annual rate of interest that the bank paid. (2mks)
b) A computer whose marked price is sh.40 000 is sold at sh. 56 000 on hire purchase terms.
i) Wafula bought the computer on hire purchase terms. He paid a deposit of 25% of the hire purchase price and cleared the balance by equal monthly instalments of sh.2 625. Calculate the number of instalments. (3mks)
ii) Had Wafula bought the computer on cash price terms, he would have been allowed a discount of 12 ½ % on marked price. Calculate the difference between the cash price and hire purchase price and express it as a percentage of the cash price. (3mks)
A garden measures 10m long and 8m wide. A path of uniform width is made all round the garden. The total area of the garden and path is 168m2.
a) Find the width of the path. (4mks)
b) The path is to be covered with square concrete slabs. Each corner of the path is covered with a slab whose side is equal to the width of the path. The rest of the path is covered with slabs of side 50cm. The cost of making each corner slab is sh.600 while the of making each smaller slab is sh.50. Calculate;-
i) The number of the smaller slabs used. (3mks)
ii) The total cost of the slabs used to cover the whole path. (3mks)
A piece of wire can be folded into a rectangle whose dimensions are such that its length is 3cm longer than the width. The area of the rectangle formed is 28cm2.
a) The dimension of the rectangle. (4mks)
b) Find the perimeter of the rectangle (2mks)
c) The wire can also be folded into a circle. Find the radius and hence the area of the circle. (4mks)
The product of the first three terms of a geometric progression is 64. If the first term is a and the common ratio is r;-
a) Express r in terms of a. (2mks)
b) Given that the sum of the three terms is 14;- i) Find the value of a and r; hence write down two possible sequences each up to the 4th term. (5mks)
ii) Find the product of the 50th terms of the two sequences. (2mks)
Towns A, B and C are such that AC= BC =90km. Angle ABC= 400. The bearing of C from B is 5200W. Calculate;-
a) The bearing of A from C (3mks)
b) The bearing of C from A. (3mks)
c) Distance AB (2mks)
d) The bearing A from B. (2mks)
A box contains 5 blue and 8 white balls all similar except for the colour. 3 balls are picked at random one after the other without replacement. Find the probability that;-
a) The three balls are white. (2mks)
b) At least two are blue. (4mks)
c) Two are white and one is blue. (4mks)
a) Complete the table below for the function
b) On the grid provided, draw the graph for the function;
c) Use your graph to solve:-
ii) 4x = x2 (3mks)
Triangle ABC with vertices A(1,1), B(2,3) and C(3,2) undergoes a rotation through +900 about the origin to produce A1 B1 C1 followed by a reflection in y= x to produce A11 B11 C11.
a) Obtain by construction or otherwise the co-ordinates of A1B1C1 and A11B11C11 (7mks)
b) Describe a single transformation that maps triangle ABC onto A11B11C11. (3mks)