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KCSE 2019 Mathematics Paper 2 Questions and Answers
Determine the amplitude and the period of the function y = 3 sin (2x + 40
o
)
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1.
Simplify #(sqrt5 + 3)/(sqrt5 - 2)#.Give the answer in the form #a + b\sqrt c# where a, b and c are integers.
2.
Two types of flour, X and Y, cost Ksh 60 and Ksh 72 per kilogram respectively. The two types are mixed such that the cost of a kilogram of the mixture is Ksh 70
3.
A quantity P varies inversely as the square of another quantity L. When P = 0.625, L = 4. Determine P when L = 0.2.
4.
An arc of a circle subtends an angle of 150
o
at the circumference of the circle. Calculate the angle subtended by the same arc at the center of the circle
5.
Solve the equations: x + 3y = 13 , x
2
+ 3y
2
= 43
6.
A bag contains 6 red counters and 4 blue counters. Two counters are picked from the bag at random, without replacement.
7.
Find the coordinates of the turning point of the curve y = x
2
- 14x + 10
8.
OAB is a sector of a circle of radius r cm. Angle #AOB = 60^o#. Find, in its simplest form, an expression in terms of r and #pi# for the perimeter of the sector.
9.
In a mathematics test, the scores obtained by 30 students were recorded as shown in the table below
10.
Determine the amplitude and the period of the function y = 3 sin (2x + 40
o
)
11.
The figure ABCDEFGH represents a box. The top lid of the box is opened such that the height OT is 35 cm. Calculate the: (a) Angle the top lid makes with the plane FGHE; (b) Length BE, correct to 2 decimal places.
12.
The table below shows income tax rates in a certain year. In that year, Mawira earned a salary of Ksh 41 000 per month. Calculate Mawira's income tax per month given that a monthly tax relief of Ksh 1162 was allowed.
13.
The position vectors of points A, B and C are$AO =\binom{-3}{4}\,OB = \binom{1}{2}\,and \,OC=\binom{7}{-1}$. Show that A, B and C are collinear.
14.
The vertices of a triangle PQR are P (-3, 2), Q (0, -1) and R (2, -1). A transformation matrix M maps triangle PQR onto triangle P'Q'R' whose vertices are P'(-7, 2), Q' (2, -1) and R’ (4, -1). Find M-1 , the transformation that maps P'Q'R' onto PQR.
15.
Solve for x in Log (7x - 3) +2 log 5 = 2 + log(x + 3)
16.
The length of a shadow of a mast was measured at intervals of 1 hour and recorded as shown in the table below. (a) On the grid provided, draw the graph of length against time. (b) Determine the rate of change of the shadow length at t= 2.
17.
The first term of an Arithmetic Progression (AP) is equal to the first term of a Geometric progression (GP). The second term of the AP is equal to the fourth term of the GP while the tenth term of the AP is equal to the seventh term of the GP.
18.
Mbaka bought some plots at Ksh 400 000 each. The value of each plot appreciated at the rate of 10% per annum. a. Calculate the value of a plot after 2 years. (2 marks) b. After some time t, the value of a plot was Ksh 558 400. Find t, to the nearest month. (4 marks)...
19.
The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80 m
20.
A ship left point P(10
o
S, 40
o
E) and sailed due East for 90 hours at an average speed of 24 knots to a point R. (Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
21.
A workshop makes cupboards and tables using two artisans A and B. Every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B
22.
The amount of money contributed by a group of students during a fundraising for a needy student was as shown in the table below
23.
In the figure below, OA = a, OB = b and BX meets OY at C. OX:OA = 1:2 and BY:YA = 1:3
24.
A trapezium PQRS with vertices P (2, 2), Q (6, 2). R (6, 4) and S (2, 8) is mapped onto P'Q'R'S by a transformation matrix m = $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix} $
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