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KCSE 2019 Mathematics Paper 1 Video Questions and Answers
Given that
sin
2
x
=
cos
(
3
x
-
10
o
)
, find tan x, correct to 4 significant figures.
(1m 55s)
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1.
Without using a mathematical table or a calculator evaluate
5.4
0.025
X
3.6
2.
Express 1728 and 2025 in terms of their prime factor hence evaluate
3
√
1728
√
2025
3.
Juma left his home at 8.30 am. He drove a distance of 140km and arrived at his aunts home at 10.15 am. Determine the average speed in km/h for juma`s journey.
4.
Expand and simplify 4(q + 6) +7(q-3)
5.
In the trapezium PQRS shown below, PQ=8cm and SR = 6cm. If the area of the trapezium is
28
c
m
2
, find the perpendicular distance between PQ and SR
6.
Three villages A,B and C are such that B is 53km on a bearing of 295 from A east of B
7.
A retailer bought a bag of tea leaves, if the retailer were to repack the tea leaves into smaller packets of 40 g, 250g or 350g..
8.
Given that
sin
2
x
=
cos
(
3
x
-
10
o
)
, find tan x, correct to 4 significant figures.
9.
A tourist converted 5820 US dollars into Kenya shillings at the rate of ksh 102.10 per dollar. While in Kenya, he spent ksh450000 and converted the balance into dollars at the rate of ksh 103.00 per dollar. Calculate the amount of money to the nearest dollar that remained.
10.
Given that
(
2
4
)
and
(
3
2
)
and a = 3c - 2b, find the magnitude of a, correct to 2 decimal places.
11.
Using a ruler and pair of compasses only, construct a rhombus PQRS such that PQ = 6 cm and
∠
S
P
Q
=
75
o
. Measure the length of PR.
12.
Solve the inequality
2
x
-
1
≤
3
x
+
4
<
7
-
x
13.
Given that A=
(
2
3
4
4
)
, B=
(
x
1
2
3
)
and that AB is a singular matrix, find the value of x
14.
A trader bought two types of bulbs A and B at Ksh 60 and Ksh 56 respectively. She bought a total of 50 bulbs of both types at a total of Ksh 2872. Determine the number of type A bulbs that she bought.
15.
A bus plies between two towns P and R via town Q daily. On each day it departs from P at 8.15 a.m. and stops for 40 minutes at Q before proceeding to R. On a certain day, the bus took 5 hours 40 minutes to travel from P to Q and 3 hours 15 minutes to travel from Q to R. Find, in 24 hour clock system
16.
A rectangular water tank measures 2.4 m long, 2m wide and 1.5 m high. The tank contained some water up to a height of 0.45 m. (a) Calculate the amount of water, in litres, needed to fill up the tank. (3 marks) (b). An inlet pipe was opened and water let to flow into the tank at a rate of 10 litres..
17.
a. A line L1 passes through the points (3,3) and (5,7), Find the equation of L1 in the form y = mx + c, where m and C are constants. (3 marks) b. Another line L2 is perpendicular to L1 and passes through -2 3. in i. the equation of L2 (3 marks) ii. the x-intercept of L2 (1 mark)
18.
A triangle ABC with vertices A (-2, 2), B (1, 4) and C (-1, 4) is mapped onto a triangle A'B'C' by a reflection in the line y = x + 1 a. On the grid provided draw i. triangle ABC; ( 1 mark) ii. The line y = x + 1 (2 marks) iii. Triangle A'B'C' b. Triangle A''B''C'' is the image of triangle A'B'C'
19.
The figure below is a right pyramid VEFGH with a square base of 8 cm and a slant edge of 20cm. Points A, B, C and D lie on the slant edges of the pyramid such that VA = VB =VC = VD= 10 cm and plane ABCD is parallel to the base EFGH.
20.
The heights of 40 athletes in a county athletics competition were as shown in the table below: a. Find the value of x (1 mark) b. State the modal class (1 mark) ..
21.
The figure below represents a triangular flower garden ABC in which Ab = 4 m, BC = 5 m and
∠
B
C
A
=
30
o
.Point D lies on AC such that BD = 4m and
∠
B
D
C
is obtuse
22.
The shaded region on the graph below shows a piece of land ABCD earmarked for building a sub-county hospital. a). Write down the ordinates of curves AB and DC for x = 0, 200, 400, 600, 800, 1000 and 1200 (2 marks) b. Use trapezium rule, with 6 strips to estimate the area of the piece of land ABCD in hectares. (4 marks) c. Use mid-ordinate rule with 3 strips to estimate the area of the piece..
23.
The equation of a curve is
y
=
x
3
+
x
2
-
x
-
1
a. Determine: i.The stationary points of the curve
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