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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

Without using a calculator or mathematical tables

13/5/2023

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​Without using a calculator or mathematical tables

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Given that xo is an angle in the first quadrant such that 8sin2x + 2Cos x – 5 = 0, find tan x. (3 Marks)

10/4/2023

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question

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answer

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Show that:

6/4/2023

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question

Show that:
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answer

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Solve for x in the equation

2/1/2023

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Complete the table for y = Sin x + 2cos x

29/11/2021

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TRIGONOMETRY III | FORM 4 LEVEL | PAPER 2 QUESTIONS | SECTION B

(a) Complete the table for y = Sin x + 2cos x. (2mks)

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​(b) Draw the graph of y= sin x + 2 Cos x using a scale of 1cm to represent 30o on x-axis and 2cm to represent 1 unit on y-axis. (3mks)

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​(c) Solve sin x + 2 cos x = 0 using the graph. (2mks)

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(d) Find the range of values of x for which y≤-0.5. (3mks)

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN10

24/9/2020

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Form 4 Mathematics


Determine the amplitude and the period of the function y = 3 sin(2x + 40°).
answer
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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN21

21/9/2020

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Form 4 Mathematics


The table below shows some values of the curves y = 2 cos x and y = 3 sin x.
(a) Complete the table for values of y = 2 cos x and y = 3 sin x, correct to 1 decimal place.
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On the grid provided, draw the graphs of y = 2 cos x and y = 3 sin x for 0° ≤ x ≤ 360°, on the same axes.
(c) Use the graph to find the values of x when 2 cos x — 3 sin x = 0 
(d) Use the graph to find the values of y when 2 cos x = 3 sin x.
answers
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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN10

21/9/2020

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Form 4 Mathematics


​State the amplitude and the phase angle of the curve y = 2 sin ( 3/2 x — 30°) 
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN12

17/9/2020

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Form 4 Mathematics


Determine the amplitude, period and the phase angle of the curve: y = 5/2 sin (4θ + 60°)
answer
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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN16

15/9/2020

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Form 3 Mathematics


Find in radians, the values of x in the interval 0c ≤ x ≤ 2πc for which 2 cos2x - sin x = 1. (Leave the answer in terms of π)
answer
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN07

13/9/2020

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Form 3 Mathematics


Given that x is an acute angle and cos x = 2/5 √5 find, without using mathematical tables or a calculator, tan (90-x).
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN19

11/9/2020

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Form 4 Mathematics


The equation of a curve is given by y= 1 + 3sin x.
(a) Complete the table below for y = 1 + 3 sin x correct to 1 decimal place
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(b) (i) On the grid provided, draw the graph of y - 1 + 3 sin x for 0° ≤ x ≤ 360°.
ii) State the amplitude of the curve y = 1 + 3 sin x.
c) On the same grid draw the graph of y = tan x for 90° ≤ x ≤ 270°. 
d) Use the graphs to solve the equation ; 1+3 sin x = tan x for 90° ≤ x ≤ 270°.
answers
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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN06

8/9/2020

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Form 4 Mathematics


Determine the amplitude and period of the function, y = 2 cos (3x — 45)°.
answers
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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN023

8/9/2020

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Form 4 Mathematics



a) Complete the table below, giving your values correct to 2 decimal places.
Picture
  • b) Using the grid provided draw, on the same axes, the graph of y = cos 2x and y = sin (x+ 300) for 00< x< 1800 Take the scale: 1cm for 150 on the x axis 4cm for 1 unit on the y- axis. (4mks)
  • c) Find the periods of the curve Y = axis (1mks)
  • d) Using the graphs in part (b) above, estimate the solutions to the equation Sin (x + 300) = Cos 2x (4mks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN21

3/9/2020

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Form 4 Mathematics


(a) Complete the table below, giving the values correct to 1 decimal place.
Picture
b) On the grid provided, using the same scale and axes, draw the graphs of y = 2 sin (χ+20)0 and y = √3 cos χ for 00 ≤ χ ≤ 2400.
c) Use the graphs drawn in (b) above to determine:
 i) the value of χ for which 2sin (χ + 20) = √3 cos χ;
 ii)the difference in the amplitudes of y =2sin(χ + 20) and y =√3 cos χ.
answers
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN023

31/8/2020

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Form 4 Mathematics



​a) Complete the table below, giving your values correct to 2 decimal place.
Picture

b) Using the grid provided and the table in part (a) draw the graphs of Y = tan Ө and y = sin 2Ө.
c) Using your graphs, determine the range of values for which tan Ө>Sin 2Ө for 00 ≤ Ө ≤ 900.
Answers
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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN16

28/8/2020

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Form 4 Mathematics


The table below shows values of x and y for the function y = 2 sin 3x° in the range 00 ≤ x ≤ 1500
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(a) On the grid provided, draw the graph of y = 2 sin 3x.
(b) From the graph determine the period.
answer
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K.C.S.E Mathematics Q & A - MODEL 2011PP1QN05

26/8/2020

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Form 4 Mathematics


Given that sin (x + 60)° = cos (2x)°, find tan (x + 60)°.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN17

26/8/2020

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Form 4 Mathematics


(a) Complete the table below, giving the values correct to 2 decimal places.
Picture
(b) On the grid provided and using the same axes draw the graphs of y = cos x° and y= sin x°— cos x°  for 0° ≤  x ≤  180°.Use the scale; 1 cm for 20°on the x-axis  and 4cm fort unit on the y-axis. 
(c) Using the graph in part (b):
(i) solve the equation sin x° — cos x° 1.2; 
(ii) solve the equation cos x°=  1/2 sinx; 
(iii) determine the value of cos x° in part (c) (ii) above.
answers
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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN14

21/8/2020

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Form 4 Mathematics


Solve 4 -4 Cos 2 Cos 2 x = -1 for 00 ≤ x ≤ 3600
answer
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN19

18/8/2020

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Form 4 Mathematics


a) complete the table below, giving the values correct to 2 decimal places.
Picture
b) On the grid provided, draw the graphs of y=sin 2x and y=3cosx-2 for 00 ≤ x ≤3600 on the same axes.
 Use a scale of 1 cm to represent 300 on the x-axis and 2cm to represent 1 unit on the y-axis.
 c) Use the graph in (b) above to solve the equation 3 Cos x – sin 2x = 2.
 d) State the amplitude of y=3cosx-2.
answers
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN16

18/8/2020

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Form 4 Mathematics


Find in radians, the values of x in the interval 00≤ x ≤ 2π0+ for which 2 cos 2x=1.
 (Leave the answers in terms of π )
answer
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K.C.S.E Mathematics Q & A - MODEL 2001PP2QN015

12/8/2020

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Form 4 Mathematics



Solve the equation 4 sin2 Ө+4 cos Ө =5

For 0o ≤ Ө ≥ 360o  give the answer in degrees

aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2001PP2QN021

10/8/2020

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Form 4 Mathematics



a) Complete the table given below in the blank spaces.
Picture

  • b) On the grid provided draw, on the same axis, the graph of y = 3cos 2x and y = sin(2x +300) for 0o ≤ x ≥ 1800. Take the scale: 1cm for 150 on the axis and 2cm for 1 unit on the y-axis.
  • c) Use your graph to estimate the range of value of x for which 3 cos 2x ≤ 2sin (2x+30o).
Give your answer to the nearest degree.

Answer
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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN12

21/7/2020

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Form 4 Mathematics



Given that sin ( x + 30)0 = cos 2x0 for 00, 00 ≤ x ≤900 find the value of x. Hence find the value of cos23x0.

Answer
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