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Q&A-KCSE Mathematics 2019 with Marking Scheme

KCSE 2019 MATHEMATICS PAPER 2

KCSE 2019

KCSE 2019

KCSE 2019 MATHEMATICS PAPER 2

KCSE 2019

KCSE 2019

KCSE 2019 MATHEMATICS PAPER 2

KCSE 2019

KCSE 2019

KCSE

KCSE 2019

KCSE 2019

KCSE 2019 MATHEMATICS PAPER 2

KCSE 2019

KCSE 2019

KCSE 2019 MATHEMATICS PAPER 2

KCSE MATHS

KCSE 2019 MATHS

MATHEMATICS

KCSE 2019

MATHEMATICS

KCSE REVISION

KCSE REVISION

KCSE

mathematics

kcse maths paper 2 2019

kcse maths paper 2 2019

Ratios and Proportions

KCSE 2020 PAPER 2

KCSE 2020 PAPER 2

series and sequences

KCSE 2020 PP2 Q 2

KCSE 2020 PP2 Q 2

series and sequences

Q2 Continued

Q2 Continued

Three Dimensional Geometry (Maths Paper 2 2019 No. 11 (a) )

(Maths Paper 2 2019 No. 11 (a) )

(Maths Paper 2 2019 No. 11 (a) )

Three Dimensional Geometry (Maths Paper 2 2019 No. 11 (a) )

(Maths Paper 2 2019 No. 11 (a) )

(Maths Paper 2 2019 No. 11 (a) )

Three Dimensional Geometry (Maths Paper 2 2019 No. 11 (b) )

(Maths Paper 2 2019 No. 11 (b) )

(Maths Paper 2 2019 No. 11 (b) )

Maths Topical Answering Techniques

Construction and Loci

  • Tighten your compasses before the exam day
  • Hold campus arm for accurate construction
  • Mark intersection of arcs to identify the points to be joined
  • Interpret Loci language in terms of construction method
  • Loci of inequalities draw boundary lines then shade the region as per the rubric

Transformations

Transformations

  • The axes should have the same scale
  • All diagrams to be drawn in pencil with continuous lines
  • Label all vertices accordingly ABCD, A1B1C1, A2B2C2 etc to distinguish between objects and their images
  • Co-ordinates to be written in the spaces provided not on drawn figures

 

Errors and Approximations

The length and breadth of a rectangular card were measured to the nearest millimetre and found to be 14.5cm and 10.6cm respectively. Find the percentage error in the perimeter.                                                                                                                                               3mks

Pmax=214.55+10.65=50.4cm

Pactual=214.5+10.6=50.2cm

Pmin=214.45+10.55=50cm

 

Surds

Simplify the following expression;

 , giving your answer in the form , where a, b and c are real numbers     3mks

Further Logarithms

Evaluate without using tables;

                                4mks

 

Quadratic Equation

                                                                                       3mks    

Further Logarithms

Solve for  in the equation:      3mks

   
 

                                      

Errors and Approximations

A student expands as  ,   if he used the formula to evaluate , find the percentage error in his calculation   3mks

 

Linear Equations

A two-digit number is such that the sum of the ones and the tens digit is ten. If the digits are reversed, the new number formed exceeds the original number by 54. Find the number.                                                                                                                                      3mks

 

    

        

 

Gradient and Equation of a Line

A line parallel to line OP shown in figure below cuts the y-axis at ( ).  Find the equation of the line:                                                                                                              3mks

1

Quadratic Equation

 (a) Complete the table below for the equation, given.     1mk

b) Using a scale of  to represent 2 units in both axes, draw the graph of     (2mks)

c) Use the graph to solve the quadratic equations:                                                                                                                 

                                                      (1mk)     

i                                                        (2mks)

c) Use the graph to solve the quadratic equations:                                                                                                                 

                                                                                                                                  (1mks)     

(1.37, 0), (-4.38, 0)

                                                                      

                                                                                                                                       (2mks)

Maths Topical Answering Techniques

Graphs

Quadratic and cubic graphs

  • Fill the table as per the number of decimals given
  • Use the scale given and if not choose a scale that accommodates all table values. Scale labelling must be linear and appropriate
  • Plot all table values on the grid part
  • The curve should be smooth, continuous and behaves as the function given
  • Inspect the behaviour of the curve at the turning point by substituting a value of x at the turning point even though it is not among the table values
  • Determine straight line by subtracting the equation from the function
  • Use a ruler for the straight line
  • Interpret what 1 small square represents on both axes

Maths Topical Answering Techniques

Graphs

 Waves

 

  • Fill table as per directive
  • Use scale given
  • Determine the multiplying factor from the scale
  • Plot all points on the table
  • Draw a smooth curve passing through plotted points and behaves as the function given
  • Read points of intersection of the two functions

Maths Topical Answering Techniques

Graphs

CF (Ogive) Curve

  • Write a column for CF and upper-class limits
  • Choose a suitable scale or use a scaled graph
  • Break the x-axis or translate the y-axis and start plotting from the upper-class limit previous to the class given in the table
  • You may label the x-axis uniformly from a point then plot UCL as per the scale
  • CF must originate from the horizontal axis (NO hanging CF) by plotting zero CF against UCL of a class previous to the first-class tabulated
  • Do not commit the origin then use class limits on the scale along the x-axis
  • In case the first class starts from zero, CF should originate from the origin(Do not go to the negative) or the curve should not cross the broken axis
  • Interpret what 1 small square is on the x-axis then read medians, quartiles, percentiles etc.
  • You may also read the graph in reverse depending on the setting

Maths Topical Answering Techniques

Graphs

Histogram and Frequency Polygons

  • Check for uniform class intervals (all bars will have equal width)
  • Different class intervals; choose standard width then adjust all classes to appropriate heights i.e

 

  • Plot appropriate heights against class limits
  • Frequency density may also be used i.e 
  • A frequency polygon is appropriate heights against midpoints (may be obtained from histogram)
  • The polygon should not be open

Linear programming

  • Form correct inequalities from the given conditions
  • Plot inequalities by shading the unwanted regions
  • Obtain an objective function
  • Optimize the objective function by inspection method or by use of search lines
  • Distinguish when the solutions are whole numbers (discrete/countable) variables or when the solutions can be read to the nearest decimal place (Non-discrete or uncountable variables) e.g measurements

Non-linear to linear

  • Determine which variables to plot to get a linear graph
  • Fill the table as per the directive
  • Choose an appropriate scale
  • Determine the multiplying factor from the scale
  • Plot all points on the table
  • Draw line of best fit
  • Identify two suitable points from the line of best fit, then find the gradient and y-intercept
  • Use gradient and y-intercept to write the linear relation

 

Maths Topical Answering Techniques

Calculations and Presentation of Work

 

Fractions and decimals

  • Order of operations must be followed strictly
  • After every operation rewrite the expression afresh

Squares and square roots

  • Approximate your answer first
  • When Finding square roots from tables, numbers are not written in standard form, but  where  and n is even

Commercial Arithmetics

  • Currency conversion : take note that it is the BANK who sells to a customer or buys from a customer
  • Use of calculators may be required or not

Angles and Plane figures

  • Sum of interior angles in a polygon

Maths Topical Answering Techniques

Calculations and Presentation of Work

Cubes and cube roots

  • Express the figure in prime factors then divide by three

Reciprocals

  • Stick to the rubrics if told to use tables
  • Express the figures I the form k(1x), then read the table of reciprocals

Indices and Logarithms

  • Simplify the express to be in the same base, preferable prime factors as the base
  • Incase of the equation, have the same base on both sides then drop the base and equate the powers
  • Use mathematical tables and use logarithms tables are two different rubrics
  • For use of logs, use all logs correctly
  • Show how you change the bar into a bar that is divisible by the denominator in the case of roots
  • Divide completely incase of terminal decimals, then round to 4 s.f
  • Write your answer in standard form before writing the actual value

Gradient and Equation of straight lines

  • Equating gradient using general point is easier than getting the value of c from the equation
  • For perpendicular lines, find m1 then  ; for parallel lines

Reflection and congruence

  • Use Cartesian plane with uniform scale  both axes
  • Draw objects and images using continuous lines and label accordingly
  • Write the equation of the line of symmetry /mirror line when asked (not x-axis but y=0, not y-axis but x=0)
  • Remember the properties of congruence (SAS,SSS,AAS,RHS)

Rotation

  • Center of rotation is the intersection of perpendicular bisectors of ' and  ( Rotation may be in a Cartesian plane or not)
  • Always locate centre of rotation by giving it a letter
  • If O is the centre of rotation the angle of rotation is between line  and
  • Describe the rotation in full when asked
  • Label the object and image accordingly and write down the co-ordinates when asked
  • Order  of rotation symmetry
  • You should be able to complete a figure if order and CoR is given
  • Take note of the axis of rotation in the case of solids

Similarity and enlargement

  • Distinguish between similar triangles and congruent triangles
  • Center of enlargement is a point of intersection of lines joining A to A', B to B'  etc
  • The scale factor of enlargement is  =AO'AO
  • Describe the enlarge fully when asked for
  • Relate linear scale factor(LSF), area scale factor (ASF) and volume scale factor (VSF).

Trigonometric Ratios

  • Name angle to be calculated and locate it on the diagram
  • Avoid expression such as
  • Take note of special angles ° if the use of tables is not required

Equation of a Circle

Equation of a Circle Mathematics KCSE Question

The equation of a circle is given by     . Determine the radius and the center of the circle.

RATES OF WORK

Mary and Jane working together can cultivate a piece of land in 6 days. Mary alone can complete the work in 15 days. After  the two had worked for 4 days Mary withdrew the services . Find the time taken by Jane to complete the remaining work.    3mks

 =    

Area scale factor and determinant of a matrix

In a transformation, an object with area   is mapped onto an image whose area is  by transformation matrix. Find the value of     3mks

-

Formulae

Make Q the subject of the formula

 

RECIPROCALS

Use tables of reciprocals only to work out

Use tables of reciprocals only to work out

RECIPROCALS

Use tables of reciprocals only to work out

Use tables of reciprocals only to work out

Arithmetic progression (A.P)

An arithmetic progression is such that the first term is  -5, the last term is 135 and the sum of the progression is 975. Calculate:

 

An arithmetic progression is such that the first term is -5, the last term is 135 and the sum of the progression is 975. Calculate:

(a)The number of terms in the series                                                 4mks

975=65n

(b) The common difference of the progression                                 2mks

(b) The sum of the first three terms of a geometric progression is 27 and the first term is 36. Determine the common ratio and the value of the fourth term.                      4mks

BINOMIAL EXPANSIONS

(a) Expand 

(a) Expand 

(b) Hence find the value of  , correct to 4 decimal places when substitution is up to  

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