Maths Topics Answering Techniques

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



  • 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


Maths Topical Answering Techniques


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




  • 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


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


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


  • 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)


  • 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