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

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

**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

**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(**1**x**)*, 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
*=**A**O**'**AO* - Describe the enlarge fully when asked for
- Relate linear scale fa
*cto*r(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