36-Week WAEC Revision Programme — Mathematics
September to the May WAEC sitting. SS3 is not a year of new material so much as a year of pressure on material already met, so this is not a course to work through from the beginning — it is a testing programme. Each week you answer cold, work the ones you got wrong, and have the AI explain why you got them wrong. Anything you turn out never to have been taught, you learn there and then, and meet again three weeks later.
A week is one block of the syllabus and the prompts that cover it. You are not meant to do all of them: answer the questions first, and let what you get wrong decide which of the rest you need. Fifteen or twenty minutes a subject is a real week's work — nine subjects do not fit any other way.
Three prompts in each topic are free to try before you subscribe. One subscription opens everything this guide links to.
Every week, in this order
Start with the questions, not the explanation. The first two steps are in every week; a purpose-written mistake or pitfalls prompt appears in about half of them, and where it does not, your own wrong answers are the material for step three.
- 1. Retrieve — Answer cold, with nothing in front of you. Wrong answers are the point — they show you where the week's work is.
- 2. Drill — Work the ones you missed properly, showing every step, so you and the AI can both see where it went wrong.
- 3. Explain my error — Ask why your answer was wrong, not just what the right one is. Where the week offers a Spot My Mistake or WAEC Pitfalls prompt, use it.
- 4. Teach me — Only if the error turns out to be something you were never taught. Then come back and retrieve it again.
Number, Ratio & Financial Mathematics
↑ Jump to week- Week 1
- Quiz me: Forming a quadratic from a described area or product
- WAEC exam prep: Why the days of the week form a modulo seven system
- WAEC pitfalls: Using the arithmetic progression formula on a geometric sequence
- Teach Me: Modular arithmetic word problems
- Teach me: The formula for standard deviation of ungrouped data, and what each symbol means
- Teach Me: Perimeter and area of plane shapes
- Teach Me: Addition in modulo arithmetic
- Teach me: Substituting the linear equation into the quadratic to eliminate a variable
- Teach Me: Percentiles and deciles
- Teach me: Turning a described building task into a mensuration calculation
- Teach me: Why the days of the week form a modulo 7 system
- Teach Me: Mensuration involving pyramids
- Teach Me: Modular arithmetic clock problems
- Teach Me: Using logarithm tables for powers
- Teach me: The characteristic and the mantissa of a logarithm
- Teach me: Measuring a three-figure bearing clockwise from north
- Teach me: Why replacement leaves the probability unchanged on each draw
- Teach me: When two events are independent and the product rule applies
- Teach me: Setting out a long division in a base other than ten
- Teach me: Recognising whether a sequence is arithmetic or geometric
- Teach me: The binary multiplication table, and why it is so short
- Teach Me: Solving simultaneous linear equations by elimination
- Teach Me: Why two parallel lines must share a gradient
- Teach Me: Word problems on joint variation
- Teach me: The complement of a set and the universal set it depends on
- Teach Me: Angles of elevation and depression
- Teach Me: Addition of numbers in base 2
- Teach me: Adding logarithms to multiply, then taking the antilogarithm
- Teach Me: Subtraction in modulo arithmetic
- Teach me: Deriving the sum formula for a geometric progression
- Week 2
- Quiz Me: Basic sigma notation for series
- Quiz me: Probability drawn from a described Nigerian market situation
- Quiz Me: Volume of a cone
- Quiz me: Estimating the materials needed for a described construction job
- Quiz Me: Basic concept and definition of probability
- Quiz Me: Practical problems on distance on the earth
- Quiz Me: Word problems on inverse variation
- Quiz Me: Rationalising the denominator of surds
- Quiz Me: Multiplication and division of surds
- Quiz me: Forming the negation of a given statement
- Quiz me: Reading a four-figure logarithm table
- Quiz me: The two solution pairs a linear-and-quadratic system usually gives
- WAEC exam prep: Forming a direct variation from a described situation
- WAEC Pitfalls: Converting base 10 numbers to base 2
- Teach Me: Factorising quadratic expressions
- Teach me: The range, the quartiles and the interquartile range defined
- Teach Me: Addition of numbers in base 5
- Teach Me: Standard deviation of grouped data
- Teach Me: The concept and meaning of modulo arithmetic
- Teach Me: Trigonometric ratios of obtuse angles
- Week 3
- Quiz me: The median class and the interpolation formula
- Quiz me: The midpoint formula, and how it averages the coordinates
- Quiz me: The steps of completing the square on a monic quadratic
- Quiz Me: Trigonometric ratios of special angles (30, 45, 60 degrees)
- Quiz me: Deciding whether a given mathematical statement is true
- Quiz me: Finding the common difference from any two terms of an AP
- Quiz me: Writing the nth term of a linear sequence
- Quiz Me: Checking answers using casting out nines
- Quiz me: Solving a congruence by testing each residue in turn
- Quiz me: Probability with replacement compared with probability without it
- Quiz me: A frustum as a cone with its top cut off
- Quiz Me: The product law of logarithms
- Practice: Deciding whether a mathematical statement is true
- Practice: A four-day market cycle written as arithmetic modulo four
- Practice: The half ab sine C formula and the angle it needs
- Practice: Forming an equation about an unknown base
- Practice: Writing a bearing with three figures even when it is small
- Practice: Splitting a composite solid into parts you can calculate
- Practice: Drawing the boundary lines of an inequality region
- Practice: A savings scheme that grows by a fixed amount each month
- Practice: The sum formula for a geometric progression
- Practice: The length of a line segment on a coordinate grid
- Practice: Converting between two bases without passing through base ten
- Practice: Solving a linear inequality in one variable
- Practice: Solving two line equations simultaneously to find the meeting point
- Practice: The height of the cone removed to leave a frustum
- Practice: A power raised to a further power
- Practice: Factorising a quadratic expression into two brackets
- Quiz Me: Common mistakes in logarithm calculations
- Teach me: Forming an equation from a statement about an unknown base
- Week 4
- Quiz me: A four-day market cycle expressed as arithmetic modulo 4
- Word problem: A joint variation problem set in a Nigerian transport fare
- Word problem: Finding the base in which a given calculation is correct
- Word problem: Translating an everyday statement into logical symbols
- Word Problem: The curved surface and the flat face of a hemisphere
- Word problem: Negating a statement that contains 'all' or 'some'
- Word problem: Finding the shortest flying distance between two cities
- Word Problem: Multiplication in modulo arithmetic
- Word problem: The arc length as a fraction of the circumference
- Word Problem: Simultaneous linear inequalities
- Word Problem: Quadratic sequences
- Word Problem: Equation of a line given two points
- Word Problem: A power raised to another power
- Word Problem: Venn diagrams with three sets
- Word problem: Filling in a two-set Venn diagram from a word problem
- Word Problem: Modular arithmetic in real-life scheduling situations
- Word Problem: Combined gradient and equation of a straight line problems
- Word problem: A survey problem solved with union and intersection
- Word problem: Completing the square when the leading coefficient is not one
- Word problem: The line joining two points on a map
- Word problem: A sharing problem expressed in base five
- Word problem: Reading a value off a sine or cosine graph
- Word problem: Continuing a pattern taken from a described real situation
- Word problem: Expressing a decimal measurement in base eight
- Word problem: The volume of a described water tank made of two shapes
- Word Problem: The area formula one half ab sin C
- Word problem: A journey with two legs and the return bearing it needs
- Word problem: Predicting the next market day from a given date
- Word Problem: Three-figure bearing
- WAEC pitfalls: The total surface area of a solid hemisphere including its flat face
- Teach me: Writing a joint variation statement as an equation with a constant
Revisit from three weeks ago - Week 5
- Quiz me: Inserting an arithmetic mean between two numbers
- WAEC exam prep: A statement disproved by a single counter-example
- WAEC exam prep: Factorising by taking out a common factor first
- WAEC pitfalls: Evaluating a negative expression modulo n
- Worked Example: Using logarithm tables for roots
- Worked example: Checking a base division by multiplying back
- Worked Example: Constructing a frequency distribution table
- Worked Example: Variation problems in Nigerian market pricing contexts
- Worked Example: Constructing modulo addition and multiplication tables
- Worked example: Evaluating a negative expression in modular arithmetic
- Worked example: Turning a recurring decimal into a fraction with a geometric series
- Worked example: The area of a sector as a fraction of the whole circle
- Worked example: Finding the constant of variation from one set of values
- Worked Example: Graphical solution of linear inequalities
- Worked example: Drawing an accurate bearing diagram before calculating
- Worked example: Locating the quartiles in an ordered set of data
- Worked Example: Converting directly from one base to another base
- Worked example: Working backwards to find what day a past date fell on
- Worked Example: Addition law of probability
- Worked example: Finding the number in neither set from a Venn diagram
- Worked Example: Linear inequalities in one variable
- Worked example: The difference in longitude between two places on one parallel
- Worked Example: Word problems leading to simultaneous equations
- Worked Example: Probability using tree diagrams
- Worked Example: Set notation and types of sets
- Worked example: The angle between a line and a plane
- Worked example: Solving two line equations simultaneously to find where they meet
- Worked Example: Combining operations in modular arithmetic
Revisit from three weeks ago - Week 6
- Quiz me: Setting up a partial variation equation with two unknown constants
- WAEC exam prep: The sine and cosine of an obtuse angle
- WAEC Exam Prep: Finding common difference and common ratio
- WAEC exam prep: Longitude difference across the international date line
- WAEC exam prep: Substitution when both equations are in the same form
- WAEC Exam Prep: Midpoint of a line segment
- WAEC exam prep: Reading a WAEC-style table of data
- WAEC exam prep: A school survey in which every pupil chose at least one subject
- WAEC exam prep: The zero index and why it gives one
- WAEC exam prep: The mean deviation of an ungrouped set
- WAEC exam prep: Forming a direct variation equation from a description
- WAEC exam prep: A repeating timetable expressed as a modulus
- WAEC exam prep: Telling an arithmetic sequence from a geometric one
- WAEC exam prep: The gradient and intercept form of a line
- WAEC Exam Prep: Venn diagrams with two sets
- WAEC exam prep: The radius of a sphere from its volume
- WAEC exam prep: The total contributed over a stated number of months
- WAEC exam prep: The height of a cylinder from its volume
- WAEC exam prep: The curved surface of a hemisphere
- WAEC exam prep: Listing the subsets of a given set
- WAEC exam prep: The class midpoints used for grouped data
- WAEC exam prep: The sine, cosine and tangent of an acute angle
- WAEC exam prep: Setting up a partial variation with two constants
- WAEC exam prep: The modal class of a grouped distribution
- WAEC exam prep: Multiplying a surd by a whole number
- WAEC exam prep: Why the locus equidistant from two fixed points is their perpendicular bisector
- WAEC Exam Prep: Drawing bar charts and pie charts
- WAEC exam prep: The gradient of a line joining two negative coordinates
- WAEC exam prep: The sum of an arithmetic progression when the last term is known
- WAEC exam prep: Converting between base two and base eight directly
- WAEC exam prep: The negative characteristic of a logarithm less than one
- WAEC pitfalls: Taking the coordinates in the wrong order when finding a gradient
- Worked example: The locus of points equidistant from two fixed points
Revisit from three weeks ago - Week 7
- Quiz me: Forming a direct variation equation from a described situation
- WAEC Exam Prep: Relative frequency and experimental probability
- WAEC exam prep: The mean of a grouped distribution
- WAEC exam prep: Casting out nines as a check on a calculation
- WAEC exam prep: The notation for element, subset and empty set
- WAEC exam prep: Checking an intersection read off a graph by algebra
- WAEC exam prep: Clearing a fraction whose denominator contains the unknown
- WAEC exam prep: The total surface area of a solid hemisphere
- WAEC exam prep: The probability of two independent events both happening
- WAEC exam prep: The number of elements in a union of two sets
- WAEC Exam Prep: Cardinal points and compass bearings
- WAEC exam prep: Reading a chart of Nigerian population or trade data
- WAEC exam prep: Constructing angles of sixty and ninety degrees
- WAEC Exam Prep: Word problems on sequences and series
- WAEC exam prep: The segment two given angles stand in
- WAEC exam prep: The back bearing of a stated bearing
- WAEC exam prep: De Morgan's laws stated for two sets
- WAEC exam prep: Writing a joint variation statement as an equation
- WAEC exam prep: Subtracting logarithms to divide two numbers
- WAEC Exam Prep: Multiplication law of probability
- WAEC exam prep: Evaluating a series written in sigma notation
- WAEC exam prep: The mean of an ungrouped list of numbers
- WAEC exam prep: Finding a square root with logarithm tables
- WAEC exam prep: The place values of a binary number
- WAEC exam prep: Finding the time a stated number of hours later
- WAEC exam prep: Factorising by taking out the highest common factor
- WAEC exam prep: The sine rule applied to an obtuse-angled triangle
- WAEC exam prep: An equation solved by writing both sides to one base
- WAEC Exam Prep: Applying number bases to binary computer coding
- WAEC exam prep: The volume of a pyramid from base area and height
- WAEC exam prep: What the discriminant reveals before you solve
- WAEC pitfalls: The total surface area of a square-based pyramid
- Worked example: Converting a base five number back to base ten as a check
Revisit from three weeks ago - Week 8
- Quiz me: Multiplying two binary numbers by shifting and adding
- WAEC exam prep: Finding a side of a triangle from its area
- WAEC exam prep: Expanding a base eight number by its place values
- WAEC exam prep: The slant height needed for a cone's surface area
- WAEC exam prep: Forming an inverse variation equation
- WAEC exam prep: The arc length of a sector whose angle at the centre is reflex
- WAEC exam prep: An argument that is valid though its conclusion is false
- WAEC exam prep: The nth term formula of an arithmetic progression
- WAEC exam prep: An addition table for a small modulus
- WAEC exam prep: Simplifying an expression by collecting powers
- WAEC exam prep: Choosing the form of the sum formula for r above or below one
- WAEC exam prep: Drawing a tree diagram for two successive events
- WAEC exam prep: A base division that leaves a remainder
- WAEC exam prep: Shading the region satisfying several inequalities
- WAEC Exam Prep: Three-dimensional trigonometry problems
- WAEC exam prep: Multiplying binary numbers by shifting and adding
- WAEC Exam Prep: Cumulative frequency and the ogive
- WAEC Exam Prep: Converting fractions from base 10 to another base
- WAEC exam prep: A population growing by a fixed ratio each year
- WAEC exam prep: Adding two numbers in base five with carrying
- WAEC exam prep: The cosine rule and the included angle it needs
- WAEC exam prep: Making a letter the subject of a formula
- WAEC exam prep: The inclusive sense of or, and where it differs from exclusive
- WAEC exam prep: The splitting-the-middle-term method of factorising
- WAEC Exam Prep: Converting between indices, logarithm and surd forms
- WAEC exam prep: The value a carry represents in a given base
- WAEC exam prep: Two draws without replacement on a tree diagram
- WAEC exam prep: Negating a compound statement
- WAEC exam prep: A survey in which some respondents chose neither option
- WAEC exam prep: The equation of a line from a gradient and one point
- WAEC exam prep: The addition law when two events can overlap
- WAEC Exam Prep: Solving simple trigonometric equations
- WAEC exam prep: Why replacement leaves each draw independent
- WAEC pitfalls: The carry rule when adding in base two
- Worked example: Choosing the right form of the sum formula for r above or below 1
Revisit from three weeks ago - Week 9
- Quiz me: Finding the distance between two points from their bearings
- WAEC Exam Prep: Bearing and distance problems
- WAEC Exam Prep: Word problems on inequalities
- WAEC pitfalls: Treating the inclusive 'or' as though it were exclusive
- WAEC pitfalls: The day of the week on which a stated date fell
- WAEC pitfalls: Expanding a product of two brackets
- WAEC Pitfalls: Length of a chord
- WAEC pitfalls: The locus of points equidistant from two intersecting lines
- WAEC pitfalls: Eliminating by adding rather than by subtracting
- WAEC pitfalls: The region satisfying two inequalities at once
- WAEC pitfalls: Finding a gradient and then the equation from it
- WAEC Pitfalls: Volume of a hemisphere
- WAEC pitfalls: Making a letter under a square root the subject of a formula
- WAEC pitfalls: Dividing consecutive terms of an AP to look for a ratio
- WAEC pitfalls: Checking that a line found really is parallel
- WAEC Pitfalls: Logical reasoning in everyday Nigerian contexts
- WAEC pitfalls: The surface area of a composite solid and its hidden faces
- WAEC pitfalls: Judging a statement true from a single supporting example
- WAEC pitfalls: The shortest air route between two cities
- WAEC pitfalls: What follows validly from a stated implication
- WAEC pitfalls: Reading an intersection off a graph without checking it algebraically
- WAEC pitfalls: The identity relating sine squared and cosine squared
- WAEC Pitfalls: Using logarithm tables for multiplication
- WAEC pitfalls: Adding the probabilities of events that can happen together
- WAEC pitfalls: The gradients of two parallel lines
- WAEC pitfalls: A pricing problem where cost varies with two quantities
- WAEC pitfalls: Carrying wrongly when adding partial products in base 2
- WAEC pitfalls: The radius of a sphere from its surface area
- WAEC pitfalls: Events wrongly treated as mutually exclusive
- Teach me: When the cosine rule is needed rather than the sine rule
Revisit from three weeks ago - Week 10
- Quiz me: Using the sine rule inside a bearing diagram
- WAEC exam prep: Inserting several arithmetic means between two numbers
- WAEC Pitfalls: Interpreting statistical data from Nigerian contexts
- WAEC pitfalls: The effect of one extreme value on the mean
- WAEC pitfalls: The reference angle for an angle above ninety degrees
- WAEC pitfalls: Losing a root by dividing through instead of factorising
- WAEC Pitfalls: The two numbers that multiply to c and add to b
- WAEC pitfalls: Expressing an inequality solution in set notation
- WAEC pitfalls: The region belonging to exactly two of three sets
- WAEC pitfalls: Quoting the mean for data that contains an extreme outlier
- WAEC pitfalls: Finite, infinite and equal sets distinguished
- WAEC pitfalls: Two draws with replacement compared with two without
- WAEC pitfalls: The residue classes of a given modulus
- WAEC pitfalls: Finding the constant of a direct variation
- WAEC pitfalls: Reading the fractional digits of a converted number in the wrong direction
- WAEC pitfalls: A three-set problem in which one region is unknown
- WAEC pitfalls: Why the interpolation formula gives only an estimate
- WAEC pitfalls: Multiplying probabilities for events that are not independent
- WAEC pitfalls: The values that make an algebraic fraction undefined
- WAEC Pitfalls: Arithmetic progression: sum of n terms
- WAEC Pitfalls: Acute angle bearing
- WAEC pitfalls: A quadratic inequality with no real critical values
- WAEC pitfalls: Taking a complement without first stating the universal set
- WAEC pitfalls: The constant of an inverse variation
- WAEC pitfalls: Applying the cyclic property to a quadrilateral not drawn in a circle
- WAEC pitfalls: Inserting several geometric means between two numbers
- WAEC pitfalls: The maximum and minimum values of a cosine curve
- WAEC pitfalls: Using the equatorial radius for a parallel far from the equator
- WAEC pitfalls: The negative index as a reciprocal
- Worked example: Inserting a geometric mean between two numbers
Revisit from three weeks ago - Week 11
- Quiz me: The truth table for 'and' set beside the truth table for 'or'
- WAEC exam prep: Finding the constant of a joint variation from given values
- WAEC pitfalls: Drawing a conclusion the given data supports
- WAEC pitfalls: Filling in a truth table column in the wrong order
- WAEC pitfalls: Telling an open statement from a closed one
- WAEC pitfalls: A joint variation set in a Nigerian transport fare
- WAEC pitfalls: The place values of a fractional part in another base
- WAEC pitfalls: The probability of one of each in two draws without replacement
- WAEC Pitfalls: Combined probability problems
- WAEC pitfalls: Interpolating between two rows of a logarithm table
- WAEC pitfalls: A division by logarithms checked by estimation
- WAEC Pitfalls: Distance in nautical miles and knots
- WAEC pitfalls: Finding a cube root with logarithm tables
- WAEC pitfalls: An elevation and a depression in the same diagram
- WAEC pitfalls: Treating an implication as though it worked both ways
- WAEC pitfalls: Converting units before a mensuration calculation
- WAEC pitfalls: Predicting a market day from a given date
- WAEC Pitfalls: Bearing word problems in Nigerian travel contexts
- WAEC pitfalls: Negating a statement that contains all or some
- WAEC Pitfalls: Mensuration word problems in construction contexts
- WAEC Pitfalls: The negative characteristic of a logarithm below one
- WAEC pitfalls: A two-leg journey and the bearing needed to return
- WAEC pitfalls: Recognising the largest square factor inside a surd
- WAEC pitfalls: Leaving out one of the two circular faces of a frustum
- WAEC pitfalls: Rearranging the cosine rule to find an angle
- WAEC pitfalls: Solving a congruence by testing each residue
- WAEC Pitfalls: Earth-as-sphere word problems on flight paths between Nigerian cities
- WAEC pitfalls: Multiplying along a branch and adding across branches
- WAEC Pitfalls: Writing a probability as a fraction
- WAEC past questions: Checking a binary product by converting to base ten
- WAEC past questions: The identity relating tangent to sine and cosine
- WAEC past questions: Several means inserted between two numbers
- WAEC Past Questions: Finding the antilogarithm of numbers greater than 1
- Teach me: How many rows a truth table needs for a given number of statements
Revisit from three weeks ago - Week 12
- Quiz me: Finding a third side from two sides and the included angle
- Word problem: Using logarithms to multiply large numbers in a real calculation
- WAEC pitfalls: The number of terms needed to reach a given sum
- WAEC past questions: Comparing two Nigerian data sets fairly
- WAEC past questions: Using a logarithm to multiply two large numbers
- WAEC past questions: The number of terms needed to reach a stated sum
- WAEC past questions: Recognising direct variation in a table of values
- WAEC past questions: An angle found by combining same-segment with another theorem
- WAEC past questions: Why a sum to infinity fails when the ratio exceeds one
- WAEC Past Questions: Calculations combining standard form and logarithms
- WAEC past questions: The common difference found from two given terms
- WAEC Past Questions: Addition and subtraction of surds
- WAEC past questions: The antilogarithm that returns the final answer
- WAEC past questions: The base in which a stated calculation is correct
- WAEC past questions: A scheduling problem solved on the clock face
- WAEC past questions: Converting a decimal fraction in base two to base ten
- WAEC past questions: A base division checked by converting to base ten
- WAEC past questions: Changing the subject when the letter occurs twice
- WAEC past questions: Choosing the number of classes for a distribution
- WAEC past questions: The converse and the contrapositive of a statement
- WAEC past questions: A sequence that is arithmetic in one part and geometric in another
- WAEC past questions: An equation modulo twelve solved on the clock face
- WAEC past questions: A journey described by two successive bearings
- WAEC past questions: The assumed mean method applied to a frequency table
- WAEC past questions: An inverse variation about workers and the time taken
- WAEC past questions: An indicial equation that becomes a quadratic
- WAEC past questions: Choosing the ratio that matches the sides you are given
- WAEC past questions: The mean deviation of a grouped distribution
- WAEC past questions: A problem giving the equation and asking for the gradient
- WAEC past questions: A bearing problem solved with the cosine rule
- WAEC past questions: Finding a missing value from a stated mean
- WAEC past questions: Simplifying each surd before adding them
- WAEC past questions: An inverse variation about speed and journey time
- WAEC past questions: An expression mixing positive, negative and zero indices
- WAEC past questions: The equation of a line from its drawn graph
- Worked example: An equation modulo 12 solved on the clock face
Revisit from three weeks ago - Week 13
- Quiz me: The great circle distance formula and the radius of the earth
- Practice: The great circle distance between two points
- WAEC pitfalls: Building a modulo addition table
- WAEC past questions: The distance between two points in different quadrants
- WAEC past questions: An answer left in the wrong unit of area or volume
- WAEC past questions: Sketching a quadratic to decide which region satisfies it
- WAEC past questions: Turning an open statement into a closed one
- WAEC past questions: A negative residue quoted outside the permitted range
- WAEC past questions: The cycle length when two markets differ
- WAEC past questions: The fractional index as a root
- WAEC past questions: The second difference of a quadratic sequence
- WAEC past questions: Finding both constants of a partial variation from two pairs
- WAEC past questions: Building a modulo multiplication table
- WAEC past questions: A negative gradient and what it tells you
- WAEC past questions: The assumed mean method for grouped data
- WAEC past questions: The curved surface area of an open cylinder
- WAEC past questions: A tree diagram whose branches are not equally likely
- WAEC past questions: Factorising a four-term expression by grouping
- WAEC Past Questions: Cyclic quadrilaterals
- WAEC Past Questions: Converting base 10 numbers to base 5
- WAEC past questions: The slant height and the vertical height distinguished
- WAEC past questions: The number of years to reach a stated population
- WAEC Past Questions: Taking out the leading coefficient before completing the square
- WAEC Past Questions: Comparing measures of central tendency
- WAEC past questions: Converting base eight to base ten and checking it
- WAEC past questions: Checking a substitution solution in both equations
- WAEC past questions: The next occurrence of a repeating event
- WAEC past questions: Checking a direct base conversion by a second route
- WAEC past questions: The radius of the earth in a distance calculation
- WAEC past questions: The probability that neither of two events happens
- WAEC past questions: A probability problem combining addition and multiplication
- WAEC past questions: The operations of union, intersection and difference together
- WAEC past questions: Predicting a further value from a direct variation
- WAEC past questions: Expanding a bracket squared, and the middle term it produces
- WAEC past questions: Locating a decile on a cumulative frequency curve
- Worked Example: Converting base 5 numbers to base 10
Revisit from three weeks ago - Week 14
- Quiz me: When the mean, the median and the mode each describe data best
- Word problem: Finding what day it will be after a given number of days
- WAEC pitfalls: Finding a missing angle with the sine rule
- WAEC past questions: Borrowing the wrong value when subtracting in a base
- WAEC past questions: A tank or silo built from two familiar solids
- WAEC past questions: A conclusion that does not follow from the implication
- WAEC past questions: Spotting a conclusion that does not follow
- WAEC past questions: Two inequalities with no common solution
- WAEC past questions: Why a grouped median is an estimate
- WAEC past questions: Estimating the mode within the modal class
- WAEC past questions: Rejecting a root that makes a denominator zero
- WAEC past questions: The locus of points a fixed distance from a line
- WAEC past questions: Choosing which circle theorem a diagram calls for
- WAEC Past Questions: Probability word problems in Nigerian contexts
- WAEC past questions: Why casting out nines catches some errors and not others
- WAEC past questions: A coordinate problem set on a described plot
- WAEC Past Questions: Range and quartiles
- WAEC past questions: A sphere problem where the diameter is given instead
- WAEC past questions: Finding how long a target takes at a fixed monthly amount
- WAEC past questions: Dividing one surd by another
- WAEC past questions: The sign of each ratio in the second quadrant
- WAEC past questions: The day a stated number of days after a given date
- WAEC past questions: Adding three numbers in base five
- WAEC past questions: The angle in a semicircle as a special case
- WAEC past questions: The area of a sector when the angle is given in radians
- WAEC past-question style: Choosing between the formula and completing the square
- WAEC Past-Question Style: Clearing the denominators of an equation with algebraic fractions
- WAEC past-question style: The ambiguous case of the sine rule
- WAEC past-question style: A problem combining a bearing with an angle of elevation
- WAEC past-question style: The equation of a line written in the form y equals mx plus c
- WAEC past-question style: Comparing the mean and the median of one distribution
- Teach Me: Circle theorem word problems
Revisit from three weeks ago - Week 15
- Quiz me: Rounding a number to a stated number of significant figures
- Quiz me: Calculating percentage error from a measured and a true value
- Word problem: Giving a measured Nigerian market quantity to sensible accuracy
- Practice set: Estimating an answer by rounding each quantity first
- Exam timing: A timed set of approximation questions
- Word problem: The error in a described market measurement
- Spot my mistake: Rounding twice and drifting away from the true value
- WAEC pitfalls: Dropping trailing zeros that are in fact significant
- Spot my mistake: Dividing by the measured value instead of the true value
- Explain back: Decimal places and significant figures distinguished
- Real-life Nigeria: How many figures an answer ought to carry
- Explain back: Why percentage error is more useful than absolute error
- Teach me: Significant figures, and how to count them
- Worked example: Rounding a number whose leading digits are zeros
- Teach me: Absolute error and percentage error defined
Revisit from three weeks ago - Week 16
- Quiz me: Calculating simple interest over a stated period
- Practice set: The greatest possible error in a rounded measurement
- Exam timing: A timed set of percentage error questions
- Word problem: A Nigerian bank savings problem over several years
- Practice set: Finding the principal, rate or time from the interest
- Exam timing: A timed set of interest and depreciation questions
- WAEC pitfalls: Giving a percentage error as a negative quantity
- Spot my mistake: Applying the simple interest formula to a compound problem
- WAEC pitfalls: Using the rate as a whole number instead of a decimal
- Real-life Nigeria: How errors build up through a multi-step calculation
- Explain back: How compound interest differs from simple interest
- Real-life Nigeria: Depreciation as compound interest with a negative rate
- Worked example: The percentage error left by a rounded calculation
- Teach me: The simple interest formula and the symbols in it
- Worked example: Compound interest worked year by year and then by formula
Revisit from three weeks ago
Algebraic Processes
↑ Jump to week- Week 17
- Quiz me: Making a table of values for a quadratic
- Quiz me: Reading a solution off a graph to a stated accuracy
- WAEC-style revision: quadratic equations
- Word problem: The path of a thrown object modelled by a quadratic
- Practice set: Finding the roots from where the curve cuts the x-axis
- Exam timing: A timed set of quadratic graph questions
- Word problem: A break-even point found from two drawn lines
- Spot my mistake: Plotting a point from the wrong row of the table
- WAEC pitfalls: Joining the plotted points of a curve with straight lines
- Spot my mistake: Reading the intersection off the wrong axis
- Explain back: The line of symmetry and the turning point
- Real-life Nigeria: Reading the maximum or minimum value off the graph
- Explain back: Rearranging an equation so it can be solved from a drawn curve
- Teach me: The shape of a quadratic graph, and what the sign of a does to it
- Worked example: Sketching a quadratic from its factorised form
- Teach me: Solving an equation by finding where two graphs meet
Revisit from three weeks ago - Week 18
- Quiz me: Writing inequalities from a described set of constraints
- Practice set: Solving simultaneous equations graphically
- Exam timing: A timed set of graphical solution questions
- Word problem: A Nigerian transport loading problem as a linear programme
- Practice set: Finding the maximum of an objective function
- Exam timing: A timed set of linear programming questions
- WAEC pitfalls: Giving a graphical answer to more accuracy than the scale allows
- Spot my mistake: Shading the wrong side of a boundary line
- WAEC pitfalls: Ignoring the non-negativity constraints
- Real-life Nigeria: Where a graphical method beats an algebraic one
- Explain back: Shading the feasible region on a graph
- Real-life Nigeria: A production mix problem for a small business
- Worked example: Solving a quadratic graphically by adding a straight line
- Teach me: What linear programming sets out to optimise
- Worked example: Testing the vertices of the feasible region
Revisit from three weeks ago
Matrices & Logical Reasoning
↑ Jump to week- Week 19
- Quiz me: Adding and subtracting matrices of the same order
- Quiz me: Calculating a determinant from the four entries
- Word problem: Recording Nigerian market sales in a matrix
- Practice set: Multiplying a matrix by a scalar
- Exam timing: A timed set of matrix operations
- Word problem: A problem in which a singular matrix leaves no solution
- Spot my mistake: Multiplying matrices whose orders do not match
- WAEC pitfalls: Assuming matrix multiplication is commutative
- Spot my mistake: Forgetting to swap the leading diagonal when inverting
- Explain back: When two matrices can be multiplied at all
- Real-life Nigeria: The identity matrix, and what it does
- Explain back: The inverse of a 2 by 2 matrix and the formula for it
- Teach me: A matrix, and what its order means
- Worked example: Multiplying a 2 by 3 matrix by a 3 by 2 matrix
- Teach me: The determinant of a 2 by 2 matrix
Revisit from three weeks ago - Week 20
- Quiz me: Identifying the coefficient matrix and the constant matrix
- Practice set: Finding the inverse of a given 2 by 2 matrix
- Exam timing: A timed set of determinant and inverse questions
- Word problem: A two-commodity pricing problem solved by matrices
- Practice set: Cramer's rule as an alternative method
- Exam timing: A timed set of matrix-method simultaneous equations
- WAEC pitfalls: Dividing by a determinant of zero
- Spot my mistake: Multiplying by the inverse on the wrong side
- WAEC pitfalls: Writing the coefficients out of order in the matrix
- Real-life Nigeria: What a zero determinant tells you about a system
- Explain back: Solving by multiplying through by the inverse matrix
- Real-life Nigeria: Recognising a system that has no unique solution
- Worked example: Verifying an inverse by multiplying back to the identity
- Teach me: Writing a pair of simultaneous equations in matrix form
- Worked example: Solving a 2 by 2 system by the matrix method
Revisit from three weeks ago
Vectors & Geometrical Transformations
↑ Jump to week- Week 21
- Quiz me: Writing a vector in component form
- Quiz me: The vector joining two points, found from their position vectors
- Word problem: A displacement problem solved with vectors
- Practice set: Multiplying a vector by a scalar
- Exam timing: A timed set of vector component questions
- Word problem: Dividing a line in a given ratio using vectors
- Spot my mistake: Adding vectors by adding their magnitudes
- WAEC pitfalls: Dropping the negative sign when reversing a vector
- Spot my mistake: Subtracting the position vectors in the wrong order
- Explain back: Adding and subtracting vectors by components
- Real-life Nigeria: The resultant velocity of a boat crossing a river
- Explain back: The midpoint of a line segment in vector form
- Teach me: A vector as a magnitude together with a direction
- Worked example: Finding the magnitude and direction of a vector
- Teach me: The position vector of a point relative to the origin
Revisit from three weeks ago - Week 22
- Quiz me: Finding the image of a point under a translation
- Practice set: Finding a point that divides a segment internally
- Exam timing: A timed set of position vector questions
- Word problem: Describing the move of an object on a described plan
- Practice set: Combining two translations into one
- Exam timing: A timed set of translation questions
- WAEC pitfalls: Confusing a position vector with a displacement vector
- Spot my mistake: Adding the column vector to the wrong coordinate
- WAEC pitfalls: Writing a column vector with its components reversed
- Real-life Nigeria: The centroid of a triangle found from its vertices
- Explain back: Why translation preserves both shape and size
- Real-life Nigeria: Translation in a pattern or tiling design
- Worked example: Proving three points are collinear with vectors
- Teach me: A translation described by a column vector
- Worked example: Finding the translation that maps one shape onto another
Revisit from three weeks ago - Week 23
- Quiz me: Reflecting a point in the x-axis and in the y-axis
- Quiz me: Rotating a point 90 degrees about the origin
- Word problem: A symmetry problem taken from a described Nigerian pattern
- Practice set: Reflecting a shape in a line parallel to an axis
- Exam timing: A timed set of reflection questions
- Word problem: A turning problem taken from a described machine part
- Spot my mistake: Reflecting in an axis but keeping the original sign
- WAEC pitfalls: Reflecting in y equals x by negating instead of swapping
- Spot my mistake: Rotating clockwise when the question says anticlockwise
- Explain back: Reflecting a point in the line y equals x
- Real-life Nigeria: The lines of symmetry of a described figure
- Explain back: Rotating a point 180 degrees about the origin
- Teach me: Reflection and the mirror line
- Worked example: Finding the mirror line from an object and its image
- Teach me: Rotation, and its centre, angle and direction
Revisit from three weeks ago - Week 24
- Quiz me: Finding the image of a point under a given enlargement
- Practice set: Rotating a shape about a point other than the origin
- Exam timing: A timed set of rotation questions
- Word problem: Scaling a described building plan up to real size
- Practice set: The effect of an enlargement on area
- Exam timing: A timed set of enlargement questions
- WAEC pitfalls: Assuming a positive angle of rotation means clockwise
- Spot my mistake: Measuring the scale factor from the wrong centre
- WAEC pitfalls: Assuming a negative scale factor simply shrinks a shape
- Real-life Nigeria: Rotational symmetry and its order
- Explain back: What a fractional scale factor does to a shape
- Real-life Nigeria: Scale drawings and the scales printed on maps
- Worked example: Finding the angle of rotation from an object and its image
- Teach me: Enlargement, and its centre and scale factor
- Worked example: Finding the centre of enlargement from object and image
Revisit from three weeks ago
Geometry, Mensuration & Trigonometry
↑ Jump to week- Week 25
- Quiz me: Choosing class boundaries and drawing the bars of a histogram
- Explain back: Splitting a composite solid into shapes you can calculate
- Spot My Mistake: Expansion of algebraic expressions
- Spot My Mistake: Modular arithmetic calendar and day-of-week problems
- Spot my mistake: Adding the characteristics wrongly when the numbers differ in size
- Spot My Mistake: Volume of a cylinder
- Spot my mistake: Using the slant height where the vertical height is needed
- Spot my mistake: The cosine of the latitude in the distance formula
- Spot My Mistake: Sets word problems in Nigerian school survey contexts
- Spot my mistake: The exterior angle of a cyclic quadrilateral
- Spot my mistake: Using class limits where class boundaries are required
- Spot My Mistake: Angle at the centre and angle at the circumference
- Spot my mistake: Leaving gaps between the bars of a histogram
- Spot My Mistake: Converting units correctly in mensuration problems
- Spot My Mistake: The relationship between indices and logarithms
- Spot My Mistake: The sine rule stated
- Spot my mistake: Identifying the right-angled triangle hidden inside a solid
- Spot my mistake: The truth table for 'if p then q'
- Spot my mistake: Measuring a bearing clockwise from the wrong reference line
- Spot My Mistake: Inverse variation
- Spot my mistake: Confusing joint variation with partial variation
- Explain back: Why a partial variation has a fixed part and a varying part
- Explain back: Repeated division by five, reading the remainders upward
- Explain back: Reading the solutions as the points where a line meets a curve
- Explain It Back: Describing the earth as a sphere: points and lines
- Explain back: Finding an endpoint when the midpoint and one end are known
- Explain It Back: Number base word problems in everyday Nigerian contexts
- Explain It Back: Surface area of a cone
- Explain back: Constructing 60, 90 and 45 degrees with ruler and compasses
- Explain back: Repeated multiplication of the fractional part by the new base
- Explain It Back: Surface area of a sphere
- Explain back: Rearranging the cosine rule to find an unknown angle
- Teach me: Converting an acute angle bearing to a three-figure bearing
Revisit from three weeks ago
Calculus
↑ Jump to week- Week 26
- Quiz me: The increment notation, and what happens as h tends to zero
- Word problem: Finding an instantaneous speed from a distance function
- Practice set: Differentiating x cubed from first principles
- Exam timing: A timed set of first-principles derivations
- Spot my mistake: Cancelling h before the limit has been taken
- WAEC pitfalls: Leaving h in the final answer
- Explain back: Differentiating x squared from first principles
- Real-life Nigeria: Why first principles justifies the power rule
- Teach me: The limit definition of the derivative
- Worked example: Differentiating a linear function from first principles
Revisit from three weeks ago - Week 27
- Quiz me: Differentiating a sum of powers term by term
- Word problem: The derivative of a profit function in a Nigerian business
- Practice set: Differentiating polynomials with fractional indices
- Exam timing: A timed set of polynomial differentiations
- Spot my mistake: Forgetting to reduce the index by one
- WAEC pitfalls: Differentiating a product as though it were a sum
- Explain back: Why the derivative of a constant is zero
- Real-life Nigeria: Finding the gradient function of a given polynomial
- Teach me: The power rule for differentiation
- Worked example: Differentiating a polynomial with negative indices
Revisit from three weeks ago - Week 28
- Quiz me: Evaluating the derivative at a given value of x
- Word problem: The steepness of a described road modelled by a curve
- Practice set: Finding where a curve has a given gradient
- Exam timing: A timed set of gradient-at-a-point questions
- Spot my mistake: Reading the gradient off the curve instead of off the derivative
- WAEC pitfalls: Substituting into the original function instead of the derivative
- Explain back: The gradient of a chord set against the gradient of a tangent
- Real-life Nigeria: The equation of the normal to a curve at a point
- Teach me: The gradient of a curve as the gradient of its tangent
- Worked example: Finding the equation of a tangent at a point
Revisit from three weeks ago - Week 29
- Quiz me: Solving the derivative equal to zero to locate stationary points
- Quiz me: Relating the rate of change of volume to that of radius
- Word problem: Maximising the area of a rectangular plot with fixed fencing
- Practice set: Finding the maximum value a function reaches
- Exam timing: A timed set of maximum and minimum problems
- Word problem: A tank filling problem solved with related rates
- Spot my mistake: Calling every stationary point a maximum
- WAEC pitfalls: Omitting to test the nature of a stationary point
- Spot my mistake: Differentiating with respect to the wrong variable
- Explain back: The second derivative test for a maximum or a minimum
- Real-life Nigeria: Minimising the cost of a described Nigerian container
- Explain back: The chain rule connecting two related rates
- Teach me: Stationary points, and where the derivative is zero
- Worked example: Sketching a cubic using its stationary points
- Teach me: What dy by dx means as a rate of change
Revisit from three weeks ago - Week 30
- Quiz me: The rule for integrating a power of x
- Practice set: Practice on two rates of change linked by a chain rule
- Exam timing: A timed set of rate of change problems
- Word problem: Recovering a distance function from a velocity function
- WAEC pitfalls: Substituting the numbers before differentiating
- Spot my mistake: Forgetting the constant of integration in an indefinite integral
- Real-life Nigeria: A rate of change problem taken from Nigerian manufacturing
- Explain back: Why the constant of integration is needed
- Worked example: A ladder sliding down a wall as a related-rate problem
- Teach me: Integration as the reverse of differentiation
Revisit from three weeks ago - Week 31
- Quiz me: Evaluating a definite integral between two limits
- Practice set: Integrating expressions with negative and fractional indices
- Exam timing: A timed set of polynomial integrations
- Word problem: The area of a described plot bounded by a curve
- Practice set: The area between two curves
- Exam timing: A timed set of definite integral evaluations
- WAEC pitfalls: Dividing by the original index instead of the new one
- Spot my mistake: Subtracting the limits in the wrong order
- WAEC pitfalls: Ignoring an area that lies below the axis
- Real-life Nigeria: Finding a curve from its gradient function and one point on it
- Explain back: Why the constant of integration cancels in a definite integral
- Real-life Nigeria: A total quantity found from a rate function over an interval
- Worked example: Integrating a polynomial term by term
- Teach me: The definite integral and its limits
- Worked example: The area between a curve and the x-axis
Revisit from three weeks ago
Statistics
↑ Jump to week- Week 32
- Quiz me: The union and the intersection of two sets defined
- Practice: A circle theorem problem set in a described real object
- Practice: The characteristic of a number between nought and one
- Practice: Multiplication in modular arithmetic
- Practice: Drawing histograms
- Practice: Reducing a large number to its residue
- Practice: The triangle that a bearing problem hides
- Practice: When an implication counts as false
- Practice: The binary multiplication table and why it is short
- Practice: Writing the sine rule the way round that suits the unknown
- Practice: The amplitude and period of a sine curve
- Practice: Bringing a negative number into its residue class
- Practice: The truth table for conjunction and for disjunction
- Practice: Mutually exclusive events and adding their probabilities
- Practice: The equation of a line from its two intercepts
- Practice: Turning an everyday Nigerian statement into logical symbols
- Practice: Borrowing across two columns in a base subtraction
- Practice: The union and the intersection of two sets
- Practice: Forming a joint variation equation with a constant
- Practice: Solving one linear and one quadratic equation simultaneously
- Practice: Distance along a parallel far from the equator
- Practice: An hour hand as arithmetic modulo twelve
- Practice: The volume of a hemisphere sitting on a cylinder
- Practice: Standard deviation of ungrouped data
- Spot my mistake: The amplitude and the period of a sine curve
- Explain back: Why standard deviation measures spread better than the range does
- Explain back: Why opposite angles of a cyclic quadrilateral add to 180 degrees
- Explain back: The condition on the common ratio for a sum to infinity to exist
- Explain back: Recognising direct variation from a table of values
- Explain back: Why grouped data gives an estimated rather than an exact median
- Explain back: Rejecting a root that makes no sense in the situation described
- Explain It Back: Converting base 2 numbers to base 10
- Explain It Back: Great circles and small circles
- Teach me: Bringing a negative number into the correct residue class
Revisit from three weeks ago - Week 33
- Quiz me: Building a cumulative frequency table
- Word problem: Reading the number above a threshold from an ogive
- Practice set: Estimating quartiles and percentiles from an ogive
- Exam timing: A timed set of cumulative frequency questions
- Spot my mistake: Plotting cumulative frequency at the class midpoint
- WAEC pitfalls: Reading the quartiles off the wrong axis
- Explain back: Plotting a cumulative frequency curve at the upper class boundaries
- Real-life Nigeria: Comparing two distributions from their ogives
- Teach me: Drawing a frequency polygon from a frequency table
- Worked example: Estimating the median from a cumulative frequency curve
Revisit from three weeks ago - Week 34
- Quiz me: Calculating the mean before finding the deviations
- Word problem: Comparing the consistency of two Nigerian farmers' yields
- Spot my mistake: Letting positive and negative deviations cancel
- Explain back: Why the absolute value is taken in mean deviation
- Teach me: Mean deviation, and what it measures
Revisit from three weeks ago - Week 35
- Quiz me: Calculating the angle for each sector of a pie chart
- Practice set: The mean deviation of grouped data
- Exam timing: A timed set of mean deviation calculations
- Word problem: Presenting a Nigerian household budget as a pie chart
- WAEC pitfalls: Dividing by the wrong number of items
- Spot my mistake: Drawing sector angles that do not total 360 degrees
- Real-life Nigeria: Mean deviation set beside standard deviation
- Explain back: Drawing a bar chart with equal bar widths
- Worked example: The mean deviation of an ungrouped data set
- Teach me: When a pie chart suits data better than a bar chart
Revisit from three weeks ago - Week 36
- Quiz Me: Subtraction of numbers in different bases
- Practice set: Converting between a pie chart and a bar chart
- Exam timing: A timed set of chart drawing and reading questions
- WAEC pitfalls: Comparing two pie charts of different totals directly
- Real-life Nigeria: Choosing the right chart for a given set of data
- Worked example: Reading a quantity from a pie chart given the total
Revisit from three weeks ago