G3N
NERDC · 45 topics

Mathematics

G3N tutors you through the full NERDC Mathematics syllabus offline — from Theme 1: Number and Numeration, Theme 2: Basic Operations, Theme 3: Measurement and more — with adaptive lessons, instant quizzes, flashcards and exam-ready summaries.

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Syllabus

What you’ll cover in Mathematics.

The complete topic outline G3N teaches, mapped to the NERDC curriculum.

Primary 4

4 topics
Theme 1: Number and Numeration
  • Understanding Numbers
    • Identify whole numbers from 0 to 10,000 as the set of non-negative integers used for counting
    • Apply place value system: identify the place value of digits in units, tens, hundreds, and thousands positions
    • Distinguish between the place value (position worth: 10⁰, 10¹, 10², 10³) and face value (the digit itself: 0-9)
    • Read and write numbers from 0-10,000 in both numerals and words accurately
    • Compare two numbers using symbols: greater than (>), less than (<), equal to (=); order sets of three or more numbers
    • Identify number patterns: skip counting (by 2s, 5s, 10s), arithmetic sequences with common differences
    • Extend sequences and predict the next terms in a pattern using addition or multiplication rules
    • Represent numbers on a number line and use it to show order, magnitude, and number relationships
  • Fractions
    • Define fractions as parts of a whole: numerator (number of parts) and denominator (total equal parts)
    • Identify and classify simple fractions: unit fractions (1/2, 1/3, 1/4), proper fractions (numerator < denominator)
    • Represent fractions using visual models: pie charts divided into equal parts, number lines with fractional markings
    • Identify fractions of a set: select part of a group of objects to represent a given fraction
    • Compare simple fractions with the same denominator using inequality symbols (>, <, =)
    • Order three or more fractions with like denominators from smallest to largest
    • Identify and generate equivalent fractions by multiplying both numerator and denominator by the same number
    • Convert between different representations: fractions to diagrams, diagrams to fractions, fractions to words
Theme 2: Basic Operations
  • Addition and Subtraction
    • Add 3-digit numbers with regrouping: regroup ones to tens, tens to hundreds; verify with estimation
    • Add 3-digit numbers without regrouping: align digits by place value and add column by column
    • Subtract 3-digit numbers with regrouping: borrow from higher place values when needed
    • Subtract 3-digit numbers without regrouping: align and subtract each column, checking answers by addition
    • Apply addition properties: commutative (a+b=b+a), associative ((a+b)+c=a+(b+c)), identity (a+0=a)
    • Apply subtraction properties: understand subtraction is not commutative (a-b ≠ b-a), identity (a-0=a)
    • Solve one-step word problems involving addition and subtraction using real-world contexts
    • Apply mental arithmetic strategies: compensating (round then adjust), breaking numbers apart, using patterns
  • Multiplication and Division
    • Understand multiplication as repeated addition: 3 × 4 means 3 groups of 4
    • Multiply by 2, 3, 4, 5, and 10 using skip counting, arrays, and number lines
    • Apply multiplication properties: commutative (a×b=b×a), associative ((a×b)×c=a×(b×c)), identity (a×1=a), zero property (a×0=0)
    • Understand division as repeated subtraction: how many groups of 3 in 12? as inverse of multiplication
    • Divide using arrays and grouping: 12 ÷ 3 means dividing 12 into 3 equal groups
    • Apply division concepts to practical sharing problems: distribute equally among groups
    • Identify the relationship between multiplication and division: if 3×4=12, then 12÷3=4 and 12÷4=3
    • Solve multiplication and division word problems using real-world contexts (groups, arrays, measurement)
Theme 3: Measurement
  • Length and Distance
    • Measure length using standard units: centimeters (cm) for small objects, meters (m) for larger distances
    • Use measuring instruments correctly: position the metre rule with zero mark at the start; read measurements at eye level
    • Identify relationships between units: 1 meter = 100 centimeters; 1 meter = 10 decimeters
    • Compare and order lengths: arrange objects or distances by measuring and using inequality symbols
    • Estimate lengths before measuring: develop benchmarks (height of a door ≈ 2m, width of a fingernail ≈ 1cm)
    • Perform addition and subtraction with measurements: combine lengths (3m 45cm + 2m 30cm), find differences
    • Solve practical problems involving length: finding perimeter of rectangles, planning distances
    • Convert measurements: express 250cm as 2m 50cm; express 1m 80cm in centimeters
  • Mass and Capacity
    • Measure mass using kilograms (kg) for heavier objects and grams (g) for lighter objects
    • Identify relationships between units: 1 kilogram = 1000 grams
    • Use balance scales and electronic scales correctly; understand accuracy and limitations
    • Measure capacity in liters (l) for larger volumes and milliliters (ml) for smaller volumes
    • Identify relationships between capacity units: 1 liter = 1000 milliliters
    • Compare and order masses: determine which object is heavier by measuring with appropriate units
    • Compare and order capacities: determine which container holds more by measuring volumes
    • Perform addition and subtraction with mass and capacity: combine quantities (2kg + 1500g), find differences
  • Time
    • Tell time to the hour on analogue clocks: identify positions of hour and minute hands
    • Tell time to the half-hour: recognize when minute hand points to 6 (30 minutes past)
    • Identify days of the week in order and recognize recurring 7-day pattern
    • Identify months of the year and their sequence; recognize 12-month yearly cycle
    • Identify seasons and their characteristics: when they occur, associated months and weather patterns
    • Sequence events in time: order activities by what happens first, next, last; use time language
    • Calculate simple time intervals: how long from 9am to 12pm? from 2:30pm to 4:00pm?
    • Read and use calendars: find specific dates, count days between events, identify day of week for a date
Theme 4: Geometry
  • 2D Shapes
    • Identify circles by their characteristic curved shape with no corners or straight sides
    • Identify triangles as 3-sided polygons with 3 vertices; classify by side length (equilateral, isosceles, scalene)
    • Identify rectangles as 4-sided polygons with 4 right angles and opposite sides equal
    • Identify squares as special rectangles with all 4 sides equal length and 4 right angles
    • Identify pentagons (5 sides), hexagons (6 sides), and octagons (8 sides); recognize regular vs. irregular polygons
    • Describe shape properties: number of sides, vertices, angles; straight vs. curved edges
    • Sort shapes by attributes: number of sides, shape of angles, line symmetry, regularity
    • Compare and contrast shapes: identify similarities and differences between different 2D shapes
  • 3D Shapes
    • Identify cubes as 3D shapes with 6 square faces, 12 edges, and 8 vertices; recognize all edges are equal
    • Identify cuboids (rectangular prisms) as 3D shapes with 6 rectangular faces, 12 edges, and 8 vertices
    • Identify cylinders as 3D shapes with 2 circular faces and 1 curved surface; recognize they have no vertices or edges
    • Identify spheres as perfectly round 3D shapes with no faces, edges, or vertices; all points equidistant from center
    • Identify pyramids as 3D shapes with a polygonal base and triangular faces meeting at an apex (vertex)
    • Describe 3D shape properties: number of faces, edges, vertices, shape of faces
    • Compare and contrast 3D shapes: identify similarities (both have faces) and differences (different numbers of vertices)
    • Build 3D shapes using materials: construct cubes, cuboids, and other shapes with paper, straws, or blocks

Primary 5

5 topics
Theme 1: Number and Numeration
  • Whole Numbers
    • Identify and read whole numbers from 0 to 100,000 in numerals and words
    • Identify place value of each digit: ones, tens, hundreds, thousands, ten-thousands positions
    • Determine the value of a digit: multiply the digit by its place value (e.g., 5 in 50,000 has value 50,000)
    • Compare numbers using symbols (>, <, =) and order sets of numbers from smallest to largest or vice versa
    • Round numbers to the nearest 10, 100, and 1,000 using place value and the rounding digit rule
    • Recognize Roman numerals I to XX and convert between Roman numerals and Arabic numerals
    • Identify even and odd numbers; understand divisibility by 2 (even) and odd numbers
    • Identify prime numbers (1, 3, 5, 7, 11, 13, 17, 19) and composite numbers
  • Fractions and Decimals
    • Identify and classify fractions: proper (1/5, 3/4), improper (5/4, 7/3), and mixed numbers (1 2/3)
    • Compare and order fractions with the same denominator: use inequality symbols (1/3 < 2/3 < 3/3)
    • Identify equivalent fractions: 1/2 = 2/4 = 3/6; generate equivalents by multiplying or dividing
    • Simplify fractions to lowest terms: divide both numerator and denominator by their GCD
    • Understand decimal notation: recognize that 0.5 means 5 tenths (5/10), 0.25 means 25 hundredths (25/100)
    • Read and write decimals to tenths and hundredths: 0.7, 0.45, 1.85
    • Compare and order decimals: 0.3 < 0.5 < 0.8; recognize that 0.50 = 0.5
    • Convert between fractions and decimals: 1/4 = 0.25, 3/5 = 0.6; verify using division
Theme 2: Basic Operations
  • Addition and Subtraction with larger numbers
    • Add 4-digit and 5-digit numbers with regrouping using the column method; verify with estimation
    • Subtract 4-digit and 5-digit numbers with regrouping; borrow from multiple columns when necessary
    • Apply addition strategies: use commutative property to change order (e.g., 5000+237 or 237+5000), break numbers into parts
    • Apply mental calculation strategies: compensate (if adding 99, add 100 then subtract 1), use complements to 10 or 100
    • Estimate sums and differences by rounding to nearest 10, 100, or 1,000; use estimates to check reasonableness
    • Solve multi-step word problems requiring addition and subtraction: plan solution, show work, verify answer
    • Add and subtract money: find totals of purchases, calculate change, compare prices
    • Apply operations to measurements: combine lengths (1m 45cm + 2m 60cm), find temperature differences
  • Multiplication and Division
    • Recall and apply multiplication tables 2 to 10 fluently and automatically
    • Multiply a 2-digit number by a 1-digit number using arrays, area models, or the distributive property
    • Apply partial products strategy: 23 × 4 = (20 × 4) + (3 × 4) = 80 + 12 = 92
    • Perform long division with 1-digit divisors: use repeated subtraction or standard algorithm
    • Interpret remainders: express as fractions (12 ÷ 5 = 2 R2 = 2 2/5), round up or down based on context
    • Apply division to practical problems: share equally among groups, measure how many groups fit
    • Use the relationship between multiplication and division to solve problems: if 4 × 7 = 28, then 28 ÷ 7 = 4
    • Apply properties of multiplication: commutative (4×5=5×4), associative ((2×3)×4=2×(3×4)), zero property
Theme 3: Measurement
  • Length, Mass, and Capacity
    • Convert between metric units: 1m = 100cm, 1km = 1000m; express measurements in different units
    • Perform calculations with measurements: add 2m 45cm + 3m 30cm = 5m 75cm
    • Convert between mass units: 1kg = 1000g; express 2kg 500g as 2500g
    • Perform calculations with mass: combine weights (1.5kg + 2.3kg), find mass differences
    • Convert between capacity units: 1L = 1000mL; express 2L 250mL as 2250mL
    • Perform calculations with capacity: combine volumes, determine remaining liquid
    • Calculate perimeter of rectangles and squares: add all side lengths or use formulas (P=2l+2w for rectangles, P=4s for squares)
    • Calculate area of rectangles and squares: use the formula A = length × width; apply to square units
  • Time
    • Tell time to the nearest minute on analogue clocks; read minute markings accurately
    • Convert between 12-hour and 24-hour (military) time: 3:30pm = 15:30 in 24-hour time
    • Calculate time intervals using a timeline or mental calculation: from 2:45pm to 5:15pm is 2 hours 30 minutes
    • Identify leap years (divisible by 4, with exceptions); count days in each month
    • Use calendars to find specific dates and calculate days between events
    • Understand relationship between time units: 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours
    • Read timetables for transport (bus, train) or school schedules; plan activities using timetables
    • Calculate durations of events: find how long from start time to end time using hour or minute intervals
  • Money
    • Identify Nigerian currency: naira (N) and kobo (K); recognize coin and note denominations
    • Express money amounts using correct notation: N50.50 (50 naira, 50 kobo)
    • Perform addition and subtraction with money: find totals of purchases, calculate change
    • Multiply money amounts: calculate total cost (price per item × quantity of items)
    • Divide money amounts: split costs equally among people, find price per unit
    • Make change from given amounts: determine coins/notes needed to make exact change
    • Solve word problems involving money: budgeting, comparing prices, calculating profit and loss
    • Use money calculations in real situations: shopping, saving, comparing value
Theme 4: Geometry
  • 2D and 3D Shapes
    • Identify properties of triangles: classify by sides (equilateral, isosceles, scalene) and by angles (right, acute, obtuse)
    • Identify properties of quadrilaterals: rectangles (opposite sides equal, 4 right angles), squares (all sides equal, 4 right angles), parallelograms, trapezoids
    • Identify properties of pentagons (5 sides), hexagons (6 sides), and regular vs. irregular polygons
    • Calculate interior angles of triangles: understand that sum = 180°; use to find missing angles
    • Identify and draw lines of symmetry on 2D shapes; recognize shapes with rotational symmetry
    • Identify reflections and reflected images; understand that reflections are mirror images
    • Plot and identify coordinates in the first quadrant: point (3,4) is 3 units right, 4 units up
    • Apply coordinate geometry to solve problems: find distance between points, identify shapes from coordinates
Theme 5: Data Handling
  • Data Collection and Representation
    • Create tally charts to record data: use tally marks in groups of 5 (||||) for easy counting
    • Organize data in frequency tables: list items with their counts
    • Draw and interpret bar charts: use consistent scale, label axes clearly (horizontal and vertical)
    • Draw and interpret pictographs: use symbols to represent data, choose appropriate scale (each symbol = 2 or 5 items)
    • Convert between different data representations: create bar chart from tally chart, pictograph from table
    • Read and interpret bar charts: identify highest/lowest values, compare frequencies
    • Read and interpret pictographs: multiply symbol count by scale to find actual values
    • Identify the mode (most frequent value) in a dataset from frequency table or chart

Primary 6

5 topics
Theme 1: Number and Numeration
  • Whole Numbers and Decimals
    • Read and write whole numbers to 1,000,000 in numerals and words; identify place values (units to millions)
    • Compare and order whole numbers using inequality symbols; arrange in ascending/descending order
    • Round whole numbers to the nearest 10, 100, 1,000, or 10,000 using rounding rules
    • Understand decimal place value: tenths (0.1), hundredths (0.01), thousandths (0.001)
    • Read and write decimal numbers to 2 decimal places with understanding: 3.25 is 3 ones + 2 tenths + 5 hundredths
    • Compare and order decimal numbers: 0.25 < 0.5 < 0.75; understand that 0.5 = 0.50 = 0.500
    • Round decimal numbers to the nearest whole number or to 1 decimal place
    • Use decimals in context: express measurements (1.5m), money (N50.75), and data
  • Fractions
    • Identify and classify fractions: proper (3/8), improper (7/5), mixed numbers (2 3/8), and unit fractions (1/n)
    • Add and subtract fractions with like (same) denominators: 1/4 + 2/4 = 3/4
    • Find fractions of quantities: calculate 3/4 of 20 by dividing 20 ÷ 4, then multiplying by 3 = 15
    • Generate and identify equivalent fractions: 1/2 = 2/4 = 3/6; simplify by dividing by GCD
    • Compare fractions with unlike denominators by finding common denominators or converting to decimals
    • Convert fractions to decimals and percentages: 1/4 = 0.25 = 25%
    • Order fractions from smallest to largest using various strategies (common denominators, decimal conversions)
    • Understand improper fractions and mixed numbers: 7/4 = 1 3/4; convert between representations
Theme 2: Basic Operations
  • Operations with Large Numbers
    • Add and subtract 6-digit numbers accurately using the column method with multiple regrouping steps
    • Multiply 3-digit numbers by 2-digit numbers using the standard algorithm or area model
    • Perform long division with 2-digit divisors using the standard algorithm (divide, multiply, subtract, bring down)
    • Interpret remainders as whole numbers, fractions, or decimals depending on the problem context
    • Add and subtract decimal numbers (to 2 decimal places): align decimal points, carry and borrow as needed
    • Multiply and divide decimal numbers: understand how the decimal point moves in the answer
    • Apply operations to solve multi-step word problems requiring multiple calculations
    • Use estimation and mental math strategies to check if answers are reasonable
Theme 3: Measurement
  • Metric Measurements
    • Convert between metric units confidently: km↔m, m↔cm, g↔kg, mL↔L, using multiplication/division by powers of 10
    • Perform multi-step conversions: convert 2.5km to meters, then to centimeters
    • Calculate perimeter of various shapes: triangles (add all sides), rectangles (2l+2w), irregular shapes (sum all sides)
    • Calculate area of rectangles and right triangles: rectangles (l×w), triangles (1/2 × base × height)
    • Calculate volume of rectangular solids using the formula: V = length × width × height
    • Identify and interpret scale on maps: if 1cm represents 10km, find actual distances from map measurements
    • Apply scale factors: enlarge or reduce measurements by a given scale factor
    • Solve practical problems involving area and volume: carpeting a room, filling a container
  • Time, Money and Temperature
    • Calculate time differences accurately: from 9:35am to 2:50pm = 5 hours 15 minutes
    • Convert between time units: minutes to seconds, hours to minutes, days to hours
    • Perform calculations with time: add 2 hours 30 minutes + 1 hour 45 minutes = 4 hours 15 minutes
    • Understand 12-hour and 24-hour time formats; convert between them (3:15pm = 15:15)
    • Perform currency conversions and calculate with money: total costs, change from purchase, exchange rates (if applicable)
    • Apply percentage increases and decreases to money: calculate discount prices, tax on purchases
    • Read temperature scales: Celsius (common in Nigeria); identify positive and negative temperatures
    • Calculate temperature changes: find the difference between two temperatures
Theme 4: Geometry
  • Advanced Geometric Concepts
    • Classify triangles by sides: equilateral (3 equal sides), isosceles (2 equal sides), scalene (no equal sides)
    • Classify triangles by angles: acute (all angles < 90°), right (one 90° angle), obtuse (one angle > 90°)
    • Identify properties of quadrilaterals: rectangles (4 right angles, opposite sides equal), squares (all sides equal, 4 right angles), parallelograms, trapezoids
    • Measure angles using a protractor; identify acute (< 90°), right (= 90°), obtuse (> 90°), and straight (= 180°) angles
    • Identify lines of symmetry in 2D shapes; count total lines of symmetry for regular shapes
    • Identify rotational symmetry: recognize when a shape looks the same after rotating less than 360°
    • Identify transformations: translations (slides), reflections (flips), rotations (turns); describe using coordinates
    • Plot points on a coordinate system in all four quadrants; identify coordinates of given points
Theme 5: Data Handling and Algebra
  • Statistics and Probability
    • Create line graphs by plotting points and connecting with straight lines; interpret trends shown
    • Create and interpret pie charts: understand that each section represents a fraction of the total
    • Calculate the mean (average): sum all values then divide by the number of values
    • Identify the median (middle value) by arranging data in order; find middle value(s)
    • Identify the mode (most frequent value) in a dataset
    • Calculate the range: find the difference between the highest and lowest values
    • Interpret data using statistical measures: compare data sets using mean, median, mode, range
    • Understand probability as likelihood: express as fractions, decimals, or percentages (0 to 1 scale)
  • Introduction to Algebra
    • Identify number patterns and sequences: describe the rule (add 3 each time, multiply by 2)
    • Extend sequences using the identified rule; find the next 3 terms in a sequence
    • Use letters to represent unknown numbers: n = 5, x = 10; understand letters as variables
    • Write simple equations to represent situations: if x is the unknown, y = x + 3 means 'y is 3 more than x'
    • Solve simple equations using inverse operations: if x + 5 = 12, then x = 12 - 5 = 7
    • Identify function relationships: input-output tables showing how one quantity changes with another
    • Write rules for functions: if input is n, then output is 2n + 1; create and complete input-output tables
    • Apply algebraic thinking to solve problems: represent unknown values with variables, use equations

JSS 1

5 topics
Theme 1: Number Systems and Operations
  • Integers and Number Operations
    • Define whole numbers as natural numbers (1, 2, 3...) plus zero; represent on a number line
    • Define integers as whole numbers and their negatives (...-3, -2, -1, 0, 1, 2, 3...); understand positive and negative values
    • Locate integers on a number line with zero at center; use opposites (3 and -3 are opposites, 3 units from zero)
    • Compare integers using inequality symbols; order sets of integers from smallest to largest
    • Add integers: positive + positive = positive; negative + negative = negative; use a number line for mixed signs
    • Subtract integers using the rule: a - b = a + (-b); change subtraction to addition of the opposite
    • Multiply integers: positive × positive = positive; negative × negative = positive; positive × negative = negative
    • Divide integers using the same sign rules as multiplication; understand division by zero is undefined
  • Fractions, Decimals, and Percentages
    • Perform operations with fractions: add, subtract with unlike denominators by finding LCD (Least Common Denominator)
    • Multiply fractions: multiply numerators and denominators; simplify before or after multiplying
    • Divide fractions by multiplying by the reciprocal: a/b ÷ c/d = a/b × d/c
    • Perform operations with decimals: add, subtract (align decimal points), multiply (count decimal places in answer)
    • Divide decimals: use long division; move decimal point in divisor to make whole number
    • Convert between fractions and decimals: 1/4 = 0.25 (divide numerator by denominator)
    • Convert fractions and decimals to percentages: multiply by 100 (0.25 = 25%; 1/4 = 25%)
    • Calculate percentages of quantities: find 20% of 80 by converting to decimal (0.20 × 80 = 16)
Theme 2: Estimation, Approximation, and Significant Figures
  • Rounding and Estimation
    • Round to decimal places: identify the digit in that place; look at the next digit (< 5 round down, ≥ 5 round up)
    • Round to significant figures (sf): identify the required sf by counting from the first non-zero digit
    • Apply rounding rules: 7.456 rounded to 2 sf = 7.5; 0.04563 rounded to 2 sf = 0.046
    • Estimate quantities by rounding to convenient values: 47 × 23 ≈ 50 × 20 = 1000
    • Use estimation to check reasonableness of answers: verify that calculations are approximately correct
    • Understand degree of accuracy: a measurement of 50cm might be accurate to the nearest cm (between 49.5 and 50.5)
    • Apply significant figures to scientific data: understand precision limitations of measurements
    • Estimate using one or more significant figures based on context: engineering requires more precision than rough calculations
Theme 3: Indices and Standard Form
  • Powers and Indices
    • Define powers (exponents/indices): 2³ means 2 × 2 × 2 = 8; the base is 2, the index is 3
    • Calculate powers: 2² = 4, 3² = 9, 2³ = 8, 10⁴ = 10,000; recognize squares and cubes
    • Apply the law of indices for multiplication: aᵐ × aⁿ = aᵐ⁺ⁿ (e.g., 2² × 2³ = 2⁵)
    • Apply the law of indices for division: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (e.g., 2⁵ ÷ 2² = 2³)
    • Apply the law of indices for powers of powers: (aᵐ)ⁿ = aᵐⁿ (e.g., (2²)³ = 2⁶)
    • Recognize zero and negative indices: a⁰ = 1 (for a ≠ 0); a⁻ⁿ = 1/aⁿ (e.g., 2⁻² = 1/4)
    • Express very large numbers in standard form (scientific notation): 4,200,000 = 4.2 × 10⁶
    • Express very small numbers in standard form: 0.00042 = 4.2 × 10⁻⁴
Theme 4: Measurement and Geometry
  • Measurements and Mensuration
    • Convert metric units using powers of 10: 1km = 10³m, 1m = 10²cm, 1cm = 10mm
    • Convert between derived metric units: 1m² = 10⁴cm²; 1cm³ = 10⁻⁶m³
    • Calculate perimeter of irregular polygons: add all side lengths; use known relationships for regular polygons
    • Calculate area of rectangles (l×w), triangles (1/2×b×h), parallelograms (b×h), trapezoids (1/2×(a+b)×h)
    • Calculate volume of rectangular prisms: V = l×w×h; volume of triangular prisms: V = (1/2×b×h)×l
    • Calculate surface area: find total area of all faces of 3D shapes
    • Interpret scale on maps and diagrams: if 1cm = 5km, find actual distances by measuring on map
    • Apply scale factors to enlarge or reduce measurements: multiply all dimensions by the scale factor
  • Geometry
    • Identify angles: adjacent (next to each other), vertically opposite (equal when two lines intersect), corresponding (equal, formed by parallel lines and a transversal)
    • Calculate angle sums: angles on a straight line = 180°; angles in a triangle = 180°; angles in a quadrilateral = 360°
    • Identify properties of parallel lines cut by a transversal: corresponding angles equal, alternate angles equal
    • Classify triangles by sides and angles; calculate missing angles using triangle angle sum
    • Identify properties of special quadrilaterals: rectangles (opposite sides equal, diagonals equal), squares (all sides equal, diagonals equal and perpendicular)
    • Apply transformations: identify translations (slides), reflections (flips across a line), rotations (turns about a point)
    • Describe transformations using vector notation for translations or degrees/direction for rotations
    • Plot and identify coordinates in all four quadrants of a Cartesian plane
Theme 5: Algebra and Relations
  • Algebraic Expressions and Equations
    • Simplify algebraic expressions by combining like terms: 3x + 2x = 5x; 4a + 3a² (cannot combine)
    • Expand brackets using the distributive property: 3(x + 2) = 3x + 6; -2(a - 3) = -2a + 6
    • Identify and use variables to represent unknown values or changing quantities
    • Write expressions for word problems: if x is a number, 'five more than twice a number' = 2x + 5
    • Solve linear equations using inverse operations: if 3x + 2 = 11, subtract 2 (3x = 9), divide by 3 (x = 3)
    • Solve equations with variables on both sides: 2x + 3 = x + 7; rearrange to collect x terms on one side
    • Solve linear inequalities: 2x + 5 > 11 → 2x > 6 → x > 3; represent solution on a number line
    • Identify patterns in sequences: describe arithmetic sequences (constant difference), geometric sequences (constant ratio)

JSS 2

5 topics
Theme 1: Algebraic Processes
  • Manipulating Algebraic Expressions
    • Expand single brackets: a(b+c) = ab + ac; apply with positive and negative coefficients
    • Expand double brackets using FOIL or distribution: (a+b)(c+d) = ac + ad + bc + bd; (x+3)(x-2) = x² - 2x + 3x - 6 = x² + x - 6
    • Recognize perfect square trinomials: (a+b)² = a² + 2ab + b²; (a-b)² = a² - 2ab + b²
    • Factor by finding the Greatest Common Factor (GCF): 6x² + 3x = 3x(2x + 1)
    • Factor quadratic expressions: x² + 5x + 6 = (x+2)(x+3); use the 'reverse FOIL' method
    • Identify and simplify algebraic fractions: (x²+3x)/(x+3) = x(x+3)/(x+3) = x (for x ≠ -3)
    • Add and subtract algebraic fractions: find common denominators, combine numerators
    • Multiply algebraic fractions: (a/b) × (c/d) = (ac)/(bd); simplify before multiplying
Theme 2: Ratio, Proportion, and Rate
  • Ratio and Proportion
    • Express ratios in simplest form: 12:18 = 2:3 by dividing both by the GCD
    • Compare quantities using ratios: determine which mixture is 'stronger' by comparing ratios
    • Use ratios to divide quantities: divide 60 in the ratio 2:3:1 by finding the total parts (6) and calculating each share
    • Understand direct proportion: if y is directly proportional to x (y ∝ x), then y = kx where k is the constant
    • Solve direct proportion problems: if 5kg costs N2,000, find cost of 8kg
    • Understand inverse proportion: if y is inversely proportional to x (y ∝ 1/x), then y = k/x
    • Solve inverse proportion problems: if 4 workers complete a job in 6 days, how long for 3 workers?
    • Calculate rate and speed: speed = distance ÷ time; solve problems involving motion (cars, runners)
Theme 3: Geometry and Mensuration
  • Advanced Geometric Topics
    • Calculate interior angles of polygons using the formula: sum = (n-2) × 180°, where n = number of sides
    • Calculate exterior angles of regular polygons: exterior angle = 360°/n; interior + exterior = 180°
    • Identify parts of circles: radius (center to edge), diameter (2 × radius), circumference (perimeter), arc (part of circumference)
    • Calculate circumference: C = 2πr = πd; use π ≈ 3.14 or 22/7
    • Calculate area of circles: A = πr²; recognize relationship between radius and area
    • Identify and calculate sector and segment areas: sector (pie-slice), segment (between chord and arc)
    • Calculate surface area of 3D shapes: find total area of all faces (prisms, pyramids, cylinders, spheres)
    • Calculate volume of 3D shapes: rectangular prisms (l×w×h), triangular prisms, pyramids (1/3×base area×height), cylinders (πr²h)
Theme 4: Coordinate Geometry and Trigonometry
  • Coordinate Systems
    • Plot coordinates on a Cartesian plane in all four quadrants; identify coordinates of given points
    • Calculate distance between two points using the distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²]
    • Find the midpoint of a line segment: midpoint = ((x₁+x₂)/2, (y₁+y₂)/2)
    • Interpret linear equations in the form y = mx + c where m is gradient (slope) and c is y-intercept
    • Calculate gradient (slope) of a line: m = (y₂-y₁)/(x₂-x₁); positive slope (↗), negative slope (↖), zero slope (horizontal)
    • Plot linear graphs: find y-intercept (c), use gradient to find other points, draw line
    • Interpret real-life relationships as linear graphs: distance-time graphs (speed), cost-quantity graphs
    • Identify parallel lines: equal gradients; perpendicular lines: gradients multiply to -1
Theme 5: Statistics and Probability
  • Data Analysis
    • Plan and conduct data collection using surveys or observations; identify potential bias in sampling methods
    • Organize data in frequency tables and grouped frequency distributions (class intervals)
    • Calculate statistical measures: mean (average), median (middle value), mode (most frequent), range (max - min)
    • Calculate mean from grouped data using midpoint of class intervals
    • Identify quartiles: Q1 (25th percentile), Q2 (median), Q3 (75th percentile); calculate interquartile range (IQR = Q3 - Q1)
    • Represent data using histograms (continuous data), bar charts (discrete data), and frequency polygons
    • Compare distributions using mean, median, range, or IQR
    • Calculate theoretical probability: P(event) = (number of favorable outcomes)/(total number of outcomes)

JSS 3

5 topics
Theme 1: Further Algebraic Processes
  • Advanced Algebra
    • Solve quadratic equations by factoring: x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = -2 or -3
    • Solve quadratic equations by completing the square: x² + 4x + 1 = 0 → (x+2)² = 3
    • Apply the quadratic formula: x = [-b ± √(b²-4ac)]/(2a) for ax² + bx + c = 0
    • Identify the discriminant: b² - 4ac determines number of real roots (positive = 2 roots, zero = 1 root, negative = no real roots)
    • Plot and interpret quadratic graphs: identify vertex (turning point), axis of symmetry, roots (x-intercepts)
    • Identify characteristics of quadratic graphs: opens upward (a > 0) or downward (a < 0), vertex position
    • Perform polynomial operations: add, subtract, and multiply polynomials
    • Divide polynomials using long division or synthetic division
Theme 2: Matrices and Vectors
  • Matrices and Vectors
    • Define matrices as rectangular arrays of numbers arranged in rows and columns; use notation like A₃ₓ₂ (3 rows, 2 columns)
    • Perform matrix addition and subtraction: add corresponding elements; matrices must have same dimensions
    • Perform matrix multiplication: (A×B)ᵢⱼ = sum of (row i of A × column j of B); calculate AB and BA separately
    • Understand matrix properties: commutative, associative, distributive where applicable; AB ≠ BA in general
    • Calculate determinants of 2×2 matrices: det(A) = ad - bc for [[a,b],[c,d]]
    • Find the inverse of a 2×2 matrix: A⁻¹ = (1/det(A)) × [[d,-b],[-c,a]]
    • Solve systems of linear equations using matrices: write Ax = b and solve for x = A⁻¹b
    • Define vectors as quantities with magnitude and direction; represent as column vectors or arrows
Theme 3: Trigonometry and Mensuration
  • Trigonometric Ratios
    • Define trigonometric ratios for right triangles: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
    • Recall exact values: sin(30°) = 1/2, sin(45°) = √2/2, sin(60°) = √3/2 and corresponding cosine and tangent values
    • Calculate trigonometric ratios using a calculator for any angle between 0° and 90°
    • Use inverse trigonometric functions: if sin θ = 0.5, then θ = sin⁻¹(0.5) = 30°
    • Solve right-angled triangles: find unknown sides using trig ratios, find unknown angles using inverse trig
    • Apply Pythagoras' theorem in problem-solving: a² + b² = c² for right triangles
    • Extend trigonometry to non-right triangles using the Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
    • Apply the Cosine Rule for non-right triangles: a² = b² + c² - 2bc·cos(A)
Theme 4: Circles and Coordinate Geometry
  • Circle Geometry and Advanced Coordinate Methods
    • Understand circle properties: all radii equal, diameter = 2r, circumference = 2πr, area = πr²
    • Identify angle relationships in circles: angle at center = 2 × angle at circumference (on same arc), angles in same segment equal
    • Identify tangent-radius property: tangent perpendicular to radius at point of contact
    • Apply chord properties: perpendicular from center bisects the chord
    • Identify cyclic quadrilaterals: opposite angles sum to 180°
    • Write circle equations: (x-h)² + (y-k)² = r² for circle with center (h,k) and radius r
    • Find tangent lines to circles: use perpendicularity and point conditions
    • Identify intersections of lines and curves: solve simultaneous equations to find points of intersection
Theme 5: Advanced Statistics and Probability
  • Statistical Analysis and Probability
    • Understand normal distributions: bell-curve shape, symmetrical about mean, defined by mean μ and standard deviation σ
    • Identify properties of normal distributions: 68% data within ±1σ, 95% within ±2σ, 99.7% within ±3σ
    • Calculate z-scores: z = (value - mean)/standard deviation; use to standardize and compare data
    • Calculate correlation coefficient: measure of how closely variables are related (r ranges from -1 to 1)
    • Interpret positive correlation (r > 0), negative correlation (r < 0), and no correlation (r ≈ 0)
    • Apply linear regression: find line of best fit (y = mx + c) to predict values from data
    • Distinguish correlation from causation: two variables correlated does not mean one causes the other
    • Calculate compound probability: P(A and B) = P(A) × P(B) for independent events

SSS 1

6 topics
Theme 1: Algebra and Sets
  • Set Theory
    • Set notation and operations
    • Venn diagrams and applications
    • Union, intersection, complement
    • Cardinality and finite/infinite sets
  • Algebraic Manipulation
    • Polynomial expressions and operations
    • Factorization techniques
    • Rational expressions
    • Algebraic fractions
Theme 2: Equations and Inequalities
  • Linear Equations and Systems
    • Solving linear equations
    • Systems of linear equations
    • Graphical solutions
    • Applications to real problems
  • Quadratic Equations
    • Solving quadratic equations
    • Factoring and completing the square
    • Quadratic formula
    • Nature of roots
  • Inequalities
    • Linear inequalities
    • Quadratic inequalities
    • Systems of inequalities
    • Graphical representation
Theme 3: Functions and Relations
  • Functions and Graphs
    • Function notation and domain/range
    • Composite functions
    • Inverse functions
    • Graphing functions
  • Types of Functions
    • Linear functions
    • Quadratic functions
    • Cubic and polynomial functions
    • Rational functions
Theme 4: Sequences and Series
  • Arithmetic and Geometric Sequences
    • Arithmetic progressions
    • Geometric progressions
    • General terms
    • Sum of sequences
  • Series Applications
    • Arithmetic series
    • Geometric series
    • Binomial expansion
    • Sum formulas
Theme 5: Geometry and Mensuration
  • Properties of Geometrical Shapes
    • Properties of triangles and quadrilaterals
    • Circle theorems and properties
    • Angles and angle relationships
    • Congruence and similarity
  • Area and Volume
    • Perimeter and area of shapes
    • Surface area of 3D objects
    • Volume of solids
    • Mensuration applications
Theme 6: Trigonometry
  • Trigonometric Ratios
    • Sine, cosine, tangent ratios
    • Solving right triangles
    • Trigonometric identities
    • Angles of elevation and depression

SSS 2

5 topics
Theme 1: Further Algebra
  • Logarithms and Indices
    • Laws of indices
    • Logarithmic functions
    • Logarithmic equations
    • Exponential equations
Theme 2: Calculus Introduction
  • Limits and Continuity
    • Concept of limits
    • Continuity of functions
    • Limit theorems
    • Asymptotes
  • Derivatives
    • Rate of change and derivatives
    • Differentiation rules
    • Chain rule and product rule
    • Applications of derivatives
  • Applications of Differentiation
    • Maximum and minimum values
    • Curve sketching
    • Optimization problems
    • Rates of change applications
Theme 3: Integration
  • Indefinite Integration
    • Antiderivatives
    • Integration rules
    • Integration by substitution
    • Integration by parts
  • Definite Integration
    • Definite integrals
    • Area under curves
    • Applications of definite integrals
    • Numerical integration
Theme 4: Coordinate Geometry
  • Straight Lines and Curves
    • Equation of lines
    • Slopes and gradients
    • Distance between points
    • Equation of circles
Theme 5: Statistics and Probability
  • Statistical Analysis
    • Data collection and organization
    • Measures of central tendency
    • Measures of dispersion
    • Distribution analysis
  • Probability Theory
    • Probability concepts
    • Conditional probability
    • Probability distributions
    • Binomial and normal distributions

SSS 3

5 topics
Theme 1: Advanced Calculus
  • Advanced Differentiation and Integration
    • Higher order derivatives
    • Partial derivatives
    • Multiple integrals
    • Advanced integration techniques
Theme 2: Vectors and Matrices
  • Vector Algebra
    • Vector notation and operations
    • Dot and cross products
    • Vector equations of lines and planes
    • Applications of vectors
  • Matrices and Determinants
    • Matrix operations
    • Determinants and inverses
    • Solving systems using matrices
    • Eigenvalues and eigenvectors
Theme 3: Complex Numbers
  • Complex Number Theory
    • Complex number operations
    • Polar form of complex numbers
    • De Moivre's theorem
    • Complex roots and equations
Theme 4: Differential Equations
  • Solving Differential Equations
    • First-order differential equations
    • Second-order differential equations
    • Applications of differential equations
    • Numerical methods
Theme 5: Advanced Statistics
  • Statistical Inference
    • Sampling distributions
    • Hypothesis testing
    • Confidence intervals
    • Regression and correlation
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