Mathematics

WASSCE · NECO · UTME · NABTEB

Number Base

A number base of a numeral system indicates how many unique digits, including zero, are present in that number system.

1Definition of Number Base3 min · 4 questions→
🔒Converting to Different BasesFinish "Definition of Number Base" first
🔒Converting from Base 2 to Base 10Finish "Converting to Different Bases" first
🔒Converting from any Base to Base 10Finish "Converting from Base 2 to Base 10" first
🔒Converting from Base 10 to Base 2Finish "Converting from any Base to Base 10" first
🔒Converting from Base 10 to any other BaseFinish "Converting from Base 10 to Base 2" first
🔒Decimal Base-10Finish "Converting from Base 10 to any other Base" first

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Fractions

Definition: A fraction means part of a region or part of a group.

1Fractions3 min · 4 questions→
🔒Decimals as a FractionFinish "Fractions" first
🔒Converting Recurring Decimal to FractionFinish "Decimals as a Fraction" first
🔒Fractions as Word ProblemFinish "Converting Recurring Decimal to Fraction" first

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Approximation

We don't always have to calculate or measure things precisely but we might only need to have a rough idea or to calculate only to a certain degree of accuracy.

1Approximation3 min · 4 questions→
🔒Rounding Off (I)Finish "Approximation" first
🔒Decimal PlacesFinish "Rounding Off (I)" first
🔒Significant FiguresFinish "Decimal Places" first
🔒Percentage ErrorFinish "Significant Figures" first

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Percentages

A percentage is a proportion often expressed as a number out of 100.

1Percentages3 min · 4 questions→
🔒Percent and PercentageFinish "Percentages" first
🔒Applications of PercentagesFinish "Percent and Percentage" first

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Profit and Loss

For the purpose of comparison, we usually express the actual profit or loss as a percentage of cost price.

1Introduction3 min · 4 questions→
🔒Profit & LossFinish "Introduction" first
🔒Percentage ProfitFinish "Profit & Loss" first
🔒Percentage LossFinish "Percentage Profit" first

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Ratio, Rates and Proportion

To get a grasp of this course, it is essential for you to be familiar with each individual term in relation to the context of mathematics.

1Ratio & Rate3 min · 4 questions→
🔒ProportionFinish "Ratio & Rate" first
🔒Applications of Ratio, Rate & ProportionFinish "Proportion" first

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Change of Subject of Formula

The subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign.

1Introduction3 min · 4 questions→
🔒Solved Problems 1Finish "Introduction" first
🔒Solved Problems 2Finish "Solved Problems 1" first

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Simple and Compound Interest

Simple interest is a quick and easy method of calculating the interest charge on a loan. In other words, it is determined by multiplying the daily interest rate

1Simple Interest3 min · 4 questions→
🔒Examples of Simple InterestFinish "Simple Interest" first
🔒Compound InterestFinish "Examples of Simple Interest" first
🔒Compound Interest General FormulaFinish "Compound Interest" first
🔒Finding Present ValuesFinish "Compound Interest General Formula" first
🔒Compounding PeriodsFinish "Finding Present Values" first
🔒Interest Rate & Number of PeriodsFinish "Compounding Periods" first
🔒AmountFinish "Interest Rate & Number of Periods" first

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Substitution and Simplification

To simplify an expression means that you are writing an algebraic expression in a form that is easier to use if you want to do something else with the expressio

1Simplification of Brackets4 min · 4 questions→
🔒Expansion of Perfect SquaresFinish "Simplification of Brackets" first
🔒Meaning of SubstitutionFinish "Expansion of Perfect Squares" first
🔒Solving Simple EquationsFinish "Meaning of Substitution" first
🔒Sign RulesFinish "Solving Simple Equations" first
🔒Solved ProblemsFinish "Sign Rules" first
🔒Example 2Finish "Solved Problems" first

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Indices

An exponential or indicial equation is a combination of indices and all other forms of equations. It is very easy to solve once you have a good knowledge of the

1Rules for Solving Exponential (Indicial) Equations3 min · 4 questions→
🔒Law of IndicesFinish "Rules for Solving Exponential (Indicial) Equations" first

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Standard Form

The standard form of a decimal number is mostly referred to as "scientific notation" in Britain.

1Standard Form of a Decimal Number3 min · 4 questions→
🔒Standard Form of an EquationFinish "Standard Form of a Decimal Number" first
🔒Standard Form of a Linear EquationFinish "Standard Form of an Equation" first
🔒Standard Form of a PolynomialFinish "Standard Form of a Linear Equation" first
🔒Standard Form of a Quadratic EquationFinish "Standard Form of a Polynomial" first

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Logarithm

From indices, we have that 2^3 = 8 where 2 is the base and 3 is the power. On the other hand, we can write that the log of 8 to base 2 is equal to 3, denoted thu

1Understanding Logarithms3 min · 4 questions→
🔒Laws of LogarithmsFinish "Understanding Logarithms" first
🔒Use of Log TablesFinish "Laws of Logarithms" first
🔒AntilogarithmFinish "Use of Log Tables" first

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Surds

In Mathematics, we have to always leave our final answer in a neat and complete context so that no value is lost. For example, we agree that √5 = 2.236067977499

1Introduction to Surds3 min · 4 questions→
🔒Simplifying Expressions Involving SurdsFinish "Introduction to Surds" first
🔒Addition & Subtraction of SurdsFinish "Simplifying Expressions Involving Surds" first
🔒Multiplication & Division of SurdsFinish "Addition & Subtraction of Surds" first
🔒Conjugates & Rationalization of SurdsFinish "Multiplication & Division of Surds" first
🔒Evaluating the Square Root of SurdsFinish "Conjugates & Rationalization of Surds" first

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Sets

Set is the collection of well-defined objects. By definition, it means that anyone should be able to tell whether the object belongs to a particular collection

1Definition of Sets3 min · 4 questions→
🔒Set Theory RulesFinish "Definition of Sets" first
🔒Types of SetsFinish "Set Theory Rules" first
🔒Operations on Sets (Union & Intersection)Finish "Types of Sets" first
🔒Operations on Sets (Difference and Complement)Finish "Operations on Sets (Union & Intersection)" first
🔒Properties of Intersection of a SetFinish "Operations on Sets (Difference and Complement)" first
🔒Venn DiagramsFinish "Properties of Intersection of a Set" first
🔒Set Operations & Venn DiagramsFinish "Venn Diagrams" first
🔒Set Operations & Venn Diagrams IIFinish "Set Operations & Venn Diagrams" first
🔒Examples of Venn DiagramFinish "Set Operations & Venn Diagrams II" first

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Variation

In Mathematics we usually deal with two types of quantities; variable quantities (or variables) & constant quantities (or constants). If the value of a quantity

1Introduction4 min · 4 questions→
🔒Types of VariationFinish "Introduction" first
🔒Direct VariationFinish "Types of Variation" first
🔒Inverse VariationFinish "Direct Variation" first
🔒Joint VariationFinish "Inverse Variation" first
🔒Combined VariationFinish "Joint Variation" first
🔒Partial VariationFinish "Combined Variation" first

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Inequalities

In a simple term, any equation without the sign of equality is known as inequality.

1Introdution to Inequalities4 min · 4 questions→
🔒Properties of InequalitiesFinish "Introdution to Inequalities" first
🔒Addition & Subtraction of InequalitiesFinish "Properties of Inequalities" first
🔒Multiplication & Division of InequalitiesFinish "Addition & Subtraction of Inequalities" first
🔒ExamplesFinish "Multiplication & Division of Inequalities" first

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Binary Operation

A binary operation ∗ on a set S is a function

1What is Binary Operation4 min · 4 questions→
🔒Properties of Binary OperationFinish "What is Binary Operation" first
🔒Types of Binary OperationsFinish "Properties of Binary Operation" first
🔒Identity ElementFinish "Types of Binary Operations" first

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Polynomials

The word "polynomial" means “many terms”. It implies a mathematical expression consisting of numbers, letters, and numerical superscripts. Before we look into p

1Polynomial3 min · 4 questions→
🔒Degree of a PolynomialFinish "Polynomial" first
🔒Types of polynomialsFinish "Degree of a Polynomial" first
🔒Polynomial FunctionFinish "Types of polynomials" first
🔒Addition of PolynomialsFinish "Polynomial Function" first
🔒Subtraction of PolynomialsFinish "Addition of Polynomials" first
🔒Multiplication of PolynomialFinish "Subtraction of Polynomials" first
🔒Division of PolynomialFinish "Multiplication of Polynomial" first
🔒Examples on PolynomialsFinish "Division of Polynomial" first

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Patterns of Sequence

Patterns are series or sequence that repeats.

1Patterns3 min · 4 questions→
🔒ExampleFinish "Patterns" first
🔒SequenceFinish "Example" first
🔒SeriesFinish "Sequence" first
🔒The General FormulaFinish "Series" first

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Arithmetic Progression

A sequence in which the terms either increase or decrease in equal steps is called an arithmetic progression.

1Introduction3 min · 4 questions→
🔒Denotations in A.P.Finish "Introduction" first
🔒Properties of an A.P.Finish "Denotations in A.P." first
🔒Formula for Nth Term of an A.P.Finish "Properties of an A.P." first
🔒ExamplesFinish "Formula for Nth Term of an A.P." first
🔒Arithmetic MeanFinish "Examples" first

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Geometric Progression

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio

1Introduction3 min · 4 questions→
🔒The Nth Term of a G. P.Finish "Introduction" first
🔒Sum of a G.P. SeriesFinish "The Nth Term of a G. P." first
🔒General FormulaFinish "Sum of a G.P. Series" first
🔒Geometric MeanFinish "General Formula" first
🔒ExampleFinish "Geometric Mean" first

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Simultaneous Linear Equation

Simultaneous implies occurring at the same time.

1Introduction3 min · 4 questions→
🔒Elimination MethodFinish "Introduction" first
🔒Substitution MethodFinish "Elimination Method" first
🔒Graphical MethodFinish "Substitution Method" first

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Factorization

To understand the concept of this topic, we must understand "Term and Factor".

1Concept of Terms & Factors3 min · 4 questions→
🔒Meaning of FactorsFinish "Concept of Terms & Factors" first
🔒Meaning of MultiplesFinish "Meaning of Factors" first
🔒ExpansionFinish "Meaning of Multiples" first
🔒Meaning of FactorizationFinish "Expansion" first
🔒Factorization ExampleFinish "Meaning of Factorization" first

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Quadratic Equations

Quadratic equation refers to a polynomial equation that has a general form of

1Introduction3 min · 4 questions→
🔒Solving Quadratic EquationsFinish "Introduction" first
🔒Meaning of FactorizationFinish "Solving Quadratic Equations" first
🔒Factorization of Quadratic EquationFinish "Meaning of Factorization" first
🔒Factorizing by Grouping of Terms of ExpressionFinish "Factorization of Quadratic Equation" first
🔒Factorization of Difference of Two SquaresFinish "Factorizing by Grouping of Terms of Expression" first
🔒Factorization of Perfect SquaresFinish "Factorization of Difference of Two Squares" first
🔒Solved ProblemsFinish "Factorization of Perfect Squares" first
🔒Quadratic FormulaFinish "Solved Problems" first
🔒Graphical MethodFinish "Quadratic Formula" first
🔒Notes on Graphical MethodFinish "Graphical Method" first
🔒Sum & Product of Quadratic RootsFinish "Notes on Graphical Method" first
🔒Solved Problem using Graphical Method IFinish "Sum & Product of Quadratic Roots" first
🔒Solved Problem using Graphical MethodFinish "Solved Problem using Graphical Method I" first

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Mensuration

Mensuration deals with the development of formulas to measure areas and volumes of different geometrical figures; such as cubes, cuboids, cylinders, cones and s

1Introduction2 min · 4 questions→
🔒PerimeterFinish "Introduction" first
🔒AreaFinish "Perimeter" first
🔒Circumference, Area & Arc of a CircleFinish "Area" first
🔒Sector of a CircleFinish "Circumference, Area & Arc of a Circle" first
🔒Segment of a CircleFinish "Sector of a Circle" first
🔒CubeFinish "Segment of a Circle" first
🔒CylinderFinish "Cube" first
🔒ConeFinish "Cylinder" first

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Triangles and Polygons

Triangles are three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal ang

1Triangles4 min · 4 questions→
🔒Types of TrianglesFinish "Triangles" first
🔒Area of a TriangleFinish "Types of Triangles" first
🔒Pythagoras TheoremFinish "Area of a Triangle" first
🔒PolygonsFinish "Pythagoras Theorem" first
🔒Types of PolygonFinish "Polygons" first
🔒ParallelogramFinish "Types of Polygon" first
🔒RhombusFinish "Parallelogram" first
🔒SquareFinish "Rhombus" first
🔒RectangleFinish "Square" first
🔒TrapeziumFinish "Rectangle" first
🔒Interior Angles of PolygonsFinish "Trapezium" first
🔒* Interior angle = sum of interior angle/nFinish "Interior Angles of Polygons" first
🔒Exterior Angles of PolygonsFinish "* Interior angle = sum of interior angle/n" first

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Circle Geometry

Geometry is the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. In other

1Meaning of Geometry3 min · 4 questions→
🔒Radius & Diameter of a CircleFinish "Meaning of Geometry" first
🔒Area & Circumference of a CircleFinish "Radius & Diameter of a Circle" first
🔒Chord, Tangent & SecantFinish "Area & Circumference of a Circle" first
🔒Arc of a CircleFinish "Chord, Tangent & Secant" first
🔒Sector of a CircleFinish "Arc of a Circle" first
🔒Equation of a CircleFinish "Sector of a Circle" first
🔒Parametric formFinish "Equation of a Circle" first
🔒Point-formFinish "Parametric form" first
🔒Circle Theorems IFinish "Point-form" first
🔒Circle Theorems IIFinish "Circle Theorems I" first
🔒Circle Theorems IIIFinish "Circle Theorems II" first
🔒Circle Theorems IVFinish "Circle Theorems III" first

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Geometry of Straight Lines

Coordinate geometry is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two

1Terminologies3 min · 4 questions→
🔒Cartesian PlaneFinish "Terminologies" first
🔒Equation of a Line in Cartesian PlaneFinish "Cartesian Plane" first
🔒Slope/Gradient of a Straight Line IFinish "Equation of a Line in Cartesian Plane" first
🔒Slope/Gradient of a Straight Line IIFinish "Slope/Gradient of a Straight Line I" first
🔒Negative SlopeFinish "Slope/Gradient of a Straight Line II" first
🔒Angles between Lines IFinish "Negative Slope" first
🔒Angles between Lines IIFinish "Angles between Lines I" first
🔒Angles between Intersecting LinesFinish "Angles between Lines II" first
🔒Distance FormulaFinish "Angles between Intersecting Lines" first
🔒Midpoint TheoremFinish "Distance Formula" first
🔒Section FormulaFinish "Midpoint Theorem" first

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Trigonometry

The sine ("sin") and cosine ("cos") are the two most prominent trigonometric functions. All other trig functions can be expressed in terms of them. In fact, the

1Sine of Angles3 min · 4 questions→
🔒Cosine of AnglesFinish "Sine of Angles" first
🔒Tangent of AnglesFinish "Cosine of Angles" first
🔒Sine, Cosine & Tangent of Acute AnglesFinish "Tangent of Angles" first
🔒SineFinish "Sine, Cosine & Tangent of Acute Angles" first
🔒Trigonometric Ratios of 30° & 60°Finish "Sine" first
🔒Trigonometric Ratios of 45°Finish "Trigonometric Ratios of 30° & 60°" first
🔒Sine, Cosine & Tangent of Angles (0° to 360°)Finish "Trigonometric Ratios of 45°" first
🔒Graph of TangentFinish "Sine, Cosine & Tangent of Angles (0° to 360°)" first

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Latitude and Longitude

The earth is oblate spheroidal in shape with a radius often approximated to 6400km. It rotates about the north-south axis, the north end of the axis being the n

1Terminologies4 min · 4 questions→
🔒LatitudeFinish "Terminologies" first
🔒Important Lines of Latitude IFinish "Latitude" first
🔒LongitudeFinish "Important Lines of Latitude I" first
🔒Solved Problems IFinish "Longitude" first
🔒Solved Problems IVFinish "Solved Problems I" first

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Bearing and Distance

Bearing can be defined as the clockwise angular movement between two distant places.

1Bearing3 min · 4 questions→
🔒Rules for Solving Bearing & DistanceFinish "Bearing" first
🔒Bearing of a Point IFinish "Rules for Solving Bearing & Distance" first
🔒Bearing of a Point IIFinish "Bearing of a Point I" first
🔒Proof of Cosine RuleFinish "Bearing of a Point II" first
🔒Using The Cosine RuleFinish "Proof of Cosine Rule" first
🔒Proof of Sine RuleFinish "Using The Cosine Rule" first
🔒Using the Sine RuleFinish "Proof of Sine Rule" first

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Angle of Elevation and Depression

The three terms related to angle of elevation are:

1Terminologies3 min · 4 questions→
🔒Angle of ElevationFinish "Terminologies" first
🔒Angle of Elevation FormulaFinish "Angle of Elevation" first
🔒Solved Problems on Angle of Elevation IFinish "Angle of Elevation Formula" first
🔒Solved Problems on Angle of Elevation IIFinish "Solved Problems on Angle of Elevation I" first
🔒Angle of DepressionFinish "Solved Problems on Angle of Elevation II" first
🔒Angle of depression is basically used to get the distance of two objects where the angles Finish "Angle of Depression" first
🔒Angle of Depression FormulaFinish "Angle of depression is basically used to get the distance of two objects where the angles " first
🔒Solved Problems on Angle of DepressionFinish "Angle of Depression Formula" first
🔒Angle of Elevation & Depression ComparisonFinish "Solved Problems on Angle of Depression" first

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Differentiation

Function: A function is defined as a relation from a set of inputs to the set of outputs on which each input is exactly associated with one output. It is repres

1Terminologies4 min · 4 questions→
🔒Meaning of DifferentiationFinish "Terminologies" first
🔒Gradient Function of a CurveFinish "Meaning of Differentiation" first
🔒Power RuleFinish "Gradient Function of a Curve" first
🔒Sum RuleFinish "Power Rule" first
🔒Product RuleFinish "Sum Rule" first
🔒Chain RuleFinish "Product Rule" first
🔒Derivatives of Algebraic FunctionsFinish "Chain Rule" first
🔒Differentiation from First Principle IFinish "Derivatives of Algebraic Functions" first
🔒Differentiation with Respect to x (I)Finish "Differentiation from First Principle I" first
🔒Applications of DifferentiationFinish "Differentiation with Respect to x (I)" first

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Integration

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, that is, it is used for finding functio

1Concept of Integration4 min · 4 questions→
🔒Integration of Algebraic ExpressionsFinish "Concept of Integration" first
🔒Integration of Simple Trigonometric ExpressionFinish "Integration of Algebraic Expressions" first

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Statistics

Statistics is the study of the collection, analysis, presentation, organization and interpretation of data.

1Meaning of Statistics3 min · 4 questions→
🔒Frequency DistributionFinish "Meaning of Statistics" first
🔒Frequency Distribution TableFinish "Frequency Distribution" first
🔒Grouped Frequency Distribution IFinish "Frequency Distribution Table" first
🔒Grouped Frequency Distribution IIFinish "Grouped Frequency Distribution I" first
🔒Cumulative Frequency TableFinish "Grouped Frequency Distribution II" first
🔒PictogramFinish "Cumulative Frequency Table" first
🔒Bar Chart IFinish "Pictogram" first
🔒HistogramFinish "Bar Chart I" first
🔒Difference between Histogram & Bar GraphFinish "Histogram" first
🔒Pie ChartFinish "Difference between Histogram & Bar Graph" first
🔒Mean (Ungrouped Data)Finish "Pie Chart" first
🔒Median (Ungrouped Data)Finish "Mean (Ungrouped Data)" first
🔒Median (Grouped Data) IFinish "Median (Ungrouped Data)" first
🔒WhereFinish "Median (Grouped Data) I" first
🔒Mode (Ungrouped Data)Finish "Where" first
🔒Mode (Grouped Data) IFinish "Mode (Ungrouped Data)" first
🔒PencentilesFinish "Mode (Grouped Data) I" first
🔒DecilesFinish "Pencentiles" first
🔒QuartilesFinish "Deciles" first

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Measure of Dispersion

Dispersion helps to understand the distribution of a set of data. When a data set has a large value, the values in the set are widely scattered; when it is smal

1Introduction3 min · 4 questions→
🔒RangeFinish "Introduction" first
🔒Interquartile Range IFinish "Range" first
🔒Interquartile Range IIFinish "Interquartile Range I" first
🔒Mean DeviationFinish "Interquartile Range II" first
🔒Mean Deviation (Ungrouped Data)Finish "Mean Deviation" first
🔒Mean Deviation (Grouped Data)Finish "Mean Deviation (Ungrouped Data)" first
🔒Variance & Standard Deviation (Ungrouped Data)Finish "Mean Deviation (Grouped Data)" first
🔒Variance & Standard Deviation (Grouped Data)Finish "Variance & Standard Deviation (Ungrouped Data)" first

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Permutation and Combination

Permutation has to do with each of the various ways a set of objects can be arranged. It is the changing of the arrangement of several items, with respect to th

1Permutation4 min · 4 questions→
🔒Solved Problems on Permutation IFinish "Permutation" first
🔒Solved Problems on Permutation IIFinish "Solved Problems on Permutation I" first
🔒CombinationFinish "Solved Problems on Permutation II" first
🔒Solved Problems on Combination IFinish "Combination" first
🔒Solved Problems on Combination IIFinish "Solved Problems on Combination I" first

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Probability

Probability is a numerical description of how likely an event is to occur or how likely it is that a proposition is true.

1Meaning of Probability3 min · 4 questions→
🔒TerminologiesFinish "Meaning of Probability" first
🔒IllustrationsFinish "Terminologies" first
🔒Probability in GeneralFinish "Illustrations" first
🔒Experimental ProbabilityFinish "Probability in General" first
🔒P(2) = 3/20 = 0.15Finish "Experimental Probability" first
🔒Theoretical Probability IFinish "P(2) = 3/20 = 0.15" first
🔒Theoretical Probability IIFinish "Theoretical Probability I" first
🔒Solved Problems on Mutually Exclusive Event IFinish "Theoretical Probability II" first
🔒(v)P(neither red or blue) = P(R or B)1 = 1 - P(R or B)Finish "Solved Problems on Mutually Exclusive Event I" first
🔒Non Mutually Exclusive Events IFinish "(v)P(neither red or blue) = P(R or B)1 = 1 - P(R or B)" first
🔒Non Mutually Exclusive Events IIFinish "Non Mutually Exclusive Events I" first
🔒Independent EventFinish "Non Mutually Exclusive Events II" first
🔒Solved Problems on Independent Event IFinish "Independent Event" first
🔒Solved Problems on Independent Event IIFinish "Solved Problems on Independent Event I" first
🔒Conditional ProbabilityFinish "Solved Problems on Independent Event II" first

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