WAEC Syllabus for Mathematics 2023, Know the Tips to Crack this Exam

WAEC Mathematics Exam 2023

The WAEC Mathematics exam is an important examination conducted by the West African Examinations Council (WAEC) for students in West African countries. It is designed to assess the mathematical knowledge and skills of secondary school students at the senior secondary level. The WAEC Mathematics exam covers various topics in mathematics, including algebra, geometry, trigonometry, calculus, statistics, and probability. The questions are structured to test the students' understanding of concepts, ability to solve problems, and apply mathematical principles in real-life situations.

The exam is usually divided into multiple sections, each focusing on specific areas of mathematics. The questions range from multiple-choice questions to structured and essay-type questions. Students are required to provide clear and concise answers, show their workings, and demonstrate a solid understanding of the mathematical concepts being tested. To prepare for the WAEC Mathematics exam, students are advised to thoroughly study their textbooks, practice solving different types of mathematical problems, and familiarize themselves with the exam format. It is crucial to understand the underlying concepts and formulas and practice applying them to solve problems effectively.

During the exam, time management is key. Students should allocate sufficient time to each section, carefully read and analyze each question, and plan their answers accordingly. It is important to show all necessary steps and calculations to earn maximum marks, as partial credit is often awarded for correct approaches.

The WAEC Mathematics exam requires critical thinking, logical reasoning, and problem-solving skills. It challenges students to think analytically and apply mathematical principles to solve complex problems. It also helps develop their ability to interpret and analyze data, make accurate calculations, and draw meaningful conclusions.

Scoring well in the WAEC Mathematics exam can have a significant impact on a student's overall academic performance and future educational opportunities. A strong performance in mathematics opens doors to various science, technology, engineering, and mathematics (STEM) fields and is often a prerequisite for admission into higher education institutions.

In conclusion, the WAEC Mathematics exam is a comprehensive assessment of students' mathematical knowledge and skills. It requires diligent preparation, understanding of key concepts, and practice in solving a variety of mathematical problems. By dedicating time and effort to studying and mastering the subject, students can enhance their chances of achieving excellent results in this important examination.

WAEC Syllabus for Mathematics 2023

Aim of the Syllabus

The syllabus aims to test candidates:

1. Mathematical competency and computational skills;
2. understanding of mathematical concepts and their relationship to the     acquisition of entrepreneurial skills for everyday living in the global world;
3. ability to translate problems into mathematical language and solve them using appropriate methods;
4.  ability to be accurate to a degree relevant to the problem at hand;
5. logical, abstract and precise thinking.

This syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use their National teaching syllabuses or curricula.

Examination Scheme

There will be two papers, Papers 1 and 2, which must be taken.

Paper 1

It will consist of fifty multiple-choice objective questions drawn from the common areas of the syllabus, to be answered in 1½ hours for 50 marks.

Paper 2

It will consist of thirteen essay questions in Sections A and B, to be answered in 2½ hours for 100 marks.

Candidates will be required to answer ten questions in all.

Section A

It will consist of five compulsory questions, elementary, with 40 marks.

The questions will be drawn from the common areas of the syllabus.

Section B

It will consist of eight questions of greater length and difficulty. 

The questions shall include a maximum of two drawn from parts of the syllabuses that may not be peculiar to candidates’ home countries.

Candidates will be expected to answer five questions for 60 marks.

Brain Teaser: Find the Odd One in 10 Seconds

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Optical Illusion: Can You Try to Find the Hidden Number in 10 Seconds?

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WAEC Mathematics Syllabus

The aims of the syllabus are to test candidates’:

1. mathematical competency and computational skills;
2. understanding of mathematical concepts and their relationship to the acquisition of entrepreneurial skills for everyday living in the global world;
3. ability to translate problems into mathematical language and solve them using appropriate methods;
4. ability to be accurate to a degree relevant to the problem at hand;
5. logical, abstract and precise thinking.

This syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use their own National teaching syllabuses or curricular for that purpose.

EXAMINATION SCHEME

There will be two papers, Papers 1 and 2, both of which must be taken.

PAPER 1:

Will consist of fifty multiple-choice objective questions, drawn from the common areas of the syllabus, to be answered in 1½ hours for 50 marks.

PAPER 2:

Will consist of thirteen essay questions in two sections – Sections A and B, to be answered in 2½ hours for 100 marks. Candidates will be required to answer ten questions in all.

Section A

Will consist of five compulsory questions, elementary in nature carrying a total of 40 marks. The questions will be drawn from the common areas of the syllabus.

Section B

Will consist of eight questions of greater length and difficulty. The questions shall include a maximum of two which shall be drawn from parts of the syllabuses which may not be peculiar to candidates’ home countries. Candidates will be expected to answer five questions for 60marks.

Detailed WAEC Syllabus for general Mathematics

The topics, contents and notes are intended to indicate the scope of the questions which will be set. The notes are not to be considered as an exhaustive list of illustrations/limitations.

A. NUMBER AND NUMERATION

( a ) Number bases

1. conversion of numbers from one base to another.
2. Basic operations on number bases.

(b) Modular Arithmetic

1. Concept of Modulo Arithmetic.
2. Addition, subtraction and multiplication operations in  modulo arithmetic.
3. Application to daily life.

( c ) Fractions, Decimals and Approximations

1. Basic operations on fractions and decimals.
2. Approximations and significant figures.

( d ) Indices

1. Laws of indices
2. Numbers in standard form (scientific notation)

(e) Logarithms

1. Relationship between indices and logarithms e.g. y = 10k implies log10y = k.
2. Basic rules of logarithms e.g.
   log10(pq) = log10p + log10q
   log10(p/q) = log10p – log10q
   log10pn = nlog10p.
3. Use of tables of logarithms      and antilogarithms.

Calculations involving multiplication, division, powers and roots.

(f) Sequence and Series

1. Patterns of sequences.
2. Arithmetic progression (A.P.)
3. Geometric Progression (G.P.)
   Determine any term of a given sequence. The notation Un = the nth termof a sequence may be used.

Simple cases only, including word problems. (Include sum for A.P. and exclude sum for G.P).

( g ) Sets

1. Idea of sets, universal sets, finite and infinite sets, subsets, empty sets and disjoint sets.
   Idea of and notation for union, intersection and complement of sets.
2. Solutionof practical problems involving classification using Venn diagrams.

Notations: { }, P’( the compliment of P).

(h) Logical Reasoning

Simple statements. True and false statements. Negation of statements, implications.
Use of symbols: use of Venn diagrams.

(i) Positive and negative integers, rational numbers

1. The four basic operations on rational numbers.
2. Match rational numbers with points on the number line.
3. Notation: Natural numbers (N), Integers ( Z ), Rational numbers ( Q ).

(j) Surds (Radicals)

1. Simplification and rationalization of simple surds.
2. Surds of the form , a and a where a is a rational number and b is a positive integer.
3. Basic operations on surds (exclude surd of the form ).

* (k) Matrices and Determinants

1. Identification of order, notation and types of matrices.
2. Addition, subtraction, scalar multiplication and multiplication of matrices.
3. Determinant of a matrix

(l) Ratio, Proportions and  Rates

1. Ratio between two similar quantities.
   Proportion between two or more similar quantities.
2. Financial partnerships, rates of work, costs, taxes, foreign exchange, density (e.g. population), mass, distance, time and speed.

( m ) Percentages

Simple interest, commission, discount, depreciation, profit and loss, compound interest, hire purchase and percentage error.

*(n) Financial Arithmetic

1. Depreciation/ Amortization.
2. Annuities
3. Capital Market Instruments

(o) Variation

Direct, inverse, partial and joint variations.
Application to simple practical problems.

B. ALGEBRAIC PROCESSES

(a) Algebraic expressions

1. Formulating algebraic expressions from given situations
2. Evaluation of algebraic expressions

( b ) Simple operations on algebraic expressions

1. Expansion
2. Factorization

(c) Solution of Linear Equations

1. Linear equations in one variable
2. Simultaneous linear equations in two variables.
3. Drawing tangents to curves to determine the gradient at a given point.

(d) Change of Subject of a Formula/Relation

1. Change of subject of a formula/relation.
2. Substitution.

(e) Quadratic Equations

1. Solution of quadratic equations
2. Forming quadratic equation with given roots.
3. Application of solution of quadratic equation in practical problems.

(f) Graphs of Linear and Quadratic functions.

1. Interpretation of graphs, coordinate of points, table of values, drawing quadratic graphs and obtaining roots from graphs.
2. Graphical solution of a pair  of equations of the form: y = ax2 + bx + c and y = mx + k.

(g) Linear Inequalities

1. Solution of linear inequalities in one variable and representation on the number line.
2. *Graphical solution of linear inequalities in two variables.
3. *Graphical solution of simultaneous linear inequalities in two variables.

(h) Algebraic Fractions

Operations on algebraic fractions with:

1. Monomial denominators
2. Binomial denominators

Simple cases only e.g. + = ( x0, y 0).

(i) Functions and Relations

Types of Functions
One-to-one, one-to-many, many-to-one, many-to-many.

Functions as a mapping, determination of the rule of a given mapping/function.

C. MENSURATION

(a) Lengths and Perimeters

1. Use of Pythagoras theorem, *§ªsine and cosine rules to determine lengths and distances.
2. Lengths of arcs of circles, perimeters of sectors and segments.
3. Longitudes and Latitudes.

(b) Areas

1. Triangles and special  quadrilaterals – rectangles, parallelograms and trapeziums.
2. Circles, sectors and segments of circles.
3. Surfaceareas of cubes, cuboids, cylinder, pyramids, right triangular prisms, cones and spheres.

Areas of similar figures. Include area of triangle = ½ base x height and ½absinC.
Areas of compound shapes.
Relationship between the sector of a circle and the surface area of a cone.

(c) Volumes

1. Volumes of cubes, cuboids, cylinders, cones, right pyramids and spheres.
2. Volumes of similar solids

Include volumes of compound shapes.

D. PLANE GEOMETRY

(a) Angles

1. Angles at a point add up to  360 degree.
2. Adjacent angles on a straight      line are supplementary.
3. Vertically opposite angles are       equal.

(b) Angles and intercepts on parallel lines.

1. Alternate angles are equal.
2. Corresponding angles are equal.
3. Interior opposite angles are supplementary
   **ª
4. Intercept theorem.

(c) Triangles and Polygons.

1. The sum of the angles of a triangle is 2 right angles.
2. The exterior angle of a triangle equals the sum of the two interior opposite angles.
3. Congruenttriangles.
4. Propertiesof special triangles – Isosceles, equilateral, right-angled, etc
5. Properties of special quadrilaterals – parallelogram, rhombus,  square, rectangle, trapezium.
6. Propertiesof similar   triangles.
7. Thesum of the angles of a  polygon
8. Property of exterior angles  of a polygon.
9. Parallelograms on the same base and between the same       parallels are equal in area.

( d ) Circles

1. Chords.
2. The angle which an arc of a  circle subtends at the centre of the circle is twice that  which it subtends at any point on the remaining part  of the circumference.
3. Anyangle subtended at the circumference by a diameter is a right angle.
4. Angles in the same segment  are equal.
5. Angles in opposite segments are supplementary.
6. Perpendicularity of tangent and radius.
7. If a tangent is drawn to a circle and from the point  of contact a chord is drawn, each angle which this chord makes with the tangent is equal to the angle in the alternate segment.
8. Angles subtended by chords in a circle and at the centre. Perpendicular bisectors of chords.

( e) Construction

1. Bisectors of angles and line segments
2. Line parallel or perpendicular to a given line.
3. Angles e.g. 90o, 60o, 45o, 30o, and an angle equal to a given angle.
4. Triangles and quadrilaterals from sufficient data.

(f) Loci

Knowledge of the loci listed below and their intersections in 2 dimensions.

1. Points at a given distance from a given point.
2. Points equidistant from two given points.
3. Points equidistant from two given straight lines.
4. Points at a given distance from a given straight line.

E. COORDINATE GEOMETRY OF  STRAIGHT LINES

1. Concept of the x-y plane.
2. Coordinates of points on the x-y plane.

F. TRIGONOMETRY

(a) Sine, Cosine and Tangent of an angle.

1. Sine, Cosine and Tangent of acute angles.
2. Use of tables of trigonometric ratios.
3. Trigonometric ratios of 30o, 45o and 60o.
4. Sine, cosine and tangent of angles from 0o to 360o.
5. Graphs of sine and cosine.
6. Graphsof trigonometric ratios.

(b) Angles of elevation and depression

1. Calculating angles of elevation and depression.
2. Application to heights and distances.

(c) Bearings

1. Bearing of one point from another.
2. Calculation of distances and angles

G. INTRODUCTORY CALCULUS

1.  Differentiation of algebraic  functions.
2. Integration of simple Algebraic functions.
   Concept/meaning of differentiation/derived function, , relationship between gradient of a curve at a point and the differential coefficient of the equation of the curve at that point. Standard derivatives of some basic function e.g. if y = x2, = 2x. If s = 2t3 + 4, = v = 6t2, where s = distance, t = time and v = velocity. Application to real life situation such as maximum and minimum values, rates of change etc.

Meaning/ concept of integration, evaluation of simple definite algebraic equations.

H. STATISTICS AND PROBABILITY

(a) Statistics

1. Frequency distribution
2.  Pie charts, bar charts, histograms and frequency polygons
3. Mean, median and mode for both discrete and grouped data.
4. Cumulative frequency curve (Ogive).
5. Measures of Dispersion: range, semi inter-quartile/inter-quartile range, variance, mean deviation and standard deviation.

(b) Probability

1.  Experimental and theoretical probability.
2.  Addition of probabilities for      mutually exclusive and      independent events.
3. Multiplication of probabilities      for independent events.

I. VECTORS AND TRANSFORMATION

Vectors in a Plane

1. Vectors as a directed line segment.
2. Cartesian components of a vector
3. Magnitude of a vector, equal vectors, addition and subtraction of vectors, zero vector, parallel vectors, multiplication of a vector by scalar.

Transformation in the Cartesian Plane

1. Reflection of points and shapes in the Cartesian Plane.
2. Rotation of points and shapes in the Cartesian Plane.
3. Translation of points and shapes in the Cartesian Plane.
4. Enlargement

UNITS

Candidates should be familiar with the following units and their symbols.

(A) Length

1000 millimetres (mm) = 100 centimetres (cm) = 1 metre(m).
1000 metres = 1 kilometre (km)

(B) Area

10,000 square metres (m2) = 1 hectare (ha)

(C) Capacity

1000 cubic centimeters (cm3) = 1 litre (l)

(D) Mass

milligrammes (mg) = 1 gramme (g)
1000 grammes (g) = 1 kilogramme( kg )
ogrammes (kg) = 1 tonne.

(E) Currencies

The Gambia – 100 bututs (b) = 1 Dalasi (D)
Ghana – 100 Ghana pesewas (Gp) = 1 Ghana Cedi ( GH¢)
Liberia – 100 cents (c) = 1 Liberian Dollar (LD)
Nigeria – 100 kobo (k) = 1 Naira (N)
Sierra Leone – 100 cents (c) = 1 Leone (Le)
UK – 100 pence (p) = 1 pound (£)
USA – 100 cents (c) = 1 dollar ($)
French Speaking territories: 100 centimes (c) = 1 Franc (fr)
Any other units used will be defined.

Tips for WAEC Mathematics Exam 2023

Here are some tips to help you prepare for the WAEC Mathematics Exam 2023:

• Familiarize yourself with the WAEC Mathematics syllabus. It provides a detailed outline of the topics and subtopics that will be covered in the exam. Make sure to focus your study efforts on these areas.

• Start by reviewing the fundamental concepts of mathematics. Ensure you have a strong foundation in topics such as algebra, geometry, trigonometry, and calculus. Understanding the basics will make it easier to tackle more complex problems.

• Mathematics requires practice. Solve a wide range of problems from past WAEC Mathematics exams and other reliable sources. This will help you become familiar with different question formats and improve your problem-solving skills.

• Develop effective time management skills to ensure you can complete the exam within the allocated time. Practice solving problems under timed conditions to improve your speed and accuracy.

• Be familiar with various problem-solving techniques and strategies. This includes identifying key information, breaking down complex problems into simpler steps, and applying appropriate formulas and theorems.

• In the exam, show all your workings and steps clearly. This allows the examiner to follow your thought process and award partial marks even if your final answer is incorrect. Practice presenting your solutions neatly and concisely.

• Enhance your mental math skills by practicing calculations in your head. This will help you save time during the exam and increase your confidence in solving problems without relying heavily on a calculator.

• Memorize important formulas, theorems, and identities relevant to the exam. Understanding when and how to apply them correctly will greatly assist you in solving problems efficiently.

• If you come across any challenging concepts or topics, don't hesitate to seek clarification from your teachers or classmates. Understanding the material thoroughly is essential for success in the exam.

• On the day of the exam, stay calm and maintain a positive mindset. Read each question carefully and approach them with confidence. Manage your time effectively and double-check your answers before submitting the paper.

Remember, consistent and focused preparation is key to performing well in the WAEC Mathematics Exam. By following these tips and dedicating sufficient time to study and practice, you can boost your confidence and increase your chances of achieving excellent results. 

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