**WAEC 2022 MATHEMATICS SYLLABUS GENERAL GUIDE.**

**WAEC 2022 MATHEMATICS SYLLABUS GENERAL GUIDE.**

__For all papers which involve mathematical calculations, mathematical and statistical tables published for WAEC should be used in the examination room. However, the use of non-programmable, silent and cordless calculator is allowed.__

__The calculator must not have a paper printout. Where the degree of accuracy is not specified in a question the degree of accuracy expected will be that obtainable from the WAEC mathematical tables.__

__Waec Mathematics Syllabus Waec 2022 Mathematics Syllabus__

__Waec 2022 Mathematics expo Waec2022 Mathematics Syllabus Waec 2022 Mathematics runs__

__Waec 2022 Mathematics Syllabus Waec 2022 Mathematics Syllabus__

**Trigonometrical tables**

in the pamphlet have different columns for decimal fractions of a degree, not for minutes and seconds.

__No mathematical tables other than the above may be used in the examination. It is strongly recommended that schools/candidates obtain copies of these tables for use throughout the course.__

__Candidates should bring rulers, protractors, pair of compasses and set squares for all papers.
They will not be allowed to borrow such instruments and any other materials from other candidates in the examination hall. It should be noted that some questions may prohibit the use of tables and /or calculators. The use of slide rules is not allowed.__

__Graph paper ruled in 2 mm squares, will be provided for any paper in which it is required.__

**UNITS**

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

Length

10000 millimetres (mm) = 100 centimetres (cm) = 1 metre (m)

1000 metres = 1 kilometre (km)

Area

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

Cubic Capacity

1000 cubic centimetres (cm3) = 1 litre (1)

Mass

1000 milligrammes (mg) = 1 gramme (g)

1000 grammes (g) = 1 kilogramme (kg)

**WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION**

**MATHEMATICS (CORE)/GENERAL MATHEMATICS**

__324__

**CURRENCIES**

__The Gambia – 100 bututs (b) = 1 dalasi (D)
Ghana – 100 pesewas (p) = 1 Ghana cedi GH(¢)
Liberia – 100 cents (c) = 1 dollar ($)
*Nigeria – 100 kobo (k) = 1 naira (N)
*Sierra Leone – 100 cents (c) = 1 leone (Le)
U. K. – 100 pence (p) = 1 pound (£)
U.S.A. – 100 cents (c) = 1 dollar ($)__

__French speaking territories : 100 centimes (c) = 1 franc (fr)
Any other units used will be defined.
*General Mathematics/Mathematics (Core).__

**AIMS OF THE WAEC MATHEMATICS SYLLABUS**

__The syllabus is not intended to be used as a teaching syllabus. Teachers are advised to use
their own National teaching syllabuses. The aims of the syllabus are to test:__

__(i) computational skills;
(ii) the understanding of mathematical concepts and their applications to everyday living;
(iii) the ability to translate problems into mathematical language and solve them with
related mathematical knowledge;
(iv) the ability to be accurate to a degree relevant to the problems at hand;
(v) precise, logical and abstract thinking.__

**WAEC MATHEMATICS SYLLABUS: EXAMINATION FORMAT**

__There will be two papers both of which must be taken.__

__PAPER 1 – 11/2 hours
PAPER 2 – 21/2 hours__

**WAEC MATHEMATICS SYLLABUS**

**TOPICS CONTENTS NOTES**

A. NUMBER AND NUMERATION

**(a) Number Bases**

__(i) Binary numbers__

__**(ii) Modular arithmetic__

__Conversions from base 2 to base 10 and
vice versa. Basic operations excluding
division. Awareness of other number
bases is desirable.__

__Relate to market days, the clock etc.
Truth sets (solution sets) for various open
sentences, e.g. 3 x 2 = a(mod) 4, 8 + y =
4 (mod) 9.__

**(b) Fractions, decimals and approximations**

__(i) Basic operations on
fractions and decimals.__

__(ii) Approximations and
significant figures__

__Approximations should be realistic e.g. a
road is not measured correct to the
nearest cm. Include error.__

**(c) Indices**

__(i) Laws of indices.__

__(ii) Numbers in standard
form.__

__Include simple examples of negative and
fractions indices.__

__e.g. 375.3 = 3.753 x 102
0.0035 = 3.5 x 10-3
Use of tables of squares,
square roots and reciprocals.__

**(d) Logarithms**

__(i) Relationship between
indices and
logarithms e.g.__

__y = 10k → K = log10 y__

__(ii) Basic rules of logarithms i.e.
log10 (pq) = log10P + log10q__

__log10 (p/q) = log10 P – log10q__

__log10Pn = nlog10P__

__(iii) Use of tables of logarithms,
Base 10 logarithm and
Antilogarithm tables.__

__Calculations involving
multiplication, division,
powers and square roots.__

**(e) Sequence**

__(i) Patterns of sequences.
Determine any term of a
given sequence.__

__*(ii) Arithmetic Progression (A.P)
Geometric Progression (G.P).__

__The notation Un = the nth term of
a sequence may be used.__

__Simple cases only, including word
problems. Excluding sum Sn.__

**(f) Sets**

__(i) Idea of sets, universal set,
finite and infinite sets, subsets,
empty sets and disjoint sets;
idea of and notation for union,
intersection and complement of
sets.__

__(ii) Solution of practical problems
involving classification, using
Venn diagrams.__

__Notations: ℰ,, , , , , P1
(the complement of P).
* Include commutative,
associative and distributive
properties.__

__The use of Venn diagrams
restricted to at most 3 sets.__

__**(g) Logical reasoning Simple statements. True and false
statements. Negation of
statements.__

__Implication, equivalence and valid
arguments.__

__Use of symbols : ~, , , .__

__Use of Venn diagrams preferable.__

__WEST AFRICAN SENIOR SCHOOL CERTIFICATE EXAMINATION
MATHEMATICS (CORE)/GENERAL MATHEMATICS__

__327__

**TOPICS CONTENTS NOTES**

(h) Positive and Negative

integers. Rational numbers

__The four basic operations on
rational numbers__

__Match rational numbers with
points on the number line.__

__Notation: Natural numbers (N),
Integers (Z), Rational numbers
(Q)__

__(i) Surds__

__Simplification and
Rationalisation of simple surds.__

__Surds of the form a and a b
b
where a is a rational and b is a
positive integer.__

__(j) Ratio, Proportion
and Rates__

__Financial partnerships; rates of
work, costs, taxes, foreign
exchange, density (e.g. for
population) mass, distance,
time and speed.__

__Include average rates.__

__(k) Variation__

__Direct, inverse and partial
variations.
*Joint variations.__

__Application to simple practical
problems.__

__(l) Percentages__

__Simple interest, commission,
discount, depreciation, profit
and loss, compound interest
and hire purchase.__

__Exclude the use of compound
interest formula.__

__B. ALGEBRAIC
PROCESSES__

__(a) Algebraic
Expressions__

__(i) Expression of
statements in symbols.__

__(ii) Formulating algebraic
expressions from given
situations.__

__(iii) Evaluation of algebraic
expressions.__

__eg. Find an expression for the
cost C cedis of 4 pears at x cedis
each and 3 oranges at y cedis each
C = 4x + 3y__

__If x = 60 and y = 20.
Find C.__

__(b) Simple operations on
algebraic xpressions.__

__(i) Expansion__

__(ii) Factorisation__

__e.g. (a+b) (c+d). (a+3) (c+4)__

__Expressions of the form__

__(i) ax + ay
(ii) a (b+c) +d (b+c)
(iii) ax2 + bx +c
where a,b,c are integers__

__(iv) a2 – b2__

__Application of difference of two
squares e.g.__

__492 – 472 = (49 + 47) (49 – 47)__

__= 96 x 2 = 192__

__(c) Solution of linear
equations__

__(i) Linear equations in one variable__

__(ii) Simultaneous linear equations
in two variables.__

__(d) Change of subject of
a formula/relation__

__(i) Change of subject of a
formula/relation__

__(ii) Substitution__

__e.g. find v in terms of f and u
given that__

__1 1 1
— = — + —
ƒ u v__

__(e) Quadratic
equations__

__(i) Solution of quadratic equations__

__(ii) Construction of quadratic
equations with given roots.__

__(iii) Application of solution of
quadratic equations in practical
problems.__

__Using ab = 0 either a = 0 or b
= 0
* By completing the square and
use of formula.
Simple rational roots only.
e.g. constructing a quadratic
equation.__

__Whose roots are –3 and 5/2__

__=> (x = 3) (x – 5/2) = 0.__

__(f) Graphs of Linear
and quadratic
functions.__

__(i) Interpretation of graphs,
coordinates of points, table
of values. Drawing
quadratic graphs and
obtaining roots from graphs.__

__(ii) Graphical solution of a
pair of equations of the
form__

__y = ax2 + bx + c and
y = mx + k__

__(iii) Drawing of a tangent to
curves to determine
gradient at a given point.__

__(iv) The gradient of a line__

__** (v) Equation of a Line__

__Finding:
(i) the coordinates of the
maximum and minimum
points on the graph;__

__(ii) intercepts on the axes.
Identifying axis of
Symmetry. Recognising
sketched graphs.__

__Use of quadratic graph to
solve a related equation__

__e.g. graph of y = x2 + 5x + 6
to solve x2 + 5x + 4 = 0__

__(i) By drawing relevant
triangle to determine the
gradient.__

__(ii) The gradient, m, of the line
joining the points__

__(x1, y1) and (x2, y2) is__

__y2 – y1
m =
x2 – x1__

__Equation in the form
y = mx + c or y – y1 = m(x-x1)__

**(g) Linear inequalities**

__(i) Solution of linear
inequalities in one variable
and representation on the
number line.__

__(ii) Graphical solution of linear
inequalities in two variables__

__Simple practical problems__

**** (h) Relations and functions**

__(i) Relations__

__(ii) Functions__

__Various types of relations
One – to – one,
many – to – one,
one – to – many,
many – to – many__

__The idea of a function.
Types of functions.
One – to – one,
many – to – one.__

__(i) Algebraic fractions__

__Operations on algebraic
fractions__

__(i) with monomial
denominators.__

__(ii) with binomial
denominators.__

__Simple cases only e.g.
1 1 x + y
— + — = —- (x 0, and y0)
x y xy__

__Simple cases only e.g.__

__1 + 1 = 2x – a – b
x –b x – a (x-a) (x – b)
where a and b are constants and
xa or b.__

__Values for which a fraction is
not defined e.g.
1
x + 3 is not defined for x = -3.__

**C. MENSURATION**

__(a) Lengths and Perimeters__

__(i) Use of Pythagoras
theorem, sine and cosine
rules to determine
lengths and distances.__

__(ii) Lengths of arcs of
circles. Perimeters of
sectors and Segments.__

__*(iii) Latitudes and Longitudes.__

__No formal proofs of the theorem
and rules are required.__

__Distances along latitudes and
longitudes and their
corresponding angles.__

__(b) Areas
(i) Triangles and special
quadrilaterals – rectangles,
parallelograms and trapezia.__

__(ii) Circles, sectors and
segments of circles.__

__(iii) Surface areas of cube, cuboid,
cylinder, right triangular prisms
and cones. *Spheres.__

__Areas of similar figures.
Include area of triangles is
½ base x height and *1/2 abSin C.__

__Areas of compound shapes.
Relation between the sector of a
circle and the surface area of a
cone.__

**(c) Volumes**

__(i) Volumes of cubes, cuboid,
cylinders, cones and right
pyramids. * Spheres.__

__(ii) Volumes of similar solids__

__Volumes of compound shapes.__

**D. PLANE GEOMETRY**

__(a) Angles at a point__

__(i) Angles at a point add up to
360.__

__(ii) Adjacent angles on a
straight line are supplementary.__

__(iii) Vertically opposite angles are
equal.__

__The results of these standard
theorems stated under contents
must be known but their formal
proofs are not required.
However, proofs based on the
knowledge of these theorems
may be tested.__

__The degree as a unit of measure.__

__Acute, obtuse, reflex angles.__

__(b) Angles and intercepts on parallel lines__

__(i) Alternate angles are equal.__

__(ii) Corresponding angles are equal.__

__(iii) Interior opposite angles are
supplementary.__

__*(iv) Intercept theorem__

__Application to proportional
division of a line segment.__

__(c) Triangles and other
polygons__

__(i) The sum of the angles of a
triangle is 2 right angles.__

__(ii) The exterior angle of a
triangle equals the sum of
the two interior opposite
angles.__

__(iii) Congruent triangles.__

__(iv) Properties of special
triangles – isosceles,
equilateral, right-angled.__

__(v) Properties of special
quadrilaterals –
parallelogram, rhombus,
rectangle, square,
trapezium.__

__(vi) Properties of similar
triangles.__

__(vii) The sum of the angles of a
polygon.__

__(viii) Property of exterior angles
of a polygon.__

__(ix) Parallelograms on the same
base and between the same
parallels are equal in area.__

__Conditions to be known but
proofs not required. Rotation,
translation, reflection and lines
of symmetry to be used.__

__Use symmetry where applicable.__

__Equiangular properties and ratio
of sides and areas.__

__(d) Circles__

__(i) Chords__

__(ii) The angle which an arc of a
circle subtends at the centre
is twice that which it
subtends at any point on the
remaining part of the
circumference.__

__(iii) Any angle subtended at the
circumference by a diameter
is a right angle.__

__Angles subtended by chords in a
circle, at the centre of a circle.
Perpendicular bisectors of
chords.__

__(iv) Angles in the same segment
are equal__

__(v) Angles in opposite
segments are supplementary.__

__(vi) Perpendicularity of tangent and
radius.__

__(vii) If a straight line touches a circle
at only one point 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 alternative
segment.__

__(e) Construction__

__(i) Bisectors of angles and line
segments.__

__(ii) Line parallel or perpendicular
to a given line.__

__(iii) An angle of 90º, 60º, 45º, 30º
and an angle equal to a given
angle.__

__(iv) Triangles and quadrilaterals
from sufficient data.__

__Include combination of these
angles e.g. 75º, 105º, 135º,
etc.__

__(f) Loci__

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

__(i) Points at a given distance from a
given point.__

__(ii) Points equidistant from two
given points.__

__(iii) Points equidistant from two
given straight lines.__

__(iv) Points at a given distance from
a given straight line.__

__Consider parallel and
intersecting lines.__

__E. TRIGONOMETRY__

__(a) Sine, cosine and
tangent of an angle.__

__(b) Angles of elevation
and depression.__

__(c) Bearings__

__(i) Sine, cosine and tangent
of an acute angle.__

__(ii) Use of tables.__

__(iii) Trigonometric ratios of
30º, 45º and 60º.__

__*(iv) Sine, cosine and
tangent of angles
from 0º to 360º.__

__*(v) Graphs of sine and
cosine.__

__Calculating angles of elevation and
depression. Application to heights
and distances.__

__(i) Bearing of one point from
another.__

__(ii) Calculation of distances
and angles.__

__Without use of tables.__

__Related to the unit circle.__

__0º ≤ x ≥ 360º__

__Easy problems only__

__Easy problems only__

__Sine and cosine rules may be
used.__

**E. STATISTICS AND**

**PROBABILITY**

**(a) Statistics**

__(i) Frequency distribution.__

__(ii) Pie charts, bar charts,
histograms and frequency
polygons.__

__(iii) Mean, median and mode
for both discrete and
grouped data.__

__(iv) Cumulative frequency
curve, median; quartiles
and percentiles.__

__(v) Measures of dispersion:
range, interquartile range,
mean deviation and
standard deviation from the
mean.__

__Reading and drawing simple
inferences from graphs and
interpretations of data in
histograms.__

__Exclude unequal class interval.
Use of an assumed mean is
acceptable but nor required. For
grouped data, the mode should
be estimated from the histogram
and the median from the
cumulative frequency curve.__

__Simple examples only. Note
that mean deviation is the mean
of the absolute deviations.__

**(b) Probability**

__(i) Experimental and
theoretical probability.__

__(ii) Addition of probabilities
for mutually exclusive and
independent events.__

__(iii) Multiplication of
probabilities for
independent events.__

__Include equally likely events e.g.
probability of throwing a six
with fair die, or a head when
tossing a fair coin.__

__Simple practical problems only.
Interpretation of ‘and’ and ‘or’
in probability.__

****(G) VECTORS AND TRANSPORMATIONS IN A PLANE**

__(a) Vectors in a Plane.__

__(i) Vector as a directed line
segment, magnitude,
equal vectors, sums and
differences of vectors.__

__(ii) Parallel and equal
vectors.__

__(iii) Multiplication of a
vector by a scalar.__

__(iv) Cartesian components of
a vector.__

__Column notation. Emphasis on
graphical representation.__

__Notation__

__0 for the zero__

__vector.__

__(b) Transformation in the
Cartesian Coordinate
plane.__

__(i) Reflection__

__(ii) Rotation__

__(iii) Translation__

__The reflection of points and
shapes in the x and y axes and in
the lines x = k and y = k, where
k is a rational number.
Determination of the mirror
lines of points/shapes and their
images.__

__Rotation about the origin.__

__Use of the translation vector.__

__Waec Mathematics Syllabus__

__Waec Mathematics Syllabus__

__Waec Mathematics Syllabus__

Thank you the founder of exams lord I wish if you people with a due respect to help me in all my papers.Yes,Just Subscribe and get your self registered.

Thanks

Thank you very much all the members of exams lord may God Hart roaches you all to do this without any form of cheating in Jesus name we pray amen.secondly with a due respect I wish if you people will assist me in all my papers with the thing I have, thanks.Pingback: School Resumption: NECO Candidates Should Never Dream Of Resuming School Before Others |what are you going to write this paperI too want to thank u for your help and support that you have done to this group and the rest of the the team candidate and i said may almighty God bless all of you in Jesus name amen.is this realPingback: WAEC releases 2022 WASSCE timetable |O my God finall I will be writing my waceWowYesThank you very much examlordis that trueThank you all my hope is that you will assist me in examination.Thank you every muchHIHiPingback: BEST WEBSITE FOR JAMB EXPO 2022, WAEC EXPO 2022, WAEC RUNZ, NECO RUNZ 2022,SCHOOL NEWS, UPDATES