Algebra - Main Topics Covered The CSEC Mathematics syllabus - CSEC Mathematics exam

June 09, 2025

Algebra

🧮 1. Algebra

✳️ Equations

An equation shows that two expressions are equal.

Example:
Solve:
2x+3=112x+3=11
Solution:
Subtract 3:
2x=82x=8
Divide by 2:
x=4x=4

✳️ Inequalities

Inequalities compare expressions using symbols like >, <, ≥, ≤.

Example:
Solve:
3x−5<103x−5<10
Add 5:
3x<153x<15
Divide by 3:
x<5x<5

✳️ Factorization

This means writing an expression as a product of its factors.

Example:
Factor:
x2+5x+6x2+5x+6
Find two numbers that multiply to 6 and add to 5: (2 and 3)
So:
(x+2)(x+3)(x+2)(x+3)

✳️ Algebraic Expressions

These are combinations of variables, numbers, and operations.

Example:
Simplify:
3x+2x−53x+2x−5
Combine like terms:
5x−55x−5

📐 2. Geometry

✳️ Angles

A straight line = 180°
A triangle = 180°
A right angle = 90°

Example:
If one angle in a triangle is 50° and another is 60°, the third is:
180−(50+60)=70°180−(50+60)=70°

✳️ Triangles

Equilateral: all sides and angles equal
Isosceles: two sides equal
Scalene: all sides different

✳️ Circles

Radius: from center to edge
Diameter: across the circle (2 × radius)
Circumference: C=2πrC=2πr
Area: A=πr2A=πr2

✳️ Geometric Reasoning

Use known facts to find unknown angles or sides.

📏 3. Measurement

✳️ Perimeter

Add all sides.

Example:
Rectangle: 5 cm by 3 cm
Perimeter = 2(5+3)=16 cm2(5+3)=16 cm

✳️ Area

Rectangle: A=l×wA=l×w
Triangle: A=12×b×hA=21×b×h
Circle: A=πr2A=πr2

✳️ Volume

Cube: V=s3V=s3
Cylinder: V=πr2hV=πr2h

✳️ Time & Conversions

1 hour = 60 minutes
1 km = 1000 m
1 L = 1000 mL

📊 4. Statistics

✳️ Data Collection

Use surveys, experiments, or observations.

✳️ Graphs

Bar graph: for categories
Line graph: for trends
Pie chart: for parts of a whole

✳️ Mean, Median, Mode

Mean: average
Median: middle value
Mode: most frequent

Example:
Data: 2, 4, 4, 6, 8
Mean = (2+4+4+6+8)/5=24/5=4.8(2+4+4+6+8)/5=24/5=4.8
Median = 4
Mode = 4

🔢 5. Number Theory

✳️ Operations

Add, subtract, multiply, divide.

✳️ Fractions

12+14=24+14=3421+41=42+41=43

✳️ Decimals

0.5 + 0.25 = 0.75

✳️ Percentages

20% of 50 =
20100×50=1010020×50=10

✳️ Ratios

3:2 means for every 3 of one, there are 2 of the other.

🧭 6. Vectors and Matrices

✳️ Vectors

Represent direction and magnitude.

Example:
Vector a = (3, 2)
Means 3 units right, 2 units up.

✳️ Matrices

Rectangular arrays of numbers.

Example:
Add:
[1234]+[5678]=[681012][1324]+[5768]=[610812]

📈 7. Relations, Functions, and Graphs

✳️ Linear Functions

Form: y=mx+cy=mx+c
Graph is a straight line.

Example:
y=2x+1y=2x+1
Plot points: (0,1), (1,3), (2,5)

✳️ Quadratic Functions

Form: y=ax2+bx+cy=ax2+bx+c
Graph is a curve (parabola).

Example:
y=x2−4y=x2−4
Plot: (−2,0), (0,−4), (2,0)