Exam Preparation

Grade 10 Mathematics

Simplified mathematics targeting the national curriculum. We break down complex algebraic and geometric theorems into clear, step-by-step logic frameworks ensuring exam readiness and confidence.

Exam Focused Q&A Format

01 Solving Linear Equations

Equations are like balancing scales. Whatever you do to one side, you must do to the other. Our goal is always to isolate the variable (x).

Problem: Solve for x

3x + 5 = 20

Subtract 5 from both sides

To isolate the x term, remove constants attached to it.

3x = 20 - 5
3x = 15

Divide both sides by 3

To get x by itself, neutralize the multiplication by dividing.

x = 15 ÷ 3

Final Answer

x = 5

02 Factorizing Expressions

Factorization is the reverse of expanding brackets. We look for the Highest Common Factor (HCF) that relates the terms together.

What is the HCF?

The Highest Common Factor is the largest number (or variable) that divides exactly into two or more numbers. E.g., for 12x and 16, the numerical HCF is 4.

Example:

Factorize: 4x² + 12x

Find common number: 4
Find common variable: x
Pull out (4x) and place remainder in brackets
Answer: 4x(x + 3)

Test Your Logic

Try to solve the equation before checking the answer below.

Solve for y:
2(y - 4) = 10

Expand the brackets:
2y - 8 = 10

Add 8 to both sides:
2y = 18

Divide by 2:
y = 9

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