Grade 8 Mathematics Review

Grade 8 Mathematics Review – Key Concepts Explained

Welcome to this comprehensive review designed for Grade 8 students. Each section below expands on a typical quiz question, turning a multiple‑choice prompt into a clear, step‑by‑step lesson. By the end of the course you will have reinforced your understanding of algebraic simplification, set theory, factorisation, probability, scientific notation, polygon geometry, linear equations, and volume calculations.

Simplifying Algebraic Expressions

Problem Statement

What is the simplified form of the expression 3x + 2y − x + 5y?

Concept Review

When simplifying expressions, combine like terms—terms that have the same variable raised to the same power.

• Like terms for x: 3x and −x
• Like terms for y: 2y and 5y

Step‑by‑Step Solution

1. Add the x terms: 3x − x = 2x.
2. Add the y terms: 2y + 5y = 7y.
3. Write the combined result: 2x + 7y.

The correct answer is 2x + 7y, which matches choice D.

Set Theory – Union and Intersection

Problem Statement

If n(A)=15, n(B)=12 and n(A∩B)=5, what is n(A∪B)?

Key Formula

The cardinality of the union of two sets is given by:

n(A∪B) = n(A) + n(B) − n(A∩B)

Solution

Plug the numbers into the formula:

n(A∪B) = 15 + 12 − 5 = 22

Thus the correct answer is 22 (choice A).

Factoring Quadratic Expressions for Geometry

Problem Statement

A rectangle has area given by x² + 5x + 6 cm². Which factorisation represents its dimensions?

Factoring Review

To factor a quadratic ax² + bx + c, find two numbers that multiply to ac and add to b. Here a=1, b=5, c=6.

• Numbers that multiply to 6 and add to 5 are 2 and 3.

Factorisation

Therefore:

(x + 2)(x + 3) = x² + 5x + 6

The dimensions of the rectangle are (x + 2) cm and (x + 3) cm. This matches choice D.

Basic Probability with a Six‑Sided Die

Problem Statement

What is the probability of rolling a prime number on a fair six‑sided die?

Prime Numbers on a Die

The prime numbers between 1 and 6 are 2, 3, and 5 – three favorable outcomes.

Probability Calculation

Probability = favorable outcomes / total outcomes = 3/6 = 1/2.

The correct answer is 1/2 (choice D).

Scientific Notation

Problem Statement

Express 0.00036 in standard scientific notation.

How to Convert

Move the decimal point so that only one non‑zero digit remains to the left of the point. Count the moves:

• 0.00036 → 3.6 (four places to the right)

Thus 0.00036 = 3.6 × 10⁻⁴.

Choice A is correct.

Polygon Interior Angles

Problem Statement

The sum of interior angles of a polygon is 900°. How many sides does the polygon have?

Formula for Interior Angles

Sum of interior angles = (n − 2) × 180°, where n is the number of sides.

Solve for n

Set up the equation:

(n − 2) × 180° = 900°

Divide both sides by 180°:

n − 2 = 5 → n = 7

Therefore the polygon is a heptagon (7 sides). Choice D is correct.

Finding the Gradient of a Linear Equation

Problem Statement

What is the gradient of the line given by y = 3 − 7x?

Understanding Gradient

The gradient (slope) is the coefficient of x when the equation is in the form y = mx + c. Here the equation can be rewritten as y = −7x + 3, so m = −7.

Thus the gradient is −7 (choice D).

Volume of a Cylinder

Problem Statement

A cylinder has radius 5 cm and height 10 cm. What is its volume expressed in terms of π?

Volume Formula

Volume = πr²h.

Calculate

r² = 5² = 25.
Volume = π × 25 × 10 = 250π cm³.

Choice B (250π cm³) is correct.

Putting It All Together – Study Tips

To master Grade 8 mathematics, practice each of these core skills regularly:

• Algebraic manipulation: Combine like terms and factor quadratics until the process feels automatic.
• Set theory: Memorise the union‑intersection formula and apply it to word problems.
• Probability: List outcomes first; then count the favorable ones.
• Scientific notation: Remember the rule “one digit before the decimal, adjust the exponent accordingly.”
• Geometry: Relate angle sums to side counts, and always draw a quick sketch.
• Linear equations: Identify the slope directly from the equation’s format.
• Volume calculations: Keep the basic formulas (πr²h for cylinders, ½bh for triangles, etc.) at hand.

By revisiting each concept with the explanations above, you’ll build confidence for quizzes, tests, and future math courses.