IMYC Year 8 Maths Revision

IMYC Year 8 Maths Revision – Core Concepts Explained

Welcome to this comprehensive revision guide for Year 8 mathematics. In this course we will unpack the key ideas behind each quiz question, provide clear explanations, and give you practice tips to master the topics. The content is structured for easy navigation and is SEO‑friendly, using semantic HTML elements such as headings, emphasis, and

1. Expanding Binomials

When you multiply two binomials, you apply the distributive property (also known as the FOIL method – First, Outer, Inner, Last). For the expression (x + 2)(x + 3) the steps are:

First: x·x = x²
Outer: x·3 = 3x
Inner: 2·x = 2x
Last: 2·3 = 6

Combine the middle terms (3x + 2x) to get 5x, giving the expanded form x² + 5x + 6. This is the answer you will see in the quiz.

Quick check: Which part of the multiplication gave you the 5x term? A) 2·3, B) 2x + 3x, or C) x·x? (Answer: B)

2. Factorising Quadratics

Factorising means rewriting a quadratic as a product of two binomials. For x² + 6x + 8 we look for two numbers that:

Multiply to the constant term (8)
Add to the coefficient of the middle term (6)

The pair 4 and 2 satisfies both conditions (4·2 = 8 and 4+2 = 6). Therefore:

x² + 6x + 8 = (x + 4)(x + 2).

3. Solving Quadratic Equations

To solve x² + 6x + 8 = 0 we can use the factorised form from the previous section:

(x + 4)(x + 2) = 0.

Set each factor equal to zero:

x + 4 = 0 → x = -4
x + 2 = 0 → x = -2

The solution set is x = -4 or x = -2, matching the quiz answer.

4. Understanding Map Scales

A map scale tells you how a distance on the map relates to the real‑world distance. The scale 1 cm = 5 m means every centimetre on the map represents five metres in reality.

To find the real distance for 4 cm:

4 cm × 5 m/cm = 20 m

This conversion skill is essential for geography, design, and everyday problem solving.

5. Applying Pythagoras’ Theorem

Pythagoras’ theorem relates the sides of a right‑angled triangle: a² + b² = c², where c is the hypotenuse.

Given sides 6 cm and 8 cm:

a² = 6² = 36
b² = 8² = 64
a² + b² = 36 + 64 = 100
c = √100 = 10 cm

The hypotenuse length of 10 cm is the correct answer in the quiz.

6. Direct Proportion and the Constant of Variation

When two quantities are directly proportional, they satisfy y = kx, where k is the constant of variation.

If y = 10 when x = 2:

k = y / x = 10 / 2 = 5

Thus the equation becomes y = 5x. This matches the quiz answer for the constant.

7. Writing the Equation for a Direct Proportion

Given y = 20 when x = 4, we first find the constant:

k = 20 / 4 = 5

Therefore the relationship is y = 5x. The other options (y = 4x, y = 6x, y = 2x) do not satisfy the given data.

8. Measuring Distance on a Number Line

The distance between two points on a number line is the absolute difference of their coordinates.

For points -3 and 5:

Distance = |5 - (-3)| = |5 + 3| = 8

This simple concept underpins absolute value and many algebraic manipulations.

9. Quick Revision Checklist

Remember the FOIL method for expanding binomials.
When factorising, look for two numbers that multiply to the constant term and add to the middle coefficient.
Use the factorised form to solve quadratic equations quickly.
Convert map scales by multiplying the map distance by the scale factor.
Apply Pythagoras’ theorem: square the known sides, add, then take the square root.
Identify the constant of variation k by dividing y by x for direct proportion.
Write the direct proportion equation using the constant you found.
Calculate distances on a number line using absolute differences.

10. Further Practice Resources

To deepen your understanding, explore these free online tools:

Khan Academy – Algebra: Interactive videos on expanding, factorising, and solving quadratics.
Math is Fun – Factoring: Step‑by‑step guides and practice quizzes.
Desmos Graphing Calculator: Visualise quadratic functions and their roots.
GeoGebra – Geometry Tools: Explore Pythagoras’ theorem with dynamic constructions.

By mastering these eight core concepts, you will be well‑prepared for your Year 8 maths assessments and future studies. Keep practising, use the resources above, and remember that understanding the ‘why’ behind each step is the key to long‑term success.

What is the expanded form of (x + 2)(x + 3)?

Which pair of numbers correctly factorises x² + 6x + 8?

Solving x² + 6x + 8 = 0 gives which set of solutions?

If a map scale is 1 cm = 5 m, how many metres does 4 cm represent in reality?

Using Pythagoras' theorem, what is the length of the hypotenuse when the other sides are 6 cm and 8 cm?

For a direct proportion y = kx, if y = 10 when x = 2, what is the constant k?

Which of the following equations correctly represents the direct proportion y ∝ x given y = 20 when x = 4?

What is the distance between the points -3 and 5 on a number line?

Expanding (x + 3)(x + 7) yields which quadratic expression?

Solving x² + 10x + 21 = 0 gives which pair of solutions?