Brilliance Grade 8 Mathematics Mind Map

1.0 Numbers

1.1 Integers

Understanding positive and negative numbers including zero.

Example:

If the temperature is -5°C and it rises by 8°C, the new temperature is:

-5 + 8 = 3°C

1.2 Fractions

Operations with fractions and mixed numbers.

Example:

Calculate: 2/3 + 1/4

Solution: Find common denominator (12)

= (8/12) + (3/12) = 11/12

1.3 Decimals

Decimal operations and conversions.

Example:

Convert 3/8 to a decimal:

3 ÷ 8 = 0.375

Round 0.375 to 2 decimal places: 0.38

1.4 Squares and Square Roots

Calculating squares and square roots of numbers.

Example:

Find the square root of 144:

√144 = 12 (because 12 × 12 = 144)

1.5 Rates, Ratio, Proportions and Percentages

Understanding and applying ratios, rates, and percentages.

Example:

If 5 oranges cost KSh 120, what is the cost of 8 oranges?

Cost per orange = 120 ÷ 5 = KSh 24

Cost for 8 oranges = 24 × 8 = KSh 192

2.0 Algebra

2.1 Algebraic Expressions

Simplifying and factorizing algebraic expressions.

Example:

Factorize: 3x² + 6x

= 3x(x + 2)

2.2 Linear Equations

Solving linear equations with one or two variables.

Example:

Solve: 2x + 5 = 15

2x = 15 - 5

2x = 10

x = 5

3.0 Measurements

3.1 Circles

Calculating circumference, arc length, and sector perimeter.

Example:

Find the circumference of a circle with radius 7cm (π ≈ 22/7):

C = 2πr = 2 × (22/7) × 7 = 44cm

3.2 Area

Calculating areas of various shapes.

Example:

Find the area of a rectangle with length 8cm and width 5cm:

Area = length × width = 8 × 5 = 40cm²

3.3 Money

Calculating interest, appreciation, and depreciation.

Example:

Calculate simple interest on KSh 10,000 at 5% for 3 years:

Interest = Principal × Rate × Time

= 10,000 × 0.05 × 3 = KSh 1,500

4.0 Geometry

4.1 Geometrical Constructions

Constructing geometric figures with precision.

Example:

Construct a perpendicular bisector of a 6cm line segment:

1. Draw line AB = 6cm

2. With A as center, draw arcs above and below AB

3. With B as center, draw arcs intersecting the first arcs

4. Connect the intersection points to form the perpendicular bisector

4.2 Coordinates and Graphs

Plotting points and drawing linear graphs.

Example:

Plot the points (2,3), (4,5), and (6,7) on a Cartesian plane:

1. Draw x and y axes

2. For (2,3): move 2 right on x-axis, then 3 up on y-axis

3. Repeat for other points

4. Connect the points with a straight line

4.3 Scale Drawing

Creating and interpreting scale drawings.

Example:

A map has scale 1:50,000. If two towns are 4cm apart on the map, what is the actual distance?

Actual distance = map distance × scale

= 4cm × 50,000 = 200,000cm = 2km

4.4 Common Solids

Working with 3D shapes and their properties.

Example:

Find the volume of a cube with side length 5cm:

Volume = side³ = 5 × 5 × 5 = 125cm³

5.0 Data Handling and Probability

5.1 Data Presentation and Interpretation

Creating and analyzing graphs and charts.

Example:

Find the mean of: 12, 15, 18, 20, 10

Mean = (12+15+18+20+10) ÷ 5 = 75 ÷ 5 = 15

5.2 Probability

Calculating probabilities of simple events.

Example:

What is the probability of rolling a 3 on a standard die?

Probability = Number of favorable outcomes / Total outcomes

= 1/6 ≈ 0.167 or 16.7%