Revision Guide for S3 Maths

These flashcards cover key concepts regarding areas, volumes, and properties related to circles, straight lines, and algebra.

Area of a composite shape

Split the diagram into different shapes, find the area of each, and add the areas together.

Volume of a prism

Formula: V = A * h, where A is the cross-sectional area.

Volume of a sphere

Formula: V = (4/3)πr³, where r is the radius.

Volume of a cone

Formula: V = (1/3)πr²h, where r is the radius and h is the height.

Volume of a pyramid

Formula: V = (1/3)Ah, where A is the area of the base.

Gradient of a straight line

The gradient (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

General equation of a straight line

y = mx + c, where m is the gradient and c is the y-intercept.

Equation of a vertical line

x = a, where a is the x-coordinate of every point on the line.

Equation of a horizontal line

y = b, where b is the y-coordinate of every point on the line.

Line through the origin

y = mx, where m is the gradient.

Factorising a quadratic

Look for a common factor, difference of squares, or use double brackets.

Rearranging equations

Gather unknowns on the left-hand side and numbers on the right-hand side.

Important rule for solving inequations

If you divide by a negative, the inequality symbol reverses.

How to expand brackets

Multiply each term inside the bracket by the value outside, taking care with negatives.

Adding or subtracting algebraic fractions

Fractions need a common denominator to be added or subtracted.

Simplifying algebraic fractions

Check if they can factorise and cancel if possible.

Changing the subject of a formula

Use the SADMOB order to rearrange the formula.

Adding and subtracting fractions steps

Convert mixed numbers to improper fractions, find a common denominator, perform the operation, and simplify.

Multiplying fractions steps

Multiply the numerators together and the denominators together, then simplify.

Dividing fractions steps

Convert to improper fractions, invert the second fraction, change the division to multiplication, multiply, and simplify.

Order of operations

Follow BODMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction.

Calculating compound interest

1. Add percentage to 100%, 2. Change to decimal, 3. Raise to the power of time, 4. Multiply by initial value.

Calculating depreciation

1. Subtract percentage from 100%, 2. Change to decimal, 3. Raise to the power of time, 4. Multiply by initial value.

Calculating percentage profit

Actual profit divided by cost, multiplied by 100.

Reversing a percentage change

Write % as a fraction of cost, find 1%, then find 100%.

Length of an arc formula

Arc length = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Area of a sector formula

Area = (θ/360) * πr², where θ is the angle and r is the radius.

Finding the angle of an arc

Use the relationship between arc length and radius to derive angle.

Finding the angle of a sector

Angle can be determined from area and radius relationship.

Properties of circles involving tangents

Tangent to the circle forms a right angle with the radius at the point of contact.

Using trigonometry in circles

In right-angled triangles, use Sin, Cos, or Tan to find missing lengths or angles.

Pythagorean theorem

In a right triangle, a² + b² = c², where c is the hypotenuse.

Finding angles in triangles

Use angle sum properties and relationships between angles and tangents.

Calculating lengths using trigonometry

Use sine, cosine, or tangent ratios to find the lengths of sides in right-angled triangles.