Secondary 3 Mathematics

The number being raised to a power — the a in aⁿ.

The small raised number showing how many times to multiply — the n in aⁿ.

The whole expression aⁿ — read as 'a to the power n'.

1 divided by the number. The reciprocal of a is 1/a, so a⁻ⁿ is the reciprocal of aⁿ.

Another word for index — they mean the same thing.

The index is a positive number — e.g. the 3 in a³.

The index is negative — e.g. a⁻², which becomes 1/a².

The index is 0 — any non-zero number to the power 0 equals 1, e.g. 5⁰ = 1.

An expression with variables and constants added/subtracted. e.g. 3x² + 2x − 5.

Each part separated by + or −. e.g. 3x², 2x, −5.

Number in front of variable. In 3x², coefficient is 3.

The term without variable. In 3x² + 2x − 5, constant is −5.

Terms with same variable power. 3x² and 5x² are like terms, can combine.

Highest power. Degree of 3x² + 2x − 5 is 2.

Removing brackets. (x+2)(x+3) = x² + 5x + 6.

Expression with one term. e.g. 5x².

Like 126 in primary division, it's the expression to divide. Example x² + 5x + 6 is the dividend.

Like 3 in primary division, it's what you divide by. Example x + 2 is the divisor.

The answer after division, like 42 in primary division.

What's left over if not divisible. If divisible exactly, remainder is 0.

The step-by-step division method you learned in primary school, not all at once.

The term with biggest power of x. Example in x² + 5x + 6, highest term is x².

After multiplying, always subtract, don't add!

After subtracting, pull down next term from dividend to keep dividing.

Two or more equations with the same unknowns.

Variables to find, usually x and y.

Putting one equation into another.

Adding/subtracting both to cancel one unknown.

The (x, y) pair that satisfies all equations.

Equation with highest power 1. e.g. 2x + 3y = 7.

Number in front of unknown. In 2x, coefficient is 2.

Has a solution. Two lines intersect = has solution.

Mathematical statement comparing two numbers.

Left is bigger than right. e.g. 5 > 3.

Left is smaller than right. e.g. 3 < 5.

Greater than OR equal. e.g. x ≥ 3.

Less than OR equal. e.g. x ≤ 5.

A line with numbers, used to show inequality range.

Circle on number line, means number NOT included.

When multiply/divide by negative, inequality flips direction.

Out of 100. Symbol: %. e.g. 50% = 50100 = 0.5.

Price reduction. e.g. 20% off = original × 0.8.

Price before discount.

Actual price after discount.

Extra money paid/earned for borrowing/saving.

Original amount borrowed/saved. e.g. save $1000, principal = $1000.

Interest as % of principal. e.g. annual rate 5%.

How much quantity increased in %. e.g. population grew 10%.

How much you paid to buy the goods in.

How much you sold the goods for.

Money earned. Selling price minus cost price.

Money lost. Cost price minus selling price.

Profit as percentage of cost price.

Loss as percentage of cost price.

How much you add on top of cost price to sell.

Price reduction, e.g. 20% off means pay 80%.

Original amount deposited or borrowed

Percentage of interest per period

How long, in years

Interest doesn't earn interest, calculated on principal only

Principal plus interest

Interest rate per year

Interest rate per month

Rate and time units must match

Where two lines meet, unit in degrees (°).

Two lines that never meet, same distance apart. Symbol: //.

The line that cuts through two parallel lines.

F angles. Same position on parallel lines, equal.

Z angles. Between parallel lines, on opposite sides, equal.

C angles. Between parallel lines, same side, add to 180°.

Opposite angles when two lines cross, equal.

Angles on a straight line add to 180°.

Size of flat shape. Unit: cm², m².

Space taken by 3D shape. Unit: cm³, m³.

Four-sided shape. Area = length × width.

Three-sided shape. Area = base × height ÷ 2.

Round shape. Area = πr².

Distance from centre to edge. Symbol: r.

3D rectangle. Volume = length × width × height.

3D with two circles top and bottom. Volume = base area × height.

Shape where all points are same distance from centre.

Middle of circle. Symbol: O.

Distance from centre to edge. Symbol: r.

Through centre, both ends at edge. = 2r. Symbol: d.

Perimeter of circle. = πd = 2πr.

Circumference ÷ diameter ≈ 3.14159.

Line joining two points on circle. Longest chord is diameter.

Part of the circle edge.

Information given in the question.

What we need to prove.

Step-by-step reasoning process.

Already proven result, can use directly.

Three angles of triangle add to 180°.

Opposite angles when lines cross, equal.

Same position on parallel lines, equal.

Why each step is true. e.g. Given, Vertically opposite angles equal.

To write a polynomial as a product of two or more factors.

A factor that appears in every term and can be pulled out.

Each chunk separated by + or −. 6x² + 4x has two terms.

The reverse of factorising: multiply out the brackets.

The largest number that divides both — e.g. GCD of 6 and 4 is 2.

Things multiplied together to get the original — e.g. 2 and 3 are factors of 6.

Parentheses — the common factor is written in front of the bracket.

An expression made of several terms added or subtracted — e.g. 6x² + 4x − 3.

An equation with highest power 2, e.g. x² + 5x + 6 = 0.

The x value that makes the equation true. Roots of x² + 5x + 6 = 0 are x = −2 and x = −3.

Turning x² + 5x + 6 into (x+2)(x+3).

Number in front of x². In x² + 5x + 6, coefficient of x² is 1, of x is 5.

The term without x. In x² + 5x + 6, the constant term is 6.

If A × B = 0, then A = 0 or B = 0.

Finding the roots (what x = ?).

ax² + bx + c = 0. a, b, c are numbers, a ≠ 0.

Polynomial with highest power x², e.g. x² + 5x + 6.

Break an expression into product of factors.

Draw a cross, quickly find two numbers.

Result of multiplying two numbers.

Result of adding two numbers.

The number without x, e.g. 6 in x² + 5x + 6.

Number in front of x, e.g. 3 in 3x.

Multiply back to check if correct.

Equation that's true for all x, e.g. (x+1)² = x²+2x+1.

A number times itself, e.g. x², (x+2)².

Two squares subtracted, e.g. x² − 9.

Multiply out the brackets.

Write polynomial as product, opposite of expanding.

When you see a certain arrangement, use matching formula.

Rule you can apply directly.

Multiply back to check.

The longest side of a right-angled triangle, always opposite the right angle.

A 90° angle, usually marked with a small square symbol.

A number multiplied by itself: 3² = 3 × 3 = 9.

The opposite of squaring: √9 = 3, because 3 × 3 = 9.

A triangle with one 90° angle.

The two shorter sides of a right-angled triangle (not the hypotenuse).

A math rule proven to be true. Pythagoras' theorem is one.

A fixed calculation rule — e.g. a² + b² = c².

Opposite ÷ Hypotenuse. sin θ = opp / hyp.

Adjacent ÷ Hypotenuse. cos θ = adj / hyp.

Opposite ÷ Adjacent. tan θ = opp / adj.

The side opposite angle θ (not the hypotenuse).

The side next to angle θ (not the hypotenuse).

The longest side, always opposite the right angle.

Where two sides meet, usually written as θ (theta).

Memory aid: SOH = Sin Opposite/Hypotenuse, CAH = Cos Adjacent/Hypotenuse, TOA = Tan Opposite/Adjacent.

Three common angles: 30°, 45°, 60°.

Opposite ÷ Hypotenuse.

Adjacent ÷ Hypotenuse.

Opposite ÷ Adjacent.

Two sides equal, two base angles equal.

All sides equal, all angles 60°.

Comparison of two side lengths.

Must memorise, no need to calculate in exam.

Angle between horizontal line and line of sight when looking up at object.

Angle between horizontal line and line of sight when looking down at object.

Flat line, parallel to ground.

Straight line from eye to object.

Person looking at something.

Thing being looked at, e.g. building, tree.

How high the object is above ground.

Horizontal distance between observer and object.

Equation true for any angle.

(sinθ)², i.e. sinθ times itself.

(cosθ)², i.e. cosθ times itself.

sinθ ÷ cosθ.

sin²θ + cos²θ = 1. The most important one!

Turn complicated expression into simple one.

Prove the equation is true.

Replace part with formula.

Formula that works for any triangle.

Side opposite angle A.

Side opposite angle B.

Side opposite angle C.

Side opposite the angle.

Angle-Side-Angle, know two angles and one side.

Side-Side-Angle, know two sides and angle opposite one.

Relation between two numbers.

Formula that works for any triangle, used to find sides or angles.

Side opposite angle A, always the side opposite angle A.

Side opposite angle B.

Side opposite angle C.

Angle between two sides, i.e. the angle the two sides sandwich.

Side-Angle-Side, i.e. know two sides and included angle.

Side-Side-Side, i.e. know all three side lengths.

a²+b²=c², only works for right triangles.

How much space the triangle takes up, unit is square.

One side of the triangle, usually the one at the bottom.

Perpendicular distance from vertex to base, 90° to base.

Angle between two sides, i.e. the angle the two sides sandwich.

Find area with two sides and included angle, no need to find height.

Triangle with a 90° angle.

Unit of area, e.g. m², cm².

Rule you can apply directly.

Chance of an event happening, from 0 (impossible) to 1 (certain).

The outcome we care about, e.g. 'rolling a 6'.

All possible outcomes. Dice sample space is {1,2,3,4,5,6}.

Number of outcomes that match the event. Want even number, favourable are 2,4,6 (3).

Every outcome equally likely, can't predict.

The event not happening. P(not 6) = 1 − P(6).

Every outcome has same chance. Fair die each face 16.

Line from 0 (impossible) to 1 (certain), showing probability size.

Sum divided by count. e.g. mean of 1,2,3 = (1+2+3)/3 = 2.

Middle value after sorting. e.g. median of 1,2,3 is 2.

Most frequent value. e.g. mode of 1,2,2,3 is 2.

A collection of numbers, e.g. exam scores of a class.

Ordered from small to large. Must sort before finding median.

'Average' in everyday talk usually means mean.

A number far from the rest. e.g. in 1,2,3,100, 100 is outlier.

Max minus min. e.g. range of 1,2,3,100 = 100 − 1 = 99.

Uses bar heights to show quantity. Good for comparing categories.

Connects data points with lines. Good for seeing trends.

Uses circle sectors to show proportions. Good for overall distribution.

Horizontal and vertical lines on graph, with scales.

Number interval on axis. e.g. each grid = 10 people.

Text on graph, e.g. title, category names.

How often something happens. e.g. 5 students like math.

Direction of data change. Up, down, or stable.

Collected numbers or information.

Ask people questions to collect data.

All subjects to study. e.g. whole class.

Part taken from population. e.g. ask 10 students.

Table showing how often each category appears.

Add all numbers ÷ how many.

Middle number after sorting.

Number that appears most often.

Method to calculate 'or' probability

Two events cannot happen at the same time

Two events can happen at the same time

Two sets combined

Overlap of two sets

Probability of A or B happening

Probability of both A and B happening

Diagram using circles to show sets

Method to calculate 'and' probability

One event doesn't affect the other

One event affects the other

Probability of both events happening

Probability of A given B happened

Probability under a condition

Put back after drawing

Not put back after drawing

How spread out the data is

Average of squared differences from mean

Square root of variance

Sum of all values divided by count

Difference from the mean

How spread out data is

Data is clustered together

Symbol for standard deviation

Running total of frequencies

Upper boundary of each class

The middle value

Value at 25% mark

Value at 75% mark

Upper quartile minus lower quartile

Graph with lines connecting points

Data grouped into intervals

Input x, output one y. e.g. y = 2x + 1.

Number that can change. Usually x, y.

(x, y) format, represents a point on graph.

Horizontal line on graph, represents x.

Vertical line on graph, represents y.

(0, 0) where two axes cross.

y = mx + c draws a straight line.

How steep the line is. m = rise ÷ run.

Highest power 2. e.g. x².

U-shaped curve from quadratic function.

Highest or lowest point of parabola.

Opens downward, vertex is highest point.

Opens upward, vertex is lowest point.

x values when y = 0, where line crosses x-axis.

y value when x = 0, where line crosses y-axis.

Vertical line through vertex, left and right symmetric.

Position on a plane as (x, y). e.g. (3, 2) means x=3, y=2.

Horizontal number line, positive to the right.

Vertical number line, positive upward.

How steep the line is. Slope = rise ÷ run = (y₂−y₁)/(x₂−x₁).

Where the line crosses y-axis. In y = mx + c, c is the y-intercept.

Formula for a line. Most common is y = mx + c.

(0, 0), where the two axes cross.

Flat line, slope = 0. e.g. y = 3.

Represent circle using x and y

Centre point of circle

Distance from centre to circumference

Coordinates of centre

Symbol for radius

Standard form of circle equation

Multiply out the brackets

Expanded form

All points satisfying a condition

Equal distance

Line perpendicular and midpoint of segment

Line that bisects an angle

Point given in question

Distance stays fixed

Locus equidistant from fixed point

Perpendicular bisector of two points is straight line