S4 Mathematics

Expression made of constants and variables added, subtracted and multiplied, e.g. 3x² + 2x - 5.

Each add/subtract unit in polynomial, e.g. 3x², 2x, -5 are terms.

Number in front of variable, e.g. 3 in 3x² is coefficient.

Term without variable, e.g. -5 is constant term.

Highest power, e.g. 3x² + 2x - 5 has degree 2.

Terms with same variable and power, can combine.

Remove brackets, e.g. (x+1)(x+2) = x²+3x+2.

Combine like terms, make expression simplest.

Polynomial being divided, e.g. x² + 3x + 2 in (x² + 3x + 2) ÷ (x + 1) is dividend.

Expression used to divide, e.g. (x + 1) is divisor.

Answer after division, e.g. (x² + 3x + 2) ÷ (x + 1) = x + 2, x + 2 is quotient.

Left over when can't divide fully, degree must be lower than divisor.

Like number long division, divide step by step.

Split an expression into parts.

Highest degree term, e.g. 3x² in 3x² + 2x + 1.

Remainder is a constant, no x.

Split polynomial into product of factors.

Each term in product, e.g. (x+1) and (x+2) in (x+1)(x+2) are factors.

Common in every term, e.g. 2x in 2x² + 4x is common factor.

Method to factor quadratic trinomial, find two numbers multiply to constant, add to linear coefficient.

Highest degree 2, e.g. x² + 3x + 2.

Multiply two things together.

Opposite of factorisation, expand product back to polynomial.

After factorise expand back, see if equals original.

Equation highest degree 2, e.g. x² + 5x + 6 = 0.

Answer of equation, x value that makes equation equal 0.

Find all roots of equation.

Factorise left side, then each factor equals 0 to solve.

x = (-b ± √(b² - 4ac)) / 2a, general method.

b² - 4ac, used to judge how many real roots.

Quadratic equation usually has two answers.

If A × B = 0, then A = 0 or B = 0.

Expression with > < ≤ ≥, e.g. x + 2 > 5.

All x values that satisfy inequality.

More than, symbol >.

Less than, symbol <.

Points where equals 0, split number line into three parts.

Quadratic term positive, parabola opens up.

Range between two numbers.

Line with scales, used to show range.

Small number on top right, e.g. 3 in 2³ is index.

Big number, e.g. 2 in 2³ is base.

Opposite of index, e.g. log₂8 = 3, because 2³ = 8.

a^m × a^n = a^(m+n), same base multiply, index add.

a^m ÷ a^n = a^(m-n), same base divide, index subtract.

(a^m)^n = a^(mn), power of power, index multiply.

a^x = y and log_a y = x are same thing.

Base 10, e.g. log 100 = 2.

Ordered list of numbers, e.g. 1, 3, 5, 7, ...

Difference between each term fixed, e.g. 1, 3, 5, 7 difference 2.

Ratio between each term fixed, e.g. 1, 2, 4, 8 ratio 2.

Arithmetic sequence adjacent difference, d.

Geometric sequence adjacent ratio, r.

nth number in sequence.

Add first n terms together.

First number, a.

Two equations both true, e.g. x + y = 5 and x - y = 1.

Two unknowns in equation, e.g. x and y.

Find x and y values that make both equations true.

From one equation express one variable, substitute into another.

Multiply two equations by suitable numbers, add/subtract eliminate one variable.

Have intersection, have answer.

Two lines parallel, no intersection.

Substitute answer into both equations, see if both correct.

A rule mapping each x to one output f(x).

The U-shaped graph of a quadratic.

The maximum or minimum point.

Δ=b²-4ac: predicts x-intercepts.

The vertical line through the vertex.

Where the graph crosses the x-axis.

Shifting or flipping a graph.

The y-value at the vertex when a<0.

An inequality limiting the variables.

The overlapping shaded region.

The expression to maximise or minimise.

A vertex of the feasible region.

The best corner point.

A system of inequalities.

A point used to decide which side to shade.

Involving only first powers of x and y.