Make the coefficients of one variable equal, then add or subtract equations to eliminate it.

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

$m = \frac{y_2 - y_1}{x_2 - x_1}$

aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

Question 1

What does it mean to "expand" brackets?

Accepted Answer

Multiply each term inside the brackets by the term outside: e.g. 3(x + 2) = 3x + 6.

Question 2

Expand (x + 3)(x + 5).

Accepted Answer

x² + 8x + 15 (using FOIL or the grid method).

Question 3

What does it mean to "factorise" an expression?

Accepted Answer

Write it as a product of its factors, e.g. x² + 5x + 6 = (x + 2)(x + 3).

Question 4

Factorise x² − 9.

Accepted Answer

(x + 3)(x − 3) — this is the difference of two squares.

Question 5

What is the quadratic formula?

Accepted Answer

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for ax² + bx + c = 0.

Question 6

What does the discriminant (b² − 4ac) tell you?

Accepted Answer

If > 0: two real roots. If = 0: one repeated root. If < 0: no real roots.

Question 7

How do you solve simultaneous equations by elimination?

Accepted Answer

Make the coefficients of one variable equal, then add or subtract equations to eliminate it.

Question 8

What is the gradient-intercept form of a straight line?

Accepted Answer

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

Question 9

How do you find the gradient between two points?

Accepted Answer

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Question 10

What are the rules for indices: aᵐ × aⁿ and aᵐ ÷ aⁿ?

Accepted Answer

aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

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