Year 9 Maths · KS3 notes

Indices, standard form and algebra

Clear notes with worked examples, then 4 practice questions with answers. Written by Beyond Tutors tutors for the KS3 National Curriculum.

Index laws

$x^a \times x^b = x^{a+b}$ $x^a \div x^b = x^{a-b}$ $(x^a)^b = x^{ab}$

$x^0 = 1$ $x^{-1} = \dfrac{1}{x}$

STANDARD FORM: $A \times 10^n$ with $1 \le A < 10$

46 000 000 = $4.6 \times 10^7$ 0.00032 = $3.2 \times 10^{-4}$

DOUBLE BRACKETS (multiply every term by every term)

$(x + 3)(x + 5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15$

$x^2 + 7x + 12$ : find two numbers that multiply to 12 and add to 7 → 3 and 4

$= (x + 3)(x + 4)$

Solve like equations: $3x - 4 < 11$ → $3x < 15$ → $x < 5$

(If you multiply or divide by a negative number, flip the sign.)

$x + y = 10$ and $x - y = 4$ : add them → $2x = 14$ → $x = 7$ , then $y = 3$

Try each one, then tap to see the answer and why.