Recall — GCSE Flashcards
🧮 GCSE Mathematics Flashcards
Core formulae, identities and methods — 10 free revision cards. Study them below, or add the whole deck to Recall and let FSRS spaced repetition schedule your revision so it actually sticks.
State the quadratic formula.
For $ax^2 + bx + c = 0$:
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
What is Pythagoras' theorem?
For a right-angled triangle with hypotenuse $c$:
$$a^2 + b^2 = c^2$$
$$a^2 + b^2 = c^2$$
State the three trigonometric ratios (SOH CAH TOA).
$\sin\theta = \dfrac{\text{opp}}{\text{hyp}}$
$\cos\theta = \dfrac{\text{adj}}{\text{hyp}}$
$\tan\theta = \dfrac{\text{opp}}{\text{adj}}$
$\cos\theta = \dfrac{\text{adj}}{\text{hyp}}$
$\tan\theta = \dfrac{\text{opp}}{\text{adj}}$
What is the formula for the area of a circle?
$A = \pi r^2$
And the circumference: $C = 2\pi r$ (or $\pi d$).
And the circumference: $C = 2\pi r$ (or $\pi d$).
What is the discriminant and what does it tell you?
$\Delta = b^2 - 4ac$
- $\Delta > 0$: two real roots
- $\Delta = 0$: one repeated root
- $\Delta < 0$: no real roots
- $\Delta > 0$: two real roots
- $\Delta = 0$: one repeated root
- $\Delta < 0$: no real roots
How do you find a percentage change?
$$\text{\% change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$$
Positive = increase, negative = decrease.
Positive = increase, negative = decrease.
State the laws of indices.
$a^m \times a^n = a^{m+n}$
$a^m \div a^n = a^{m-n}$
$(a^m)^n = a^{mn}$
$a^0 = 1$, $a^{-n} = \dfrac{1}{a^n}$
$a^m \div a^n = a^{m-n}$
$(a^m)^n = a^{mn}$
$a^0 = 1$, $a^{-n} = \dfrac{1}{a^n}$
What is the formula for the volume of a cone?
$V = \dfrac{1}{3}\pi r^2 h$
Curved surface area: $\pi r l$ (where $l$ is slant height).
Curved surface area: $\pi r l$ (where $l$ is slant height).
State the sine rule and cosine rule.
Sine rule: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$
Cosine rule: $a^2 = b^2 + c^2 - 2bc\cos A$
Cosine rule: $a^2 = b^2 + c^2 - 2bc\cos A$
What is the equation of a straight line?
$y = mx + c$
- $m$ = gradient = $\dfrac{\Delta y}{\Delta x}$
- $c$ = y-intercept
- $m$ = gradient = $\dfrac{\Delta y}{\Delta x}$
- $c$ = y-intercept
These 10 cards are a free starter deck — a companion for memorising the core facts, not a complete course. In the Recall app you can also paste your own class notes and have AI build decks for the topics your exam board covers.