New GCSE Maths required formulae

Question	Answer
Quadratic Formula - solve: $a$ $x^2$ + $b$ $x$ + $c$ = $0$ where $a$ $\neq$ $0$	$\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}\\ \end{array}$
Circumference of a Circle:	$2$ $\pi$ $r$ or $\pi$ $d$ where $r$ =radius, $d$ =diameter
Area of a Circle:	$\pi$ $r$ $^2$
Pythagoras theorem In any right-angled triangle where $a$ , $b$ and $c$ are the length of the sides and $c$ is the hypotenuse:	$a^2$ + $b^2$ = $c^2$
Trig: In any right-angled triangle $ABC$ where $a$ , $b$ and $c$ are the length of the sides and $c$ is the hypotenuse: $sinA$ =	$sinA$ = $\frac{a}{c}$
Trig: In any right-angled triangle $ABC$ where $a$ , $b$ and $c$ are the length of the sides and $c$ is the hypotenuse: $cosA$ =	$cosA$ = $\frac{b}{c}$
Trig: In any right-angled triangle $ABC$ where $a$ , $b$ and $c$ are the length of the sides and $c$ is the hypotenuse: $tanA$ =	$tanA$ = $\frac{a}{b}$
Sine Rule:	$\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$
Cosine Rule:	$a^2$ = $b^2$ + $c^2$ - $2$ $b$ $c$ $cosA$
Trigonometry: Area of a Triangle	$\frac{1}{2}$ $a$ $b$ $SinC$
Area of a Trapezium= (Where $a$ and $b$ are the lengths of the parallel sides and $h$ is their perpendicular separation)	$\frac{1}{2}$ ( $a$ + $b$ ) $h$
Volume of a Prism:	area of cross section × length
Compound interest: Where $P$ is the principal amount, $r$ is the interest rate over a given period and $n$ is number of times that the interest is compounded, Total accrued=	Total accrued= $\begin{array}\(P\left(1+ \frac{r}{100}\right)^n\end{array}$
Where P(A) is the probability of outcome A and P(B) is the probability of outcome B: P(A or B) =	P(A or B) = P(A) +P(B) - P(A and B)
Where P(A) is the probability of outcome A and P(B) is the probability of outcome B: P(A and B)	P(A and B) = P(A given B) P(B)
Curved surface area of a cone:	$\pi$ $r$ $l$
Surface area of a Sphere:	$4$ $\pi$ $r$ $^2$
Volume of a Sphere:	$\frac{4}{3}$ $\pi$ $r$ $^3$
Volume of a Cone:	$\frac{1}{3}$ $\pi$ $r$ $^2$ $h$
Final Velocity $v$ :	$v$ = $u$ + $at$ ( $u$ =initial velocity, $a$ =constant acceleration, $t$ =time taken)
Displacement $s$ :	$s$ = $ut$ + $\frac{1}{2}$ $a$ $t$ $^2$ ( $u$ =initial velocity, $a$ =constant acceleration, $t$ =time taken)
Velocity $v$ $^2$ :	$v$ $^2$ = $u$ $^2$ + $2$ $as$ ( $u$ =initial velocity, $a$ =constant acceleration, $s$ =displacement)

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New GCSE Maths required formulae

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