 # GCSE Maths required formulae

Flashcards by Johnny Hammer, updated more than 1 year ago 67 3 0

### Description

Required formulae for the new maths GCSE - these will NOT be given during the exam, they must be learned in advance ## Resource summary

 Question Answer Pythagoras' theorem: Right-angled triangle: a, b and c are the length of the sides and c is the hypotenuse: 73d6a972-0f3b-4938-ad88-82f6985ba9c5.png (image/png) The square of a hypotenuse is equal to the sum of the squares of the other two sides. $$a^2$$+$$b^2$$=$$c^2$$ 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: $$\pi$$$$r$$$$^2$$ 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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