GCSE Maths Formulas

\( d=\sqrt{a^2+b^2+c^2} \)

\( A+B+C+D=360^{\circ} \)

\( A+B+C=180^{\circ} \)

\( L = \frac{\theta}{360^{\circ}}\, 2\pi r \)

\( A = \frac{\theta}{360^{\circ}}\, \pi r^2 \)

\( A = \tfrac{1}{2}(a+b)h \)

\( A = \pi r^2 \)

\( A=b\,h \)

\( A=\ell\,w \)

\( A=\tfrac{1}{2} d_1 d_2 \)

\( A = \tfrac{1}{2} b h \)

\( A=\tfrac{1}{2}\,a\,P \)

\( A=\tfrac{n}{2}\,r^{2}\sin\!\left(\tfrac{2\pi}{n}\right) \)

\( C = 2\pi r \;\;\text{ or }\; C = \pi d \)

\( d=\sqrt{\ell^2+w^2} \)

\( \text{Exterior angle}=\frac{360^{\circ}}{n} \)

\( \text{Exterior angle}=\text{sum of opposite interior angles} \)

\( \text{Corresponding }\angle\text{s equal},\; \text{Alternate }\angle\text{s equal},\; \text{Co-interior }\angle\text{s sum }180^{\circ} \)

\( P' = kP,\qquad A' = k^{2}A \)

\( P=\frac{\theta}{360^{\circ}}\,2\pi r+2r \)

\( P=2(\ell+w) \)

\( P=4s \)

\( a^2 + b^2 = c^2 \)

\( d=\sqrt{\left(\tfrac{P}{2}\right)^2-2A} \)

\( \text{Exterior}=\tfrac{360^{\circ}}{n},\qquad \text{Interior}=180^{\circ}-\tfrac{360^{\circ}}{n} \)

\( L=r\theta,\qquad A=\tfrac{1}{2}r^2\theta \)

\( L'=kL,\quad A'=k^2A,\quad V'=k^3V \)

\( S=(n-2)\times180^{\circ} \)

\( S=\pi r\,\ell+\pi r^2 \)

\( S=2(\ell w+\ell h+wh) \)

\( S=2\pi r h+2\pi r^2 \)

\( S=\text{perimeter of cross-section}\times\text{length}+2\times\text{area of cross-section} \)

\( S=4\pi r^2 \)

\( \text{Opposite angles at an intersection are equal} \)

\( V=\text{area of cross-section}\times\text{length} \)

\( V=\tfrac{1}{3}\pi r^2 h \)

\( V=\ell\,w\,h \)

\( V=\pi r^2 h \)

\( V=\tfrac{1}{3}\pi h\,(R^2+r^2+Rr) \)

\( V=\tfrac{1}{3}\,\text{area of base}\times h \)

\( V=\tfrac{4}{3}\pi r^3 \)

\( V' = k^{3}V \)