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Grades
| ||\dfrac{\text{numerator}}{\text{denominator}}\times100|| | ||\dfrac{\text{numerator}}{\text{denominator}}=\dfrac{\text{number sought}}{100}|| |
| Property | Addition | Multiplication |
|---|---|---|
| ||a+b=b+a|| | ||a\times b=b\times a|| |
| ||(a+b)+c=a+(b+c)|| | ||(a\times b)\times c=a\times(b\times c)|| |
| ||a+0=0+a=a|| | ||a\times1=1\times a=a|| |
| ||a\times0=0\times a=0|| | |
| ||a+-a=-a+a=0|| | ||a\times\dfrac{1}{a}=1|| |
| ||a\times(b\pm c)=a\times b\pm a\times c|| | |
| |\text{km}| | |\text{hm}| | |\text{dam}| | |\text{m}| | |\text{dm}| | |\text{cm}| | |\text{mm}| |
| In this direction |\Rightarrow \times 10\qquad \qquad\qquad| In this direction |\Leftarrow \div 10| | ||||||
| |\text{km}^2| | |\text{hm}^2| | |\text{dam}^2| | |\text{m}^2| | |\text{dm}^2| | |\text{cm}^2| | |\text{mm}^2| |
| In this direction |\Rightarrow \times 100\qquad \qquad\qquad| In this direction |\Leftarrow \div 100| | ||||||
| |\text{km}^3| | |\text{hm}^3| | |\text{dam}^3| | |\text{m}^3| | |\text{dm}^3| | |\text{cm}^3| | |\text{mm}^3| |
| In this direction |\Rightarrow \times 1000\qquad \qquad\qquad| In this direction |\Leftarrow \div 1000| | ||||||
| Figure | Perimeter | Area | |
|---|---|---|---|
| Triangle | The sum of all sides | |A =\dfrac{b\times h}{2}| |A = \sqrt{p(p-a)(p-b)(p-c)}| |A=\dfrac{ab\sin C}{2}| | |
| Square | |P=4 \times s| | |\begin{align} A &= s \times s\\ A &= s^2 \end{align}| | |
| Rectangle | |\begin{align} P &= b+h+b+h\\ P &= 2(b+h) \end{align}| | |A=bh| | |
| Rhombus | P=|4 \times s| | |A=\dfrac{D\times d}{2}| | |
| Parallelogram | The sum of all sides | |A=bh| | |
| Trapezoid | The sum of all sides | |A=\dfrac{(B+b)\times h}{2}| | |
| Regular polygon | |P=n \times s| | |A=\dfrac{san}{2}| | |
| Any polygon | The sum of all sides | The sum of the areas of all the triangles that make up the polygon | |
| Circle | |\begin{align} d &= 2r\\\\ r &= \frac{d}{2} \end{align}| | ||\begin{align} C &= \pi d\\\\ C &= 2 \pi r \end{align}|| | |A=\pi r^2| |
| Circular arc and sector of a circle | |\displaystyle \frac{\text{Central angle}}{360^o}=\frac{\text{Arc length}}{2\pi r}| | |\displaystyle \frac{\text{Central angle}}{360^o}=\frac{\text{Area of sector}}{\pi r^2}| | |
| Total number of diagonals | Number of diagonals at each vertex | Sum of the measures of the interior angles | Measure of an interior angle |
|---|---|---|---|
| |\dfrac{n(n-3)}{2}| | |n-3| | |180(n-2)| | |\dfrac{180(n-2)}{n}| |
| Solids | Lateral area | Total area |
|---|---|---|
| Prism and cylinder | Sum of the areas of the lateral faces of the solid |A_L=P_b\times h| | Sum of the areas of all faces of the solid |A_T = A_L+2A_b| |
| Pyramid and cone | Sum of the areas of the lateral faces of the solid |A_L=\displaystyle \frac{P_b\times a}{2}| | Sum of the areas of all faces of the solid |A_T = A_L+A_b| |
| Sphere | |A=4\pi r^2| | |
| Similarity ratio (Scale factor) | Area ratio |
|---|---|
| ||k=\dfrac{\text{Length of image figure}}{\text{Length of initial figure}}|| | ||k^2=\dfrac{\text{Area of image figure}}{\text{Area of initial figure}}|| |
| Concept | Formulas |
|---|---|
| Probability | ||\text{Probability}=\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}}|| |
| Complementary probability | ||\mathbb{P}(A')=1-P(A)|| |
| Probability of incompatible events | ||\mathbb{P}(A\cup B)=\mathbb{P}(A)+\mathbb{P}(B)|| |
| Probability of compatible events | ||\mathbb{P}(A\cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(A\cap B)|| |