Year 9 Maths Formulas
Circle Formulas
1. Circumference:
C = 2\pi r or C = \pi d
Where r = radius, d = diameter.
2. Area:
A = \pi r^2
3. Arc Length:
L = \frac{\theta}{360} \cdot 2\pi r
Where \theta = central angle in degrees.
4. Sector Area:
A = \frac{\theta}{360} \cdot \pi r^2
Triangle Formulas
1. Area:
A = \frac{1}{2} \cdot b \cdot h
Where b = base, h = height.
2. Pythagoras’ Theorem (for right-angled triangles):
c^2 = a^2 + b^2
Where c = hypotenuse.
3. Perimeter:
Sum of all sides.
4. Heron’s Formula (for any triangle):
A = \sqrt{s(s-a)(s-b)(s-c)}
Where s = \frac{a+b+c}{2} (semi-perimeter).
Rectangle Formulas
1. Area:
A = l \cdot w
Where l = length, w = width.
2. Perimeter:
P = 2(l + w)
Square Formulas
1. Area:
A = s^2
Where s = side length.
2. Perimeter:
P = 4s
Parallelogram Formulas
1. Area:
A = b \cdot h
Where b = base, h = height.
2. Perimeter:
P = 2(a + b)
Where a and b = adjacent sides.
Trapezium (Trapezoid) Formulas
1. Area:
A = \frac{1}{2} \cdot (a + b) \cdot h
Where a and b = parallel sides, h = height.
2. Perimeter:
P = a + b + c + d
(Sum of all sides).
3D Shapes Formulas
Sphere
1. Surface Area:
SA = 4\pi r^2
2. Volume:
V = \frac{4}{3} \pi r^3
Cylinder
1. Surface Area:
SA = 2\pi r^2 + 2\pi r h
2. Volume:
V = \pi r^2 h
Cone
1. Surface Area:
SA = \pi r^2 + \pi r l
Where l = slant height.
2. Volume:
V = \frac{1}{3} \pi r^2 h
. Lateral Surface Area of a Cone:
A_{\text{lateral}} = \pi r l
Where:
• r = radius of the base
• l = slant height
2. Surface Area of a Cone (Total):
A_{\text{total}} = \pi r l + \pi r^2
Where:
• \pi r l = lateral surface area
• \pi r^2 = area of the base
3. Volume of a Cone:
V = \frac{1}{3} \pi r^2 h
Where:
• r = radius of the base
• h = height of the cone
Cube
1. Surface Area:
SA = 6s^2
Where s = side length.
2. Volume:
V = s^3
Rectangular Prism (Cuboid)
1. Surface Area:
SA = 2(lw + lh + wh)
2. Volume:
V = l \cdot w \cdot h
Pyramid
1. Surface Area:
SA = B + \frac{1}{2} \cdot P \cdot l
Where B = base area, P = perimeter of the base, l = slant height.
2. Volume:
V = \frac{1}{3} \cdot B \cdot h
Where h = height.
Basic Algebraic Formulas
1. Distance-Speed-Time:
\text{Distance} = \text{Speed} \times \text{Time}
Rearrange as needed:
\text{Speed} = \frac{\text{Distance}}{\text{Time}} ,
\text{Time} = \frac{\text{Distance}}{\text{Speed}} .
2. Simple Interest:
I = P \cdot R \cdot T ,
Where I = interest, P = principal, R = rate (decimal), T = time.
Polygon Formulas
1. Sum of Interior Angles:
\text{Sum of Angles} = (n - 2) \cdot 180^\circ ,
Where n = number of sides.
2. Measure of Each Interior Angle (regular polygon):
\text{Angle} = \frac{(n - 2) \cdot 180^\circ}{n} .
3. Exterior Angle of a Regular Polygon:
\text{Exterior Angle} = \frac{360^\circ}{n} .
Trigonometry Basics (if applicable for advanced-level questions)
1. Right-Angled Triangle Ratios:
\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} ,
\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} ,
\tan\theta = \frac{\text{opposite}}{\text{adjacent}} .
2. Pythagoras’ Theorem:
c^2 = a^2 + b^2 (already mentioned but essential).
3D Shape Diagonals
1. Diagonal of a Rectangular Prism:
d = \sqrt{l^2 + w^2 + h^2} .
2. Diagonal of a Cube:
d = s\sqrt{3} .
Conversions
1. Metric System:
• 1 \, \text{cm} = 10 \, \text{mm} .
• 1 \, \text{m} = 100 \, \text{cm} .
• 1 \, \text{km} = 1000 \, \text{m} .
2. Area Units:
• 1 \, \text{m}^2 = 10{,}000 \, \text{cm}^2 .
3. Volume Units:
• 1 \, \text{m}^3 = 1{,}000{,}000 \, \text{cm}^3 .
Coordinate Geometry
1. Midpoint Formula:
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) .
2. Distance Formula:
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} .
3. Equation of a Line:
y = mx + c ,
Where m = slope ( m = \frac{y_2 - y_1}{x_2 - x_1} ), c = y-intercept.
Probability and Statistics
1. Probability:
P(\text{Event}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} .
2. Mean (Average):
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} .
3. Median:
Middle value in a sorted data set.
4. Mode:
Most frequent value in a data set.