Year 9 Maths Formulas

Circumference of a circle

C = 2πr or C = πd, where r is the radius and d is the diameter.

Area of a circle

A = πr², where r is the radius.

Arc Length

L = (θ/360) * 2πr, where θ is the central angle in degrees.

Sector Area

A = (θ/360) * πr².

Area of a triangle

A = (1/2) * b * h, where b is the base and h is the height.

Pythagoras' Theorem

In right-angled triangles: c² = a² + b², where c is the hypotenuse.

Perimeter of a triangle

Sum of all sides.

Heron's Formula for triangle area

A = √[s(s-a)(s-b)(s-c], where s is the semi-perimeter.

Area of a rectangle

A = l * w, where l is the length and w is the width.

Perimeter of a rectangle

P = 2(l + w).

Area of a square

A = s², where s is the side length.

Perimeter of a square

P = 4s.

Area of a parallelogram

A = b * h, where b is the base and h is the height.

Perimeter of a parallelogram

P = 2(a + b), where a and b are adjacent sides.

Area of a trapezium (trapezoid)

A = (1/2) * (a + b) * h, where a and b are parallel sides and h is the height.

Perimeter of a trapezium

P = a + b + c + d, sum of all sides.

Surface Area of a sphere

SA = 4πr².

Volume of a sphere

V = (4/3)πr³.

Surface Area of a cylinder

SA = 2πr² + 2πrh.

Volume of a cylinder

V = πr²h.

Surface Area of a cone

SA = πr² + πrl, where l is the slant height.

Volume of a cone

V = (1/3)πr²h.

Surface Area of a cube

SA = 6s².

Volume of a cube

V = s³.

Surface Area of a rectangular prism

SA = 2(lw + lh + wh).

Volume of a rectangular prism

V = l * w * h.

Surface Area of a pyramid

SA = B + (1/2) * P * l, where B is base area and P is perimeter of the base.

Volume of a pyramid

V = (1/3) * B * h.

Distance-Speed-Time formula

Distance = Speed × Time.

Simple Interest formula

I = P * R * T, where I is interest, P is principal, R is rate, and T is time.

Sum of Interior Angles of a polygon

Sum of Angles = (n - 2) * 180°, where n is the number of sides.

Measure of Each Interior Angle of a regular polygon

Angle = [(n - 2) * 180°]/n.

Exterior Angle of a Regular Polygon

Exterior Angle = 360°/n.

Sine Ratio in a right triangle

sinθ = opposite/hypotenuse.

Cosine Ratio in a right triangle

cosθ = adjacent/hypotenuse.

Tangent Ratio in a right triangle

tanθ = opposite/adjacent.

Diagonal of a Rectangular Prism

d = √(l² + w² + h²).

Diagonal of a Cube

d = s√3.

Centimeter to Millimeter conversion

1 cm = 10 mm.

Meter to Centimeter conversion

1 m = 100 cm.

Kilometer to Meter conversion

1 km = 1000 m.

Area conversion from m² to cm²

1 m² = 10,000 cm².

Volume conversion from m³ to cm³

1 m³ = 1,000,000 cm³.

Midpoint Formula in coordinate geometry

Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Distance Formula in coordinate geometry

d = √[(x2 - x1)² + (y2 - y1)²].

Equation of a line in coordinate geometry

y = mx + c, where m is slope and c is y-intercept.

Probability Formula

P(Event) = Favorable Outcomes / Total Outcomes.

Mean (Average) Formula

Mean = Sum of all values / Number of values.

Median in statistics

Middle value in a sorted data set.

Mode in statistics

Most frequent value in a data set.