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Definitions and Formulas for Multi-Subject: Teachers of Middle Childhood
(Grade 5–Grade 9) Part Two: Mathematics
TRIGONOMETRY
sin A =
opposite
hypotenuse
cos A =
adjacent
hypotenuse
tan A =
opposite
adjacent
Law of Sines:
b
c
a
=
=
sin A
sin B
sin C
Law of Cosines: a2 = b2 + c2 – 2bc cos A
Area of a Triangle: K =
1
ab sin C
2
GEOMETRY
Area of a Triangle: A =
1
ab
2
Area of a Trapezoid: A =
1
h(b1 + b2)
2
Lateral Area of a Right Circular Cylinder: L = 2πrh
Lateral Area of a Right Circular Cone: L = πrl where l is the slant height
Surface Area of a Rectangular Prism: SA = 2lw + 2hw + 2lh
Surface Area of a Cylinder: SA = 2πr2 + 2πrh
Surface Area of a Sphere: SA = 4πr2
Volume of a Cylinder: V = πr2h
Volume of a Pyramid: V =
1
Bh where B is the area of the base
3
Volume of a Right Circular Cone: V =
Volume of a Sphere: V =
4 3
πr
3
1 2
πr h
3
Definitions and Formulas (continued)
COORDINATE GEOMETRY
Slope of a Line: m =
Δy
y 2 – y1
=
Δx
x 2 – x1
Sum of a Finite Arithmetic Series: Sn =
n(a1 + an )
2
Sum of a Finite Geometric Series: Sn =
a1(1 – r n )
1– r