eMath Challenge

Math Reference Guide

To help students build a solid mathematical foundation, all essential prefix values, unit conversion factors, and key geometric formulas for area and volume must be committed to memory. Mastering these core concepts ensures that you can perform calculations quickly and accurately, providing the fluency needed to solve more complex problems with ease.

Common Prefixes

• micro 1/1000000
• milli 1/1000
• centi 1/100
• deci 1/10
• deca 10
• hecto 100
• kilo 1000
• mega 1000000
• bi 2
• tri 3
• quad/tetra 4
• penta 5
• hexa 6
• hepta 7
• octa 8
• nona 9

Standard Units

• mm millimeter
• cm centimeter
• dm decimeter
• m meter
• km kilometer
• mg milligram
• g gram
• kg kilogram
• s second
• min minute
• h/hr hour
• ml milliliter
• l liter
• ha hectare

Conversion Factors

• 1 cm = 10 mm
• 1 dm = 10 cm
• 1 m = 10 dm or 100 cm
• 1 km = 1000 m
• 1 g = 1000 mg
• 1 kg = 1000 g
• 1 min = 60 s
• 1 h/hr = 60 min
• 1 ml = 1 cm³
• 1 l = 1000 ml or 1 dm³
• 1 ha = 10000 m²

Formulas

Perimeter

• Triangle P = a + b + c
• Square P = 4s
• Rectangle P = 2(L + W)
• Circle C = 2πr or πD

Area

• Triangle A = ½bh
• Square A = s²
• Rectangle A = LW
• Trapezoid A = ½h(b₁ + b₂)
• Circle A = πr²

Volume

• Cube V = s³
• Rectangular Prism V = LWH
• Circular Prism V = πr²h
• Prism (any) V = Ah, where A is area of the base
• Cone V = ⅓πr²h
• Sphere V = 4⁄3πr³
• Pyramid V = ⅓Ah, where A is area of the base

Sum of Interior Angles of Triangle

• ∠A + ∠B + ∠C = 180°

Sum of Interior Angles of Regular Polygon with n Sides

• ∑ = (n - 2) × 180°

Simple Interest

• I = Prt

Sum of Consecutive Numbers (from n₁ to n₂)

• ∑ = ½(n₁ + n₂)(n₂ - n₁ + 1)

Sum of Consecutive Numbers (from 1 to n)

• ∑ = ½(n)(n + 1)

Sum of n Consecutive Even Numbers (starting from 2)

• ∑ = n(n + 1)

Sum of n Consecutive Odd Numbers (starting from 1)

• ∑ = n²