MATH GEOMETRY UPCAT

nak nampucha

direct variation

y = kx

inverse variation

y = k * 1/x

perimeter of a square

p = 4s

area of a square

a = s²

perimeter of a rectangle

P = 2a + 2b

area of a rectangle

A = ab

perimeter of a triangle

P = a + b + c

area of a triangle

A = ½(bh)

perimeter of a trapezoid

P = a + b + c + d

area of a trapezoid

A = h (a+b/2)

perimeter of a parallelogram

P = 2a + 2b

area of a parallelogram

A = bh

pythagorean theorem

a² + b² = c²

common pythagorean triples

3 - 4 -5

5 - 12 - 13

7 - 24 - 25

8 - 15 -17

9 - 40 - 41

30 - 60 - 90 right triangle

1 - √3 - 2

45 - 45 - 90 right triangle

1 - 1 - √2

perimeter of a circle

P = 2πr

area of a circle

A = πr²

slope-intercept form

y = mx + b

slope formula

y₂ - y₁ / x₂ - x₁

distance formula

√(x₂ - x₁)² + (y₂ - y₁)²

parallel lines

(y - y₁) = m (x - x₁)

permutation

the order of the set matters

permutation formula

P = n!/(n - r)!

combination

order does not matter (i.e. set can be rearranged in many ways)

combination formula

C = n!/r!(n - r)!

work problems

W = Nrt

percentage of 1

100% (1.0)

percentage of 7/8

87.5% (.875)

percentage of 4/5

80% (.8)

percentage of 3/4

75% (.75)

percentage of 2/3

66.67% (.667)

percentage of 5/8

62.5% (.625)

percentage of 3/5

60% (.6)

percentage of 1/2

50% (.5)

percentage of 2/5

40% (.4)

percentage of 3/8

37.5% (.375)

percentage of 1/3

33.3% (.33)

percentage of 1/4

25% (.25)

percentage of 1/5

20% (.2)

percentage of 1/6

16.6% (.166)

percentage of 1/8

12.5% (.125)

percentage of 1/10

10% (.1)

percentage of 1/12

8.33% (.083)

mean

average of the series

median

middle value in a series arranged from lowest to highest

mode

most common value in a series