© Skolverket 2017-03-16

Formulas for national tests in mathematics 1 PREFIXES

Symbol T G M k h d c m µ n p Name tera giga mega kilo hecto deci centi milli micro nano pico Power of ten 1012 109 106 103 102 10−1 10−2 10−3 10−6 10−9 10−12

EXPONENTS For all real numbers x and y and positive numbers a and b axa y = ax+ y ax

a y= ax− y

ax

bx= ab

⎛⎝⎜

⎞⎠⎟

x

a− x = 1

ax

ax( )y = ax y axbx = ab( )x

a1n = an

a0 =1

FUNCTIONS Equation of a line y = k x +m if y = k x then y is proportional to x

Exponential function y =Cax where C and a are constants a > 0 and a ≠ 1 Power function y =Cxa where C and a are constants

GEOMETRY Pythagoras’ theorem

a2 + b2 = c2

Triangle area = bh

2

Parallelogram area = bh

Parallel trapezium area =

h a + b( )2

Circle area = π r2 = π d 2

4

circumference = 2π r = π d

Circle sector

arc length b = v360°

⋅2πr

area = v360°

⋅πr 2 = br2

© Skolverket 2017-03-16

Prism volume = Bh

Cylinder Right circular cylinder volume = π r2h mantle area = 2π r h

Pyramid volume = Bh

3

Cone Right circular cone

volume = π r2h3

curved surface area = π r s

Sphere volume = 4π r3

3

area = 4π r2

Scale area scale factor = (length scale factor)2

volume scale factor = (length scale factor)3

TRIGONOMETRY Right-angled triangle

Definitions

sin v = a

c

cos v = b

c

tan v = a

b

Unit circle OP is the radius in the unit circle. The coordinates for P is ( x1, y1 ).

Definitions sin v = y1 cos v = x1 tan v =y1x1