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© 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