Formulas for national tests in mathematics 1
PREFIXES
Symbol
Name
Power of ten
EXPONENTS
T
tera
G
giga
M
k
mega kilo
h
d
hecto deci
1012
109
106
10 2
103
(a )
x
GEOMETRY
µ
micro
n
nano
p
pico
10 −2
10 −6
10 −9
10 −12
10 −3
For all real numbers x and y and positive numbers a and b
a x a y = a x+ y
FUNCTIONS
10 −1
c
m
centi milli
y
= ax y
ax
= a x− y
y
a
ax ⎛ a ⎞
=
b x ⎜⎝ b ⎟⎠
( )
a x b x = ab
x
1
an = n a
a− x =
1
ax
a0 = 1
Equation of a line
y = k x + m if y = k x then y is proportional to x
Exponential function
y = Ca x where C and a are constants a > 0 and a ≠ 1
Power function
y = C x a where C and a are constants
Pythagoras’
theorem
Triangle
Parallelogram
Parallel trapezium
Circle
a 2 + b2 = c 2
area =
bh
2
area = bh
area =
(
h a+b
)
2
π d2
area = π r =
4
2
circumference = 2π r = π d
Circle sector
© Skolverket
2017-03-16
x
v
⋅ 2π r
360°
v
br
area =
⋅πr 2 =
360°
2
arc length b =
Prism
volume = Bh
Cylinder
Right circular cylinder
volume = π r 2 h
mantle area = 2π r h
Pyramid
volume =
Cone
Bh
3
Right circular cone
π r 2h
volume =
3
curved surface area = π r s
Sphere
4π r 3
volume =
3
2
area = 4π r
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
© Skolverket
2017-03-16
sin v = y1
cos v = x1
tan v =
y1
x1