Formulaes to Remember
This is not allowed to take to the final.
1. Use percentage as fraction A is p% of B.
p% =
A
,
B
A = p% × B,
B=
A
p%
2. Use percentage as changing Old value rise p% to new value.
p% =
(new value) − (old value)
old value
new value = (1 + p%) × (old value),
old value =
new value
1 + p%
3. Use percentage to compare Compared value is p% more than reference value.
p% =
(compared value) − (reference value)
,
reference value
compared value = (1 + p%) × (reference value),
reference value =
compared value
1 + p%
4. Compound interest formula for interest paid ONCE a year
A = P × (1 + APR)Y ,
APY = APR
5. Compound interest formula for interest paid more than once a year
µ
¶nY
APR
A=P × 1+
,
n
µ
APY =
1+
APR
n
¶n
−1
6. Compound interest formula for interest paid continuously
A = P × e(APR×Y ) ,
APY = eAPR − 1
7. Rate of change rule
rate of change =
absolute change in dependent variable
absolute change in independent variable
8. General formula for a linear model
dependent variable = (initial value) + (rate of change) × (independent variable)
Formulaes 9-12 are for a quantity growing exponentially at a rate of P % per time period.
9. Approximate doubling time formula (rule of 70)
Tdouble ≈
70
P
WARNING: Be aware of the unit!
10. Exact doubling time formula
Tdouble =
log10 2
log10 (1 + P %)
11. General formula for an exponential growth with respect to doubling time
new value = (initial value) × 2t/Tdouble
12. General formula for an exponential growth
new value = (initial value) × (1 + P %)t
Formulaes 13-16 are for a quantity decaying exponentially at a rate of P % per time period.
13. Approximate half-life formula
Thalf ≈
14. Exact half-life formula
Thalf = −
70
P
log10 2
log10 (1 − P %)
15. General formula for an exponential decay with respect to half-life
new value = (initial value) ×
µ ¶t/Thalf
1
2
16. General formula for an exponential decay
new value = (initial value) × (1 − P %)t
17. Perimeters and areas of two-dimensional objects see Examples on 11/29 for pictures
Object
Circle
Square
Rectangle
Parallelogram
Triangle
Perimeter
2πr
4l
2l + 2w
2l + 2w
a+b+c
Area
πr2
l2
lw
lh
1
2 bh
18. Surface areas and volumes of three-dimensional objects see Examples on 12/1 for pictures
Object
Sphere
Cube
Box
Cylinder
Surface area
4πr2
6l2
2lw + 2wh + 2hl
2πr2 + 2πrh
Volume
4
3
3 πr
l3
lwh
πr2 h