Math Flashcards
Leona bought a 1 year, $10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semiannually.
2 payments in one year, each half of the annual rate. Two payments of 4% interest rate
5/4
1.25
125%
7/4
1.75
175%
1/8
- 125
12. 5%
3/8
- 375
37. 5%
5/8
- 625
62. 5%
7/8
- 875
87. 5%
2/3
- 6666
66. 6%
1/6
- 16666
16. 7%
5/6
- 833
83. 3%
1/9
- 111
11. 1%
Convert a decimal to a fraction
Put the digits to the right of the decimal point. Over the appropriate power of 10. Simplify.
0.036 = 36/1000
Convert a percent to a fraction
Write over 100
OR
Convert to a decimal first then convert decimal to fraction
3.6% = 0.036 = 36/1000 = 9/250
Percent change of an original percent
% change = change in value/original value
New percent of an original percent
New % = new value /original value
Percent INCREASE of 10%
110%
Or 1.1
Percent increase of 20%
Percent increase of 25%
Percent increase of 50%
120% or 1.2 or 6/5
125% or 1.25 or 5/4
150% or 1.5 or 3/2
Percent DECREASE of 10%
90% or 0.9
Percent decrease of 20%
Percent decrease of 25%
Percent decrease of 50%
Percent decrease of 75%
80% or 0.8 or 4/5
75% or 0.75 or 3/4
50% or 1/2
25% or 1/4
If you have a variable in an exponent or exponents…
Example: 3^x = 27^4
Make the bases equals usually by breaking the given bases down to primes.
3^x = 27^4 3^x = (3^3)^4
“Each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew.”
As many = of
Can multiply
3/4x
Fractions/decimals (0-1) decrease and exponents increase
Because denominator increases.
(1/2)^2= 1/4
Pay attention to the parentheses with exponents (PEMDAS)
-2^4=-16
(-2)^4=16
When multiplying exponents with same base = ADD
When dividing exponents with the same base = SUBTRACT
x^15/x^8 = x^7
2^2 x 2^3 = 2^5
*when simplifying or solving try to get to the same base!
Nested exponents = when you raise an exponential term to an exponent, multiply the exponents
(a^5)^4 = a^20
Raise a fraction to a negative power = raise reciprocal to the equivalent positive power
(3/7)^-2 = (7/3)^2
1.4^2
2
1.7^2
3
2.25^2
5
12^2
144
13^2
169
14^2
196
15^2
225
16^2
256
25^2
625
2^3
8
3^3
27
4^3
64
5^3
125
2^4
4^2
16
2^5
32
2^6
4^3
64
2^7
128
2^8
4^4
256
2^9
512
2^10
4^5
1024
3^4
81
0=0 (combo algebra problem)
True statement, same line = infinite many solutions
0=5 (combo algebra)
False statement (i.e. Parallel lines, No solutions)
Square of a sum
(X+y) ^2 = x^2 + 2xy + y^2
Square of a difference
(X-y)^2 = x^2 - 2xy + y^2
Differences of squares
(X+y) (x-y) = x^2 - y^2
Average rate
Because the object spends more time traveling at the slower rate, the average rate will ALWAYS be closer to the SLOWER of the two rates.
Average speed
Average speed = total distance/total time
Relative Rates
- Bodies move toward each other (r1 + r2)
- Bodies move away from each other
(r1+ r2) - Bodies move in the same direction on the same path.
(r1-r2)
Counting integers (if both extremes need to be added)
(Last - First) + 1
Counting consecutive multiples, if extremes are included
(Last - First) / increment + 1
The bigger the increment the smaller the result
Properties of evenly spaced sets (ALL evenly spaced sets)
- Mean and median are equal to each other
Ex: mean if 4, 8, 12, 16, 20? Mean = 12 and median = 12 - Mean and median of the set are equal to the average of the FIRST and LAST terms.
(First + last)/ 2
Sum of consecutive integers
Sum = average x number of terms
Average of an odd number of consecutive integers will always be an integer.
Average of an even number of consecutive integers will never be an integer.
Triangle properties
Sum of 2 side lengths will always be greater than the third side length.
Any side is greater than the difference of the other 2 side lengths.
All angles = 180
Sides correspond with angles: the largest angle is opposite the longest side.
Right triangles (and triples)
A^2 + B^2 = C^2
3: 4:5
5: 12:13
8: 15:17
Sum of interior angles of a polygon
(n-2) x 180
Area of a Trapezoid
(Base 1 + Base 2) x Height/2
45: 45:90 triangle
30: 60:90 triangle
45: 45:90
x: x : x root2
30:60:90
x : x root 3 : 2x
Similar triangles
If all corresponding angles are equal AND corresponding sides are in proportion, triangle is similar.
Inscribed Angle
Inscribed angle: has its vertex on the circle itself
Inscribed angle is equal to half of the angle of the arc it intercepts.
Inscribed triangle
Inscribed triangle: if all of the vertices of the triangle are points on the circle
** RULE: if one of the sides of an inscribed triangle is the diameter of the circle, triangle must be a right triangle.
Divisibility Rules: 3 and 9
If the sum of the integer’s digits is a multiple of 3 - divisible by 3
If the sum of the integer’s is a multiple of 9 - divisible by 9
Prime numbers
2, 3, 5, 7, 11, 13, 17, 19
1 is NOT a prime number (only divisible by itself)
2 is the only even prime number
Divisibility rules: 4
Divisibility rules: 8
If the last two numbers are divisible 4.
Example:
23,456 because 56 is divisible by 4
25,678 not because 78 not divisible by 4.
If the last three numbers are divisible by 8.
Divisibility rules: 6
If the integer is divisible by both 2 and 3.
48/2 AND. 48/3
Addition/Subtraction Odd Even Rules
Even +/- Even = Even
Odd +/- Odd = Even
Even +/- Odd = Odd
Multiplication Odd/Even Rules
Even x Even = Even
Even x Odd = Even
Odd x Odd = Odd
Average of consecutive integers
(First + last)/2
Average of first and last term
Integer m has an odd number of positive factors
Odd number of factors = perfect square
