Math

Question 1

Leona bought a 1 year, $10,000 certificate of deposit that paid interest at an annual rate of 8% compounded semiannually.

Answer 1

2 payments in one year, each half of the annual rate. Two payments of 4% interest rate

Question 2

5/4

Answer 2

1.25

125%

Question 3

7/4

Answer 3

1.75

175%

Question 4

1/8

Answer 4

0. 125

12. 5%

Question 5

3/8

Answer 5

0. 375

37. 5%

Question 6

5/8

Answer 6

0. 625

62. 5%

Question 7

7/8

Answer 7

0. 875

87. 5%

Question 8

2/3

Answer 8

0. 6666

66. 6%

Question 9

1/6

Answer 9

0. 16666

16. 7%

Question 10

5/6

Answer 10

0. 833

83. 3%

Question 11

1/9

Answer 11

0. 111

11. 1%

Question 12

Convert a decimal to a fraction

Answer 12

Put the digits to the right of the decimal point. Over the appropriate power of 10. Simplify.

0.036 = 36/1000

Question 13

Convert a percent to a fraction

Answer 13

Write over 100

OR

Convert to a decimal first then convert decimal to fraction
3.6% = 0.036 = 36/1000 = 9/250

Question 14

Percent change of an original percent

Answer 14

% change = change in value/original value

Question 15

New percent of an original percent

Answer 15

New % = new value /original value

Question 16

Percent INCREASE of 10%

Answer 16

110%

Or 1.1

Question 17

Percent increase of 20%
Percent increase of 25%
Percent increase of 50%

Answer 17

120% or 1.2 or 6/5
125% or 1.25 or 5/4
150% or 1.5 or 3/2

Question 18

Percent DECREASE of 10%

Answer 18

90% or 0.9

Question 19

Percent decrease of 20%
Percent decrease of 25%
Percent decrease of 50%
Percent decrease of 75%

Answer 19

80% or 0.8 or 4/5
75% or 0.75 or 3/4
50% or 1/2
25% or 1/4

Question 20

If you have a variable in an exponent or exponents…

Example: 3^x = 27^4

Answer 20

Make the bases equals usually by breaking the given bases down to primes.

3^x = 27^4
3^x = (3^3)^4

Question 21

“Each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew.”

Answer 21

As many = of

Can multiply
3/4x

Question 22

Fractions/decimals (0-1) decrease and exponents increase

Answer 22

Because denominator increases.

(1/2)^2= 1/4

Question 23

Pay attention to the parentheses with exponents (PEMDAS)

Answer 23

-2^4=-16

(-2)^4=16

Question 24

When multiplying exponents with same base = ADD

When dividing exponents with the same base = SUBTRACT

Answer 24

x^15/x^8 = x^7

2^2 x 2^3 = 2^5

*when simplifying or solving try to get to the same base!

Question 25

Nested exponents = when you raise an exponential term to an exponent, multiply the exponents

Answer 25

(a^5)^4 = a^20

Question 26

Raise a fraction to a negative power = raise reciprocal to the equivalent positive power

Answer 26

(3/7)^-2 = (7/3)^2

Question 27

1.4^2

Answer 27

2

Question 28

1.7^2

Answer 28

3

Question 29

2.25^2

Answer 29

5

Question 30

12^2

Answer 30

144

Question 31

13^2

Answer 31

169

Question 32

14^2

Answer 32

196

Question 33

15^2

Answer 33

225

Question 34

16^2

Answer 34

256

Question 35

25^2

Answer 35

625

Question 36

2^3

Answer 36

8

Question 37

3^3

Answer 37

27

Question 38

4^3

Answer 38

64

Question 39

5^3

Answer 39

125

Question 40

2^4 | 4^2

Answer 40

16

Question 41

2^5

Answer 41

32

Question 42

2^6 | 4^3

Answer 42

64

Question 43

2^7

Answer 43

128

Question 44

2^8 | 4^4

Answer 44

256

Question 45

2^9

Answer 45

512

Question 46

2^10 | 4^5

Answer 46

1024

Question 47

3^4

Answer 47

81

Question 48

0=0 (combo algebra problem)

Answer 48

True statement, same line = infinite many solutions

Question 49

0=5 (combo algebra)

Answer 49

False statement (i.e. Parallel lines, No solutions)

Question 50

Square of a sum

Answer 50

(X+y) ^2 = x^2 + 2xy + y^2

Question 51

Square of a difference

Answer 51

(X-y)^2 = x^2 - 2xy + y^2

Question 52

Differences of squares

Answer 52

(X+y) (x-y) = x^2 - y^2

Question 53

Average rate

Answer 53

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.

Question 54

Average speed

Answer 54

Average speed = total distance/total time

Question 55

Relative Rates

Answer 55

1. Bodies move toward each other (r1 + r2) 2. Bodies move away from each other (r1+ r2) 3. Bodies move in the same direction on the same path. (r1-r2)

Question 56

Counting integers (if both extremes need to be added)

Answer 56

(Last - First) + 1

Question 57

Counting consecutive multiples, if extremes are included

Answer 57

(Last - First) / increment + 1 The bigger the increment the smaller the result

Question 58

Properties of evenly spaced sets (ALL evenly spaced sets)

Answer 58

1. Mean and median are equal to each other Ex: mean if 4, 8, 12, 16, 20? Mean = 12 and median = 12 2. Mean and median of the set are equal to the average of the FIRST and LAST terms. (First + last)/ 2

Question 59

Sum of consecutive integers

Answer 59

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.

Question 60

Triangle properties

Answer 60

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.

Question 61

Right triangles (and triples)

Answer 61

A^2 + B^2 = C^2 3: 4:5 5: 12:13 8: 15:17

Question 62

Sum of interior angles of a polygon

Answer 62

(n-2) x 180

Question 63

Area of a Trapezoid

Answer 63

(Base 1 + Base 2) x Height/2

Question 64

45: 45:90 triangle 30: 60:90 triangle

Answer 64

45: 45:90 x: x : x root2 30:60:90 x : x root 3 : 2x

Question 65

Similar triangles

Answer 65

If all corresponding angles are equal AND corresponding sides are in proportion, triangle is similar.

Question 66

Inscribed Angle

Answer 66

Inscribed angle: has its vertex on the circle itself Inscribed angle is equal to half of the angle of the arc it intercepts.

Question 67

Inscribed triangle

Answer 67

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.

Question 68

Divisibility Rules: 3 and 9

Answer 68

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

Question 69

Prime numbers

Answer 69

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

Question 70

Divisibility rules: 4 Divisibility rules: 8

Answer 70

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.

Question 71

Divisibility rules: 6

Answer 71

If the integer is divisible by both 2 and 3. 48/2 AND. 48/3

Question 72

Addition/Subtraction Odd Even Rules

Answer 72

Even +/- Even = Even Odd +/- Odd = Even Even +/- Odd = Odd

Question 73

Multiplication Odd/Even Rules

Answer 73

Even x Even = Even Even x Odd = Even Odd x Odd = Odd

Question 74

Average of consecutive integers

Answer 74

(First + last)/2 Average of first and last term

Question 75

Integer m has an odd number of positive factors

Answer 75

Odd number of factors = perfect square