Math 108 Final
10 + 0 = 10= 0+ 10
identity property of addition
Multiplying numbers with exponents
multiply the numbers, add the exponents
Find the nth term and 40th term of: 8, 1, -6, -13
nth term: -7n+5 40th term: -7 (40)+5= -275
For the following sequence find the nth term: 3, 12, 48, 192
nth term: 3 x 4n-1
Find the nth term and 40th term of: 2, 8, 14, 20, 26
nth term: 6n-4 40th term: 6(40)-4 = 236
Lydia owns a herd of horses. She sells 50 horses and then gives 1/2 of the remaining horses to her friend Kayley. If Lydia has 12 horses left, how many did she start with?
sold 50 12x2 = 24 50 + 24 = 74
Identity property of addition
0 + 4 = 4 = 4+0
zero property of multiplication
0 x 5 = 0 = 5 x 0
Base 5 Counting
1 - 1 2- 2 3- 3 4-4 5 - 1 0 6 - 1 1 7- 1 2 8- 1 3 9 - 1 4 10 - 2 0
Associative Property
(a+b) + c = a + (b+c) (grouping)
Two trains leave the station at 8 am. Train 1 returns every 30 minutes and train two returns every 45 minutes. What time after 8 am will both trains be at the station?
9:30 am Train 1: 8, 8:30, 9, 9:30, 10 Train 2: 8, 8:45, 9:30, 10:15
Use the Euclidean Algorithm to find the GCF of (112, 160)
GCF (112, 160) GCF (112, 48) GCF (48, 16) GCF (16,0) GCF= 16
1/5 of the students in a 4th grade class walk to school. 2/3 walk with siblings. If there are 45 students in the class, how many don't walk with siblings?
1/5 of 45 = 9 2/3 of 9 = 6 1/3 of 9= 3 3 students
Common Square roots
10 = 100 20 = 400 30 = 900 40 = 1600 45= 2025 50 = 2500 25= 625 15= 225
There are 75 students going on a field trip. Each van holds 10 students, how many vans are needed?
10 x 7 = 70 10 x 8 = 80 8 vans needed
Simplify the following. Write answer in exponential form: 11^6 x 11^4
11^10 (when multiplying numbers, add up the exponents)
132.3 + 6.437
138.737 (make sure to line up decimal points when adding)
Prime Numbers
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113
List all prime numbers between 20 and 40
23, 29, 31, 37
Simplify the following. Write answer in exponential form: 2^7 x 32
2^8 x 16^1 (make 32 into a number that has an exponent in it then add the one exponent to the 2)
Communative Property of Multiplication
3 x 4= 4x 3
Closure Property of Addition
3-2=1
Order fractions from smallest to largest: 2/3, 10/11, 3/5
3/5, 2/3, 10/11
30% of 80 is
30/100 = x/80 x= 24
Find the LCM of (70, 175)
5^2 x 7 x 2
Simplify the following. Write answer in exponential form: 5^11 / 5^2
5^9 (when dividing numbers subtract the exponent)
Associative Property of Addition
6 + (4+3) = (6+4) +3
inverse property of addition
6+(-6) = 6 = (-6) + 6
distributive property of multiplication over addition
7 x 4 + 7 x 3
Find the GCF of (70, 175)
70 = 7x5x2 175= 5x5x7 GCF = 7x5
11.95 + 3.7
8.25 (make sure to line up decimal points)
Find the largest 2 digit number that has exactly two factors
97
(5x7) x 4 = 5 x (4x7)
Associative (multiplication)
15+ 4 = 4 +15
Communative (addition)
16 x 12 = 16 (10+2)
Distributive (multiplication)
3 x 1 = 3 = 1 x 3
Multiplicative Identity
Is 2816 divisible by 11
Yes 2+1= 3 8+6= 14 14- 3 = 11
12 x 0 = 0 = 0 x 12
Zero property of multiplication
Commutative Property
a + b = b + a (order)
Dividing numbers with exponents
divide the numbers, subtract the exponents
Arithmetic sequences
each term is found by a difference in either addition or subtraction (6n-4)
Geometric sequences
each term is obtained by multiplying the previous term by a ratio, all nth terms start with the first number in the sequence (2 x 3 ^n-1)
Recursive Sequence
each term is obtained from previous terms (can be numbers, letters or shapes)