Math 108 Final exam questions with 100%accurate solutions + rationales

Find the nth term and 40th term of: 2, 8, 14, 20, 26

nth term: 6n-4

40th term: 6(40)-4 = 236

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

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

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)

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)

Simplify the following. Write answer in exponential form: 5^11 / 5^2

5^9 (when dividing numbers subtract the exponent)

10 + 0 = 10= 0+ 10

identity property of addition

15+ 4 = 4 +15

Communative (addition)

16 x 12 = 16 (10+2)

Distributive (multiplication)

(5x7) x 4 = 5 x (4x7)

Associative (multiplication)

3 x 1 = 3 = 1 x 3

Multiplicative Identity

12 x 0 = 0 = 0 x 12

Zero property of multiplication

Find the GCF of (70, 175)

70 = 7x5x2

175= 5x5x7

GCF = 7x5

Find the LCM of (70, 175)

5^2 x 7 x 2

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

List all prime numbers between 20 and 40

23, 29, 31, 37

Find the largest 2 digit number that has exactly two factors

97

Is 2816 divisible by 11

Yes

2+1= 3

8+6= 14

14- 3 = 11

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

Closure Property of Addition

3-2=1

Associative Property of Addition

6 + (4+3) = (6+4) +3

Communative Property of Multiplication

3 x 4= 4x 3

Identity property of addition

0 + 4 = 4 = 4+0

zero property of multiplication

0 x 5 = 0 = 5 x 0

inverse property of addition

6+(-6) = 6 = (-6) + 6

distributive property of multiplication over addition

7 x 4 + 7 x 3

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

30% of 80 is

30/100 = x/80

x= 24

Order fractions from smallest to largest: 2/3, 10/11, 3/5

3/5, 2/3, 10/11

132.3 + 6.437

138.737 (make sure to line up decimal points when adding)

11.95 + 3.7

8.25 (make sure to line up decimal points)

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

Commutative Property

a + b = b + a (order)

Associative Property

(a+b) + c = a + (b+c) (grouping)

Multiplying numbers with exponents

multiply the numbers, add the exponents

Dividing numbers with exponents

divide the numbers, subtract the exponents

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

Common Square roots

10 = 100

20 = 400

30 = 900

40 = 1600

45= 2025

50 = 2500

25= 625

15= 225

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)