MAT121 Review - Bengal Study Night

Set Theory

100

How would you define:

a) natural numbers

b) whole numbers

c) integers

d) rational numbers

e) irrational numbers

a) the counting numbers  {1, 2, 3, ...} 

b) the natural numbers and zero

c) the set containing zero and all the natural numbers and their opposites

d) the set of all numbers  p/q where p and q are integers

e) the complement of rational numbers

200

Universal - {red, orange, yellow, green, blue, purple}

P - {red, yellow, blue}

S - {orange, green, purple}

True/False:

a) Yellow 

in P

b)  

S sub P

c) 

A nn B = O/

d) 

S uu P = U

a) True

b) False

c) True

d) True

300

Let 

U={1, 2, 3, ..., 20}

List the members of each set:

a) 

{x in U|6<x<=13}

b) 

{x in U| x=n^2, n in N}

a) {7, 8, 9, 10, 11, 12, 13}

b) {1, 4, 9, 16}

400

Let 

U={a, b, c, d, e, f, g, h}

A={a, b, c, d, e}

B={b, d, f, h}

Draw a Venn Diagram that represents these sets.

500

Let 

U={a, b, c, d, e, f, g, h}

A={a, b, c, d, e}

B={b, d, f, h}

Find:

a) 

A nn B

b) 

A uu B

c) 

barA

d) 

n(barA)

a) {b, d}

b) {a, b, c, d, e, f, h}

c) {f, g, h}

d) 3

Number Theory 1

100

List all the factors and then the first 5 multiples of:

a) 12

b) 28

c) 17

a) factors: 1, 2, 3, 4, 6, 12 

multiples: 12, 24, 36, 48, 60

b) factors: 1, 2, 4, 7, 14, 28 

multiples: 28, 56, 84, 112, 140

c) factors: 1, 17 

multiples: 17, 34, 51, 68, 85

200

Classify each number as prime or composite:

2, 5, 10, 31, 51, 75

Primes: 2, 5, 31

Composites: 10, 51, 75

300

Find the prime factorization of:

a) 7,938

b) 24,750

a)  7938=2times3^4times7^2 

b) 

 24750=2times5^3times9times11 

400

Use Divisibility Tests to determine if 2,783,428 is divisible by:

a) 3

b) 4

c) 5

a) Since 

2+7+8+3+4+2+8=34

34 is not divisible by 3, so 2,783,428 is not divisible by 3.

b) The last two digits, 28, are divisible by 4, so 2,783,428 is also divisible by 4.

c) The last digit is not a 5 or 0, so 2,783,428 is not divisible by 5.

500

Find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 425 and 9025.

GCF = 25

LCM = 153,425

Number Theory 2

100

Match each property:

a) commutative              1) (2+5)+7=2+(5+7)

b) associative                 2) 7(a - 4)=(7 x a) - (7 x 4)

c) multiplicative identity  3) 81 x 1 = 81

d) distributive                 4) 19 + 12 = 12 + 19

a, 4

b, 1

c, 3

d, 2

200

Round each number to the indicated place:

a) 347, nearest hundred

b) 347, nearest ten

c) 0.347, nearest hundredth

d) 0.347, nearest tenth

a) 300

b) 350

c) 0.35

d) 0.3

300

Find the sum or difference by hand:

a) 59 + 37

b) 59 - 37

c) -59 + 37

d) -59 - (-37)

a) 96

b) 22

c) -22

d) -22

400

Find the product/quotient (with remainder) by hand:

a) 

175times13

b) 

175div13

c) 

-8 times-5

d) 

54div-9

a) 2275

b) 13 remainder 6

c) 40

d) -6

500

Use the rectangular array model to show:

a) 

4times7=28

b) 

28div4=7

Base -10 and Base-5

100

Identify the following place values in the base-10 number system using words and numbers:

___ ___ ___ . ___ ___ ___

hundreds, tens, ones . tenths, hundredths, thousandths

100, 10, 1, 1/10, 1/100, 1/1000

10^2, 10^1, 10^0, 10^-1, 10^-2, 10^-3

200

Identify the following place values in the base-5 number system using words and numbers:

___ ___ ___ . ___ ___ ___

twenty-fives, fives, ones, fifths, twenty fifths, one hundred twenty fifths

25, 5, 1, 1/5, 1/25, 1/125

5^2, 5^1, 5^0, 5^-1, 5^-2, 5^-3

300

Convert the following base-10 number to base-5:

48

48₁₀=143₅

400

Convert the following base-5 number to base-10:

423₅

423₅=113₁₀

500

Find the sum of the two base-5 numbers below (keep your answer in base-5):

423_5+14_5

423_5+14_5=442_5

Fractions

100

Rewrite each fraction in simplest terms:

a) 

84/144

b) 

208/272

c) 

- 930/1290

a)  7/12 

b)  13/17 

c)  31/43 

200

Convert the mixed number to an improper fraction and the improper fraction to a mixed number:

a) 

2 8/15

b) 

325/40

a)  38/15 

b)  8 1/8 

300

Put the following fractions in increasing order:

3/8, 15/20, 10/16, 7/10

 3/8<10/16<7/10<15/20 

400

Find the sum/difference:

a) 

9/4+ - 7/8

b) 

2 1/3 - 5 3/4

a)  11/8 = 1 3/8 

b)  -41/12 = -3 5/12 

500

Find the product/quotient:

a) 

14/15 times 60/7

b) 

4 1/2 div 3/4

a) 8

b) 6

Decimals

100

Find each of the following:

a) 

253.29times1000

b) 

253.29div10^3

c) 

34.764div10,000

d) 

34.764times10^2

a) 253,290

b) 0.25329

c) 0.0034764

d) 3,476.4

200

Write in expanded notation:

a) 24.357

b) 0.24357

a)  2times10+4times1+3times1/10+5times1/100+7times1/1000 

b)  2*1/10+4*1/100+3*1/1000+5*1/10000+7*1/100000 

300

Write each decimal as a fraction and a percent:

a) 0.19

b) 0.812

c) 4.56

a)  0.19=19/100=19% 

b)  0.812=812/1000=203/250=81.2% 

c)  4.56=4 56/100=4 14/25=456% 

400

Write each fraction as a decimal and a percent:

a) 

2/5

b) 

420/80

c) 

3/7

a)  2/5=0.4=40% 

b)  420/80=5.25=525% 

c)  3/7=0.bar(428571)=42.86% 

500

Find the answer to each by hand:

a) 3.78 + 2.4

b) 3.78 - 2.4

c) 3.78 x 2.4

d)  3.78 div 2.4 

a) 6.18

b) 1.38

c) 9.072

d) 1.575

Ratios & Proportions

100

There are 5 bananas, 9 strawberries, and 6 lemons in the produce bag. What is the ratio of:

a) bananas to strawberries

b) bananas to fruit

c) yellow fruit to non-yellow fruit

a) 

5:9 or 5/9

b) 

5:20 or 5/20=1/4

c) 

11:9 or 11/9

200

Solve each proportion:

a)  5/70=12/x 

b)  329/x=23/16 

a) x=128

b) x=228.87

300

Rice costs $2.39 for 10 oz. How much should it cost for 32 oz of rice?

32 oz would cost $7.65

400

Solve each percentage problem:

a) What is 11.5% of 63?

b) What percent of 82 is 63?

c) 36 is 120% of what number?

a) 7.245

b) 76.83%

c) 30

500

A spring jacket is on sale for 40% off. If the sale price is $58.99, what was the original price?

$147.48