Test 1 Review Sheet 4-19-17 PDF

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Test 1 Review Sheet

MATH 021

5/17

MATH 021 TEST 1 REVIEW SHEET TO THE STUDENT: This Review Sheet gives an outline of the topics covered on Test 1 as well as practice problems. Answers for all problems begin on page 9. It is suggested that you go over the definitions, examples and summaries in the ebook. It is also very important to go over your homework, labs and quizzes.

I.

Input-Output Tables

1.

For each rule, make an input-output table for integer inputs from –2 to 4. a) b)

2.

The output is four more than the input. The output is five less than the input cubed.

For the following situation, make an input-output table. Then write the rule symbolically. The input, n, is the number of pounds of rice purchased. The rice costs $1.19 per pound, and you have a store coupon for $0.75 off. The output, c, is the total cost for the rice. Use integer inputs from 1 to 5.

3.

For the following situation, make an input-output table. The nearby amusement park charges $15 for admission, which includes 5 rides. After 5 rides, each extra ride costs $1.50. The input, r, is the number of rides you take. The output, c, is the total cost for the day at the amusement park. Let r = 0, 3, 5, 6, 10, and 15 rides.

4.

Complete each table. a) Output, Input, n p = 4n – 3 1 1

b)

1

Output, P = –2n + 12 10

Input, n

2

5

4

4

3

9

5

2

19

73

19

50

50

100

100

1

Test 1 Review Sheet

MATH 021

5/17

Matilda purchased a Copy Card for $10 to use in the Bankier Library. Each copy that she makes costs $0.10. The graph illustrates the amount of money, m, left on the Copy Card after Matilda has made c copies.

5.

a)

Use the graph to complete the input-output table.

m 10

Input, c Number of copies

9 8

Ordered Pair (x, y)

0

7 Money remaining, in Dollars

Output, m Amount remaining

20

6 5

7

4

50

3

100

2 1

c 10

1

60 70 80 90 100 11

Number of copies

b)

II.

20 30 40 50

Write the practical meaning of the point (40, 6) within the context of this situation.

Sets of Numbers

To do problems 6 – 7, you should review the concepts in Section 1.2 of your workbook. You should be able to identify real numbers, rational numbers, irrational numbers, integers and whole numbers. 6.

For each of the following numbers, name all of the number sets to which it belongs: real, rational, irrational, integers, and whole numbers. 1 c) 6 d) 5 a) 1.5 b) − 3

7.

Indicate whether each statement is True or False. Then explain your answer. a) b) c) d)

Every number is either positive or negative. A number may be both an integer and a rational number. A number may be a whole number and a fraction. Any negative number is an integer.

2

Test 1 Review Sheet

MATH 021 III.

Expressions

8.

In the expression 3 x − 4 , which number is the numerical coefficient?

9.

Write each statement symbolically. Let x be the input. Rewrite percents as decimals. a) b) c) d)

10.

b)

The quotient of the opposite of 15 and –3 1 The product of and the reciprocal of 12 4

Write each sentence as an equation with x as the input and y as the output. a) b) c)

IV.

Four more than the product of two and the input The difference between five and the square of the input The square root of triple the input 1 8 % of the input 2

Translate each statement into symbols. (You do not need to simplify.) a)

11.

5/17

The output is three more than the input. The output is two less than seven times the input. The output is the quotient of double the input and nine.

Graphing

Complete each table, graph the points (x, y), and then connect them. Label the axes with appropriate scales. a) b) Output Input Input Output y = 4 x2 + 8 x + 6 x x y = −50 x + 10 (x, y) 12.

–2

–3

–1

–2

0

–1

1

0

2 13.

(x, y)

1 A salesperson earns $250 per week plus a 6 % commission on sales. a) b) c)

Make an input-output table where sales in dollars is the input and total weekly salary in dollars is the output. Use sales of 0, 100, 200, 300 and 400 dollars. Graph the ordered pairs from the table. Write the output rule symbolically.

3

Test 1 Review Sheet

MATH 021 14.

5/17

You bought a prepaid $20 card to the local coin-operated laundry. Each laundry load costs $2.50. a)

b) c) d)

Make an input-output table where the input is the number of loads and the output is the amount of money left in the card. Let y be the amount left after x loads. Show the amount left for 0 to 8 loads, in steps of 2. Graph the ordered pairs from the table. What is the symbolic rule describing the money left on the card? Write the practical meaning of the point (4, 10) in the context of this situation.

V.

Exponents and Fractions Expressions

15.

Simplify. a) 42 ÷ 2 ⋅ 6 − 32 2 b) (−4 ) c) d)

−4 4 − 3( 3 − 5)

e)

(4 − 3 )(3 − 5 )

f)

6 − 3 52 − 27

g)

7 − ( 6 − 8) + 3

2

2

3 − ( −5 )

h)

−6 − 4

16.

Explain why − x 2 is not the same as (− x ) .

17.

Evaluate each of the following expressions by substituting the value(s) of the variable(s). Then follow the rules for order of operations.

18.

2

a)

2 x − 3 y +1

x = −3, y = 7

c)

a2 + b2

a = −3, b = 4

b)

x2 + 4 x + 2

x = −2

d)

a2 + b2

a = −3, b = 4

Simplify each expression. a)

3x2 ⋅ x5

d)

ab 2 a3 b

b)

20 m6 4m 2

e)

(7xy )

c)

−4( ab)

f)

 3x    5 

3

4

2

2

4

Test 1 Review Sheet

MATH 021 19.

Simplify completely. Show work using the properties of radicals. a) b)

VI.

5/17

20 5

(3 5 )

2

c)

48 3

Properties of Numbers

To do the following problems you should be familiar with the following terms: commutative property, associative property, distributive property, terms, and factors. You may wish to refer to Section 1.5 of your workbook. 20.

Name the property (commutative or associative). a) b)

3 ⋅2 = 2 ⋅3 (5 + 7 ) + 3 = 5 + (7 + 3 )

c)

(4 ⋅ 6 ) ⋅ 9 = ( 6 ⋅ 4 ) ⋅ 9

21.

Is subtraction commutative? Give an example to support your conclusion.

22.

Is division associative? Give an example to support your conclusion.

VII.

Simplifying Expressions, Terms and Factors

23.

Give an example of two terms that are like terms.

24.

Give an example of two terms that are not like terms.

25.

How do you distinguish terms from factors?

26.

Give an example of an expression with four terms.

27.

Give an example of a one-term expression with four factors.

28.

Give an example of a term with a coefficient of 3.

29.

Simplify each expression. Use the Distributive Property, where appropriate. a)

4 ( 2 x − 3)

b)

−3( − x + 4)

c) d)

5

3x + 6 3 4ab 10ac

Test 1 Review Sheet

MATH 021

30.

e)

−2( x − 4 y − 5)

g)

f)

6x 18xy

h)

5/17 −x + 8 4 −x − 4 8

Simplify and combine like terms. d)

3( x +1) + 5( x − 2)

x − ( −3 x ) + 2 + 6 x − 2 x −1

e)

8 − 2( x − 1)

4 x 2 − 3xy − 2 y 2 − 6x 2 + 6 xy − y 2

f)

4 2 a2 + 4 − ( 6 − 3a )

a)

12 − 3 x + 5 + 6 x

b) c)

2

2

(

)

VIII. Polynomials and Evaluate Expressions 31.

Consider the expression: x 3 + 5 a) b) c)

32.

Simplify completely. a) b)

33.

Identify the constant term. What is the degree of the polynomial? Because this expression has __________ terms, it is called a __________.

(3 x (3 x

2 2

) ( − 5 x + 7 ) − (4 x

) − x +3)

− 5 x + 7 + 4 x2 − x + 3 2

c) d)

(

) ( 5 x − 3 x ( x − 8)

2 3 x2 − x + 2 − 4 7 − 7 x2

)

2

Multiply and simplify as needed. a) b) c)

(x + 7 )(x + 2 ) (4 y − 5 )( y − 3 ) 2 (z − 4 )

d) e) f)

(b + 6 )(b − 6 ) (3 x +1 )(5 x − 2 ) c (c − 12 )

IX.

Functions

34.

State the definition of a function.

35.

Fill in the Blank: The Vertical Line Test states that if a __________ line crosses a graph in more than one place, the graph is not a function. This is because for some value of __________, there would be more than one value for __________.

6

Test 1 Review Sheet

MATH 021 36.

State whether each of the following represent a function? Explain why. a)

c)

37.

x

y

−3 −2

6 3

−1

2

0 1

3 6

d)

{( 1,3) ,( 3,5) ,( 1,5) ,( 5,9)}

Interpret f ( 2000) = 1700 in the context of this situation. If the monthly rent for 1,500 square feet is $3000, write this fact using function notation.

The amount of money in dollars, m, you make at a job depends on the number of hours, h, you work. a) b) c) d)

39.

b)

Suppose you are renting a storefront for your business. The input is the size of the store, s, in square feet. The output is the monthly rent, R, so we write R= f (s). a) b)

38.

5/17

In this situation, the input is __________. The output is __________. We say __________ is a function of __________. Write the relationship using function notation.

For the function f ( x) = 7 − 2 x . a)

Find f ( −3 ) . Write your answer as an ordered pair.

b)

Find f (0 ) . Write your answer as an ordered pair.

7

Test 1 Review Sheet

MATH 021

5/17

Complete each table, graph the points (x, y), and then connect them. Label the axes with appropriate scales. Then, answer the following.

40.

i)

ii) Input x

Output f ( x) = 2 x +1

Input x

(x, y)

–1

Output 3 g( x) = − x

(x, y)

1 2

0

1

3

3

8

6

 1 g   2

a)

Find x if g ( x) = −

d)

Find x if f ( x) = 0

f ( 0)

b) 41.

c)

1 2

The function f ( x) = 18 x − 3600 gives the profit from sales of music CDs for a small music company, where x is the number of CDs sold. Complete the table below.

Number of CDs sold, x

Profit from sales , f ( x) = 18 x − 3600

( x, f ( x ) )

0 150 200 300 400 500

a)

Find f (0 ) . Give the practical meaning in the context of the situation.

b)

If f ( x) = 0 , find x. Give the practical meaning in the context of the situation.

c)

Find f ( 400) . Give the practical meaning in the context of the situation.

8

Test 1 Review Sheet

MATH 021

5/17

ANSWER KEY 1.

a)

4.

a)

x

y= x+4

Input, n

–2

2

–1

3

0

4

1 2

Output, p = 4n – 3 1 5

1

5

2

6

3 19

9 73

3

7

50

197

4

8

100

397

b) b)

x

y = x −5

–2

–13

–1

–6

1

Output, P = –2n + 12 10

0

–5

4

4

1

–4

5

2

2

3

3

22

19

–26

4

59

50

–88

100

–188

3

Input, n

2.

5.

a)

Input, n

Output, c

Input, c

Output, m

1

0.44

0

10

Ordered Pair (c, m) (0, 10)

2

1.63

20

8

(20, 8)

3

2.82

30

7

(30, 7)

4

4.01

50

5

(50, 5)

5

5.20

100

0

(100, 0)

The rule is c = 1.19 n − 0.75 .

b)

After Matilda makes 40 copies, she has $6 remaining on the Copy Card.

6.

a) b) c) d)

real, rational real, rational real, rational, integer, whole real, irrational

7.

a) b) c)

False. Zero is neither positive nor negative. True. Every integer is a rational number. True. If n is a whole number, then n/1 is a fraction. 1 False. For example, − is negative but not an 2 integer.

3. Input, r

Output, c

0

15

3

15

5

15

6

16.50

10

22.50

15

30 d) 8.

9

3

Test 1 Review Sheet

MATH 021 9.

a)

2x + 4

b)

5− x 3x 0.085x −15 −3 1 1 ⋅ 4 12

c) d) 10. a) b)

12

2

b)

20

y

10

b)

y = x+3 y = 7x − 2

c)

y=

11. a)

5/17

x

2x 9

−3

−2

−1

1

12. a) Output, y = −50 x + 10

Input, x

–2 –1 0 1 2

13. a) y = 250 + 0. 06x

(x, y)

0

250

(0, 250)

(–1, 60)

100

256

(100, 256)

10

(0, 10)

200

262

(200, 262)

–40

(1, –40)

300

268

(300, 268)

–90

(2, –90)

400

274

(400, 274)

(x, y) (–2, 110)

x

60

110

a)

120 y

b)

80 40

x −2

−1

1

2

−40 −80 b) Input, x

Output, y = 4 x2 + 8 x + 6

(x, y)

–3

18

(–3, 18)

–2

6

(–2, 6)

–1

2

(–1, 2)

0

6

(0, 6)

1

18

(1, 18)

y = 250 + 0.06 x

c) 14. a)

10

x

y = 20 − 2.50 x

(x, y)

0

20

(0, 20)

2

15

(2, 15)

4

10

(4, 10)

6

5

(6, 5)

8

0

(8, 0)

Test 1 Review Sheet

MATH 021

20 5 = 100 = 10

19. a)

b)

48 = 16 = 4 3

b)

Amount Remaining ($)

y 20

c)

15

20. a) b) c)

10

2

h)

2

Commutative Associative Commutative

4

6

22. No, division is not associative. Example: (6 ÷ 3 ) ÷ 2 ≠ 6 ÷ ( 3 ÷ 2) . ( 6 ÷ 3) ÷ 2 = 1, but

8

6 ÷ (3 ÷ 2 ) = 4 .

y = 20 − 2.50 x After 4 loads of laundry, you have $10 remaining on your pre-paid card.

23. Answers will vary. Example: x, 2x 24. Answers will vary. Example: x, 2 25. Terms are added or subtracted; factors are multiplied or divided.

117 16 –16 10 –2 0 6 4 − 5

26. Answers will vary. Example: a + b + c + d 27. Answers will vary. Example: abcd 28. Answers will vary. Example: 3a 29. a)

8 x − 12

b)

3 x − 12

and then take the opposite. For ( − x ) , you take the

c)

opposite first and then square the result. Therefore,

d)

x+2 2b 5c

16. Order of operations says that for − x , you square first 2

2

(− x )

2

=x . 2

e)

17. a) b) c) d)

–26 –2 5 7

g)

18. a)

3x7

h)

b)

5m 4

c)

−4 a 3b 3 b

d)

( )

= 3 5 3 5 = 9 25 = 9 (5 ) = 45

3 − 2 ≠ 2 − 3 . 3 − 2 = 1 , but 2 − 3 = −1 .

5

Number of Loads

15. a) b) c) d) e) f) g)

(3 5 )

21. No, subtraction is not commutative. Example:

x

c) d)

5/17

f)

30. a)

a2

e)

49x 2 y 4

f)

81x 4 625

11

−2 x + 8 y + 10 1 3y

1 x +2 4 1 1 − x− 8 2 −

3x + 17

b)

7 x2 + x + 1

c)

−2 x 2 + 3xy − 3 y 2

d)

8x − 7

e)

10 − 2 x

f)

8a + 3a + 10

2

Test 1 Review Sheet

MATH 021 31. a) b) c)

5 3 2, binomial