Quiz about Test 6 Review Sheet

Question 1

Given the piecewise function: f(x) = $${ 3x - 1 ext{ if } x < 0 ewline x^2 + 1 ext{ if } 0 \leq x \leq 3 ewline 4x + 2 ext{ if } x > 3 }$$ Find: f(1) = _______

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 2

Given the piecewise function: f(x) = $${ 3x - 2 ext{ if } x < -2 ewline x^2 + 1 ext{ if } -2 \leq x \leq 3 ewline 4x + 1 ext{ if } x > 3 }$$ Find: f(-4) = _______

Accepted Answer

-14

Answer

-10

Answer

10

Answer

2

Question 3

Given the piecewise function: f(x) = $${ 3x - 1 ext{ if } x < 0 ewline x^2 + 1 ext{ if } 0 \leq x \leq 3 ewline 4x + 2 ext{ if } x > 3 }$$ Find: f(2) = _______

Accepted Answer

4

Answer

5

Answer

3

Answer

6

Question 4

Verify if the given ordered pair is a solution of the system. Show your work!

(3, 2)

3x - y = 7

2x + 3y = 12

Accepted Answer

Yes, (3, 2) is a solution to the system.

Answer

No, (3, 2) is not a solution to the first equation.

Answer

No, (3, 2) is not a solution to the second equation.

Answer

No, (3, 2) is not a solution to either equation.

Question 5

Verify if the given ordered pair is a solution of the system. Show your work!

(3, -1)

2x + y = 5

4x - 2y = 10

Accepted Answer

Yes, (3, -1) is a solution to the system.

Answer

No, (3, -1) does not satisfy the first equation.

Answer

No, (3, -1) does not satisfy the second equation.

Answer

No, (3, -1) does not satisfy either equation.

Question 6

Solve by substitution:

y = 3x + 2

2x - y = 4

What is the solution (x, y)?

Accepted Answer

(-1, -1)

Answer

(1, 5)

Answer

(2, 8)

Answer

(0, 2)

Question 7

Solve by substitution:

2x - y = 4

x = 3y - 2

What is the solution (x, y)?

Accepted Answer

(4, 2)

Answer

(2, 0)

Answer

(1, 1)

Answer

(-2, 1)

Question 8

Solve by elimination:

2x + 3y = 12

4x - y = 10

Accepted Answer

x = 3, y = 1

Answer

x = 2, y = 2

Answer

x = 1, y = 3

Answer

x = 4, y = 0

Question 9

Solve by elimination:

3x + 4y = 10

6x + 5y = 7

Accepted Answer

x = 2, y = -1

Answer

x = 1, y = 2

Answer

x = -1, y = 3

Answer

x = 0, y = 0

Question 10

Solve using any method:

3x - 2y = 6

4x + y = 11

Accepted Answer

x = 2, y = 3

Answer

x = 1, y = 4

Answer

x = 3, y = 1

Answer

x = 0, y = 5

Question 11

Solve using any method:

4x + 5y = 9

5y - 4x = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 1

Answer

x = -1, y = 2

Answer

x = 0, y = 0

Question 12

Solve using any method:

2x + 3y = 6

y = x - 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 0

Answer

x = 0, y = 2

Answer

x = 3, y = 1

Question 13

Find the solution to the system of equations:

2x + 3y = 12

y = 4 - x

Accepted Answer

x = 3, y = 1

Answer

x = 2, y = 2

Answer

x = 0, y = 4

Answer

x = 4, y = 0

Question 14

Solve the system of equations:

3x + 2y = 12

4x - y = 5

What is the solution (x, y)?

Accepted Answer

(2, 3)

Answer

(1, 4)

Answer

(3, 2)

Answer

(4, 1)

Question 15

Solve the system of equations:

2x + 3y = 12

4x - y = 5

What is the solution (x, y)?

Accepted Answer

(3, 1)

Answer

(2, 2)

Answer

(1, 3)

Answer

(0, 4)

Question 16

The sum of two numbers is 30. One-third of the first number plus one-fourth of the second number is 10. Find the numbers.

Accepted Answer

The numbers are 20 and 10.

Answer

The numbers are 18 and 12.

Answer

The numbers are 15 and 15.

Answer

The numbers are 25 and 5.

Question 17

The sum of two numbers is 12 and their difference is 4. Find the numbers.

Accepted Answer

The numbers are 8 and 4.

Answer

The numbers are 9 and 3.

Answer

The numbers are 10 and 2.

Answer

The numbers are 7 and 5.

Question 18

There were 250 tickets sold for a college football game. Tickets were $5 for students and $10 for adults. The total amount collected was $1,750. How many of each type of ticket was sold?

Accepted Answer

150 student tickets and 100 adult tickets were sold.

Answer

125 student tickets and 125 adult tickets were sold.

Answer

100 student tickets and 150 adult tickets were sold.

Answer

175 student tickets and 75 adult tickets were sold.

Question 19

A jar of nickels and dimes contains $10.75. There are 125 coins in all. How many of each are there?

Accepted Answer

75 nickels and 50 dimes

Answer

60 nickels and 65 dimes

Answer

80 nickels and 45 dimes

Answer

55 nickels and 70 dimes

Question 20

On a table there are 25 coins, some quarters and some nickels. Their value is $2.85. How many of each are there?

Accepted Answer

15 quarters and 10 nickels

Answer

18 quarters and 7 nickels

Answer

20 quarters and 5 nickels

Answer

17 quarters and 8 nickels

Question 21

Identify the base and the exponent in the expression: $$3^7$$

Accepted Answer

Base: 3, Exponent: 7

Answer

Base: 7, Exponent: 3

Answer

Base: 3, Exponent: 3

Answer

Base: 7, Exponent: 7

Question 22

Write 5 x 5 x 5 in exponential form:

Accepted Answer

$$5^3$$

Answer

$$5^2$$

Answer

$$3^5$$

Answer

$$5^5$$

Question 23

Calculate: $$3^4$$

Accepted Answer

81

Answer

27

Answer

64

Answer

48

Question 24

Evaluate: $$5^0$$

Accepted Answer

1

Answer

0

Answer

5

Answer

-1

Question 25

Simplify: $$2^2$$

Accepted Answer

4

Answer

2

Answer

8

Answer

0

Question 26

Simplify: $$1^2$$

Accepted Answer

1

Answer

0

Answer

2

Answer

-1

Question 27

Calculate: $$3^{-2}$$

Accepted Answer

1/9

Answer

-9

Answer

1/3

Answer

9

Question 28

Convert $$10^{-4}$$ to a decimal.

Accepted Answer

0.0001

Answer

0.001

Answer

0.01

Answer

0.1

Question 29

Simplify: $$10^{-1}$$

Accepted Answer

0.1

Answer

1

Answer

10

Answer

0.01

Question 30

Evaluate: $$5^0$$

Accepted Answer

1

Answer

0

Answer

5

Answer

25

Question 31

Convert to standard form: $$4.57x10^{-4}$$ = _______

Accepted Answer

0.000457

Answer

0.00457

Answer

0.0457

Answer

0.0000457

Question 32

Write in standard form: $$3.21x10^1$$ = _______

Accepted Answer

32.1

Answer

3.21

Answer

321

Answer

0.321

Question 33

Express in standard form: $$5.432x10^6$$ = _______

Accepted Answer

5,432,000

Answer

54,320,000

Answer

543,200

Answer

543,200,000

Question 34

Evaluate the expression. Write the answer in scientific notation and standard form:

$$(3 x 10^{-10})(2 x 10^{4})$$ = _______ (scientific notation), _______ (standard form)

Accepted Answer

6 x 10^{-6}, 0.000006

Answer

6 x 10^{-5}, 0.00006

Answer

6 x 10^{-7}, 0.0000006

Answer

6 x 10^{-8}, 0.00000006

Question 35

Calculate the value of the following expression. Provide the answer in both scientific notation and standard form:

$$(3.2 x 10^3) / (8 x 10^4)$$ = _______ (scientific notation), _______ (standard form)

Accepted Answer

4 x 10^{-2}, 0.04

Answer

4 x 10^{-1}, 0.4

Answer

4 x 10^{-3}, 0.004

Answer

4 x 10^{-4}, 0.0004

Question 36

Simplify. All answers should include positive exponents only.

$$(2^3)^2$$ = _______

Accepted Answer

64

Answer

128

Answer

32

Answer

256

Question 37

Simplify. All answers should include positive exponents only.

$$(3^3)(3^2)$$ = _______

Accepted Answer

243

Answer

81

Answer

27

Answer

9

Question 38

Simplify. All answers should include positive exponents only.

$$(5^1)(5^3)$$ = _______

Accepted Answer

125

Answer

15

Answer

20

Answer

8

Question 39

Simplify. All answers should include positive exponents only.

$$(3^4)(3^{-2})$$ = _______

Accepted Answer

9

Answer

12

Answer

6

Answer

18

Question 40

Simplify. All answers should include positive exponents only.

$$(3^3)^2$$ = _______

Accepted Answer

243

Answer

729

Answer

81

Answer

27

Question 41

Simplify. All answers should include positive exponents only.

$$10^6 / 10^3$$ = _______

Accepted Answer

1000

Answer

100

Answer

10

Answer

10000

Question 42

Simplify. All answers should include positive exponents only. $$1^4/1^3$$ = _______

Accepted Answer

1

Answer

0

Answer

2

Answer

$$1^7$$

Question 43

Simplify. All answers should include positive exponents only.

$$4^5 / 4^3$$ = _______

Accepted Answer

16

Answer

64

Answer

8

Answer

4

Question 44

Simplify. All answers should include positive exponents only.

$$7^3 / 7^3$$ = _______

Accepted Answer

1

Answer

$$7^0$$

Answer

7

Answer

0

Question 45

Simplify. All answers should include positive exponents only.

$$8^3 / 8^5$$ = _______

Accepted Answer

1/64

Answer

64

Answer

8

Answer

1/8

Question 46

Simplify. All answers should include positive exponents only.

$$(3^5)(3^{-5})$$ = _______

Accepted Answer

1

Answer

0

Answer

9

Answer

27

Question 47

Determine whether the following expression is a polynomial: $$4x^3 - 5x^2 + 2x - 1$$

Accepted Answer

Yes

Answer

No, because it contains a variable in the denominator

Answer

No, because it contains a negative exponent

Answer

No, because it contains a square root

Question 48

Combine the polynomials:

(6m+3)+(2m+4) = ______

Accepted Answer

8m + 7

Answer

10m + 7

Answer

8m + 1

Answer

4m + 1

Question 49

Add/Subtract the polynomials:

(5d+7)-(2d+3) = ______

Accepted Answer

3d + 4

Answer

7d + 10

Answer

3d + 10

Answer

5d + 4

Question 50

Add/Subtract the polynomials:

$$(5b^2+4b+6)+(3b+2)$$ = ______

Accepted Answer

$$5b^2 + 7b + 8$$

Answer

$$5b^2 + 4b + 6$$

Answer

$$8b^2 + 7b + 8$$

Answer

$$5b^2 + 3b + 2$$

Question 51

Add/Subtract the polynomials: $$(5x^2+3x-2)+(4x^2+2x-3)$$ = ______

Accepted Answer

$$9x^2 + 5x - 5$$

Answer

$$9x^2 + 5x - 1$$

Answer

$$9x^2 + 6x - 5$$

Answer

$$9x^2 + 5x - 4$$

Question 52

Subtract the polynomials: $$(5x^3+4x^2+3x-1)-(2x^3+x^2+2x-3)$$ = ______

Accepted Answer

$$3x^3 + 3x^2 + x + 2$$

Answer

$$3x^3 + 3x^2 + x - 2$$

Answer

$$3x^3 + 3x^2 + 5x + 2$$

Answer

$$3x^3 + 3x^2 + 5x - 2$$

Question 53

Simplify: $$(3x^2)/9$$ = ______

Accepted Answer

$$x^2/3$$

Answer

$$x^2/9$$

Answer

$$3x^2/3$$

Answer

$$9x^2$$

Question 54

Simplify: $$(4x^3)(-2x)$$ = ______

Accepted Answer

$$-8x^4$$

Answer

$$8x^3$$

Answer

$$-6x^3$$

Answer

$$-8x^3$$

Question 55

Simplify: $$\frac{6x^7}{3x^4}$$ = ______

Accepted Answer

$$2x^3$$

Answer

$$2x^4$$

Answer

$$3x^3$$

Answer

$$3x^2$$

Question 56

Simplify: $$(3a^2b)(4a^3b^2)$$ = ______

Accepted Answer

$$12a^5b^3$$

Answer

$$7a^5b^3$$

Answer

$$12a^6b^2$$

Answer

$$-12a^5b^3$$

Question 57

Simplify: $$(3x^3)^2$$ = ______

Accepted Answer

$$9x^6$$

Answer

$$6x^3$$

Answer

$$3x^6$$

Answer

$$9x^3$$

Question 58

Simplify: $$(3y)^2$$ = ______

Accepted Answer

$$9y^2$$

Answer

$$-9y^2$$

Answer

$$3y^2$$

Answer

$$-3y^2$$

Question 59

Simplify: $$(3y^3)^3$$ = ______

Accepted Answer

$$27y^9$$

Answer

$$9y^9$$

Answer

$$3y^6$$

Answer

$$81y^9$$

Question 60

Expand: 3x(x + 5) = _______

Accepted Answer

$$3x^2 + 15x$$

Answer

$$3x^2 + 5$$

Answer

3x + 15x

Answer

$$3x^2 + 5x$$

Question 61

Expand: (x - 2)(x + 5) = _______

Accepted Answer

$$x^2 + 3x - 10$$

Answer

$$x^2 + 7x + 10$$

Answer

$$x^2 - 10x + 3$$

Answer

$$x^2 + x - 10$$

Question 62

Multiply: (3x + 2)(x - 4) = _______

Accepted Answer

$$3x^2 - 10x - 8$$

Answer

$$3x^2 - 12x + 2$$

Answer

$$3x^2 - 8x - 4$$

Answer

$$3x^2 + 2x - 8$$

Question 63

Simplify: (x + 3)(x - 3) = _______

Accepted Answer

$$x^2 - 9$$

Answer

$$x^2 + 9$$

Answer

$$x^2 - 3x + 9$$

Answer

$$x^2 + 3x - 9$$

Question 64

Multiply: (x + 4)(x + 4) = _______

Accepted Answer

$$x^2 + 8x + 16$$

Answer

$$x^2 + 16$$

Answer

$$x^2 + 4x + 4$$

Answer

$$x^2 + 4x + 16$$

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