Free Printable 2018 Algebra New Meridian Released items

1.

What is the graph of the equation $y = x^2 - x - 6$ in the xy-coordinate plane?

a)

[Graph A]

b)

[Graph B]

c)

[Graph C]

d)

[Graph D]

2.

Subtract (4x^2 - x + 6) from (3x^2 + 5x - 8).

a)

$7x^2 + 6x - 14$

b)

$-x^2+4x+2$

c)

$7x^2 + 4x - 2$

d)

$-x^2 + 6x - 14$

3.

The graph shows the function y = g(x), where g(x) represents a transformation of $f(x) = x^2$ . What is the equation for g(x)?

a)

$g(x) = (x - 2)^2 - 1$

b)

$g(x) = (x + 2)^2 - 1$

c)

$g(x) = -(x - 2)^2 + 1$

d)

$g(x) = -(x + 2)^2 + 1$

4.

Consider the graph of the function $s(x) = x^2 + 6x + 9$ . Part A The function $r(x) = k \cdot s(x)$ , where k is a constant. Which statements about the graphs of $s(x)$ and $r(x)$ are true?

a)

D. When k > 1, the graph of r(x) is a vertical compression of the graph of s(x).

b)

F. When 0 < k < 1, the graph of r(x) is a vertical compression of the graph of s(x).

c)

A. When k < 0, the vertex of the graph of r(x) is a minimum.

d)

C. When k > 1, the graph of r(x) is a vertical stretch of the graph of s(x).

e)

B. When k < 0, the vertex of the graph of r(x) is a maximum.

5.

Consider the graph of the function s(x) = $x^2 + 6x + 9$ . The graph of s(x) is translated to produce the graph of t(x), where t(x) = $x^2 + 6x + 13$ . Which is a correct description of the translation?

a)

A. vertical shift 4 units up

b)

B. vertical shift 4 units down

c)

C. horizontal shift 4 units to the left

d)

D. horizontal shift 4 units to the right

6.

The two graphs and two descriptions each represent a sequence. Choose the equation that represents each sequence for n = 1, 2, 3... Drag and drop the letter of the graph or description (A, B, C, D) to the correct box.

a)

1.

g(n) = -3/4 n + 59/4

b)

2.

f(n) = $(0.5)2^n$

c)

3.

k(n) = 5 - 5(n - 1)

d)

4.

$h(n) = (-2)(-5)^{(n-1)}$

7.

At the end of year 0, city M has a population of 23,500 that is growing at a rate of 5% per year. The population of city P at the end of year 0 is 23,000. The population of city P over a 4-year period is shown in the table. If the growth rate for each city does not change, which statement about the populations of city M and city P is true?

a)

A. City M has the greater growth rate and the larger population at the end of year 2.

b)

B. City M has the greater growth rate and the smaller population at the end of year 2.

c)

C. City P has the greater growth rate and the larger population at the end of year 2.

d)

D. City P has the greater growth rate and the smaller population at the end of year 2.

8.

Members of a high school sports team are selling boxes of popcorn and boxes of pretzels for a fundraiser. They earn $2 for every box of popcorn they sell and $5 for every box of pretzels. The members want to earn at least $500 from all sales.

Let x represent the number of boxes of popcorn sold and y represent the number of boxes of pretzels sold.

What inequality represents the number of boxes of popcorn and the number of pretzels that need to be sold to reach the goal of earning at least $500

a)

2x + 5y ≥ 500

b)

5x + 2y ≥ 500

c)

(2 + x)(5 + y) ≥ 500

d)

(5 + x)(2 + y) ≥ 500

9.

Members of a high school sports team are selling boxes of popcorn and boxes of pretzels for a fundraiser. They earn $2 for every box of popcorn they sell and $5 for every box of pretzels. The members want to earn at least $500 from all sales.

A line exists that serves as the boundary for the points making up the solution set of the inequality representing the numbers of boxes of popcorn and boxes of pretzels sold. Consider the line graphed in the xy-coordinate plane. What would be the interpretation, in context, of its slope?

a)

For every increase of 2 boxes of popcorn sold, 5 more boxes of pretzels need to be sold to earn $500.

b)

For every increase of 2 boxes of popcorn sold, 5 fewer boxes of pretzels need to be sold to earn $500.

c)

For every increase of 5 boxes of popcorn sold, 2 more boxes of pretzels need to be sold to earn $500.

d)

For every increase of 5 boxes of popcorn sold, 2 fewer boxes of pretzels need to be sold to earn $500.

10.

Members of the team believe they can sell at least 40 boxes of pretzels. Which graph represents the solution in the xy-coordinate plane of the system of inequalities that represents the numbers of boxes of popcorn and boxes of pretzels that need to be sold with the constraint that at least 40 boxes of pretzels will be sold?

a)

(Graph A)

b)

(Graph B)

c)

(Graph C)

d)

(Graph D)

11.

For which combinations of boxes of popcorn and pretzels sold will the team meet the goal of earning at least $500? Select all that apply.

a)

30 boxes of popcorn and 80 boxes of pretzels

b)

60 boxes of popcorn and 80 boxes of pretzels

c)

75 boxes of popcorn and 70 boxes of pretzels

d)

80 boxes of popcorn and 60 boxes of pretzels

e)

100 boxes of popcorn and 60 boxes of pretzels

12.

Bella has a tomato garden. The data in the table show the number of tomato seeds planted in her first and second years and the numbers of tomatoes harvested each year. Bella will plant 120 tomato seeds in her third year.

Bella predicts that she will harvest 3,240 tomatoes in the third year. Do you agree with her prediction? Justify your answer and show all work

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13.

The tomatoes were harvested during July, August and September of each year. The data are shown in the table.

If Bella harvests 3,240 tomatoes during the third year, how many tomatoes do you think she will harvest in each of the months: July, August, and September?

Justify your answers for each month by showing all work

4 lines

14.

Of the students who responded that they attended at least one game, what percent were seniors?

(a)

15.

Consider the given system of equations:
$2x + y = 1$
$y = x^2 - 2x - 3$
Select the correct points in the coordinate plane that represent the solutions to the given system of equations.

16.

What type of function is represented by the data in the table?

Justify your answer

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17.

Consider a family that generates 18 loads of laundry in a week. Based on the data in the table, what is the total number of people in the family?

Show work to justify your answer

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18.

A group of students bakes 100 cookies to sell at the school bake sale. The students want to ensure that the price of each cookie offsets the cost of the ingredients. If all the cookies are sold for $0.10 each, the net result will be a loss of $4. If all the cookies are sold for $0.50 each, the students will make $36 profit. Write the linear function p(x) that represents the net profit from selling all the cookies, where x is the price of each cookie? Then determine how much profit the students will make if they sell the cookies for $0.60 each

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19.

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. The quadratic function A(w) represents the area A, in square inches, of the rectangle for a given value of w. Which function gives the area as a function of the width?

a)

$A(w) = 7w - w^2$

b)

A(w) = $2w^2 - 7$

c)

$A(w) = 7w - 2w^2$

d)

$A(w) = 2w^2 - 7w$

20.

The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. If the area of the rectangle is 60 square inches, what is the width of the rectangle?

(a)

21.

What is an equivalent form of the function f(x) = $-x^2 - 8x - 12$ that reveals the zeros of the function?

a)

$f(x) = -(x + 4)^2 + 4$

b)

$f(x) = -(x - 4)^2 + 4$

c)

f(x) = -(x + 2)(x + 6)

d)

f(x) = -(x - 2)(x - 6)

22.

The formula $A=\frac{1}{2}S^2$ expresses the area, A, of an isosceles right triangle in terms of the length, s, of a leg of the triangle. Which equation expresses the length of a leg of an isosceles right triangle in terms of the area?

a)

s = $\frac{\sqrt[]{a}}{2}$

b)

$s = \sqrt{A^2/2}$

c)

s = 2√A

d)

s = √2A

23.

A T-shirt company bought a new packaging and tracking system for $100,000. The formula $V = 100,000(1 - 0.125)^y$ models the value of the system V, in dollars, after depreciating for y years. In this formula, what is the meaning of the term $(1 - 0.125)$ ?

a)

The value of the system will be $0 in 12.5 years.

b)

The value of the system will decrease by $12.50 each year.

c)

The value of the system will decrease by 12.5% each year.

d)

The value of the system will continue to decrease for 125 years.

24.

A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. Juice Mixture Table: Juice Made (ounces): 200, 600, 1,000, 1,400 Concentrate Remaining (ounces): 280, 200, 120, 40 Part A How many ounces of concentrate were in the original container before any juice was made?

(a)

25.

A certain amount of concentrate is mixed with water to create a juice. The table shows the amount of concentrate, in ounces remaining, in the original container after x ounces of juice are made. Juice Mixture Table: Juice Made (ounces): 200, 600, 1,000, 1,400 Concentrate Remaining (ounces): 280, 200, 120, 40 Part B How many ounces of juice can be made using the whole container of concentrate?

(a)

26.

Which graph showing the relation between x and y represents y as a function of x? Select all that apply.

a)

E. [Graph E]

b)

A. [Graph A]

c)

C. [Graph C]

d)

B. [Graph B]

e)

D. [Graph D]

27.

Which statement(s) can be interpreted from the equation for an automobile cost, $C(t) = 28,000(0.73)^t$ , where $C(t)$ represents the cost and $t$ represents the time in years? Select all correct statements.

a)

$28,000 represents the initial cost of an automobile that appreciates 27% per year over the course of t years.

b)

The equation is neither exponential decay nor exponential growth.

c)

The equation is an exponential growth equation.

d)

$28,000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.

e)

The equation is an exponential decay equation.

28.

Which expression is equivalent to $((1 - r)^2 + r)((1 - r)^2 - r)$ ?

a)

$(1 - r)^4 - r^2$

b)

$2(1 - r)^2 + 2r$

c)

$(1 - r)^2(1 - r)(1 + r)$

d)

$(1 - r)^4 + 2r(1 - r)^2 + r^2$

29.

Which expression is equivalent to $((1 - x)^2 - 2x^2)((1 - x)^2 + 2x^2) + 4x^4$ ?

a)

$(1 - x)^4$

b)

$2(1 - x)^2 + 4x^4$

c)

$(1 - 3x^2)(1 + x^2) + 4x^4$

d)

$(1 - x)^4 + 4x^2(1 - x)^2 + 8x^4$

30.

A system of linear equations for the variables x and y is shown.

For what value of c, if any, will this system have no solution? Justify your answer

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31.

A system of linear equations for the variables x and y is shown.

For what value of c, if any, will this system have exactly one solution. Then solve the system using the value of c that you chose. Explain each step of your solution.

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32.

Darren tracked the number of employees in his company over a six-year period. In the graph x represents the years since 2006 and y represents the number of employees. The coordinates for one data point, P, are shown. Find the average rate of change in the number of employees per year by using the data for year 0 and year 6. Round your answer to the nearest tenth.

(a)

33.

Determine if the equation has a real solution or no real solution

Categorize the following

Real Solutiuon

No Real Solution

34.

Gianna's monthly profit for selling candles is represented by the function p(x)=7.5x-200, where x represents the number of candels sold. Complete the table so that each value in the domain is assigned the correct value in the range.

a)250

b)512.5

c)120

d)67

e)450

f)712.5

g)5,050

1

2

3

1)

2)

3)

35.

The scatter plot shows the price, in cents, of a postage stamp used to mail a letter in the United States for the years from 1958 to 2014. Also shown is the line of fit to model the data.

The equation of the line of fit is y=-0.71 + 0.86x, where y represents the predicted price, in cents, of a stamp and x represents the number of years since 1958.

a)

The model estimates an increase, on average of, 0.71 cents per year in the price of a stamp

b)

The model estimates a decrease, on average of, 0.71 cents per year in the price of a stamp

c)

The model estimates an increase, on average of, 0.86 cents per year in the price of a stamp

d)

The model estimates an decrease, on average of, 0.86 cents per year in the price of a stamp

36.

The scatter plot shows the price, in cents, of a postage stamp used to mail a letter in the United States for the years from 1958 to 2014. Also shown is the line of fit to model the data.

The equation of the line of fit is y=-0.71 + 0.86x, where y represents the predicted price, in cents, of a stamp and x represents the number of years since 1958.

a)

The model overpredicts the actual price of a stamp for the time period from 1958 to 1963

b)

The model underpredicts the actual price of a stamp for the time period from 1958 to 1963

c)

The model overpredicts the actual price of a stamp for 1958 and underpredicts the actual price for 1963

d)

The model underpredicts the actual price of a stamp for 1958 and overpredicts the actual price for 1963

2018 Algebra New Meridian Released items

Total questions: 36

Worksheet time: 44mins

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