Free Printable Intermediate Algebra -- Practice EOC

1.

A system of equations is shown below. $3x-2y=23$

$x-3y=3$ Which system of equations has the same solution as the system of equations shown?

a)

A.

$2x-5y=7$ $3x+y=13$

b)

B.

$2x+5y=7$ $3x-y=13$

c)

C.

$5x-3y=39$ $2x-y=16$

d)

D.

$5x+3y=39$ $2x+y=16$

2.

A certain type of lily plant is growing in a pond in such a way that the number of plants is growing exponentially. The number of plants, N, in the pond at time, t, is modeled by the function $N(t)=ab^t$ , where a and b are constants and t is measured in months. The table represents the function.

Which equation can be used to find the number of plants in the pond at time t?

a)

$N(t)=150\cdot\left(\frac{1}{3}\right)^t$

b)

$N(t)=50\cdot\left(\frac{1}{3}\right)^t$

c)

$N(t)=50\cdot\left(3\right)^t$

d)

$N(t)=150(3)^t$

3.

The graph of $f(x)=2^x$ is graphed below. The function g(x) is a transformation of f(x). Which equation best represents the transformed graph g(x)?

a)

$g\left(x\right)=2^{x-4}-2$

b)

$g(x)=2^{x+3}-2$

c)

$g(x)=2^{x-2}-3$

d)

$g(x)=2^{x+2}-3$

4.

The diagram below shows the ages of 4 students in a class. Kellen says that this example is NOT a function because more than one student is 13 years old. Do you agree with Kellen? Why or why not?

a)

I agree with Kellen that it is NOT a function because no y-values can repeat in a function.

b)

I do not agree with Kellen. This is a function because y-values can repeat as long as no x-value repeats.

c)

I agree with Kellen that it is NOT a function because true functions only originate from the Funxioun region of France.

d)

I do not agree with Kellen. This is a function because x-values can repeat as long as no y-value repeats.

5.

Which equation does not match the parabola below?

a)

y = (x + 3)(x - 1)

b)

y = x² + 2x - 3

c)

y = (x - 3)(x + 1)

d)

y = (x + 1)² - 4

6.

Sophia is selling bracelets and necklaces at her stall. She sells each bracelet for $6.25 and each necklace for $12.50. In one day she sold a total of 15 bracelets and necklaces and made $125. How many necklaces did Sophia sell?

a)

5

b)

6

c)

9

d)

10

7.

Which number is a zero of the function y = 2x² + 5x - 3?

a)

-1/2

b)

1/2

c)

3

d)

5

8.

Solve the following equation for x.

$2+4x-3x=x+2$

a)

No Solution

b)

All Real Numbers

c)

x = 0

d)

x = 2

9.

Simplify completely.

$2\sqrt{160}$

a)

$2\sqrt{8}$

b)

$8\sqrt{10}$

c)

$4\sqrt{40}$

d)

$2\sqrt{28}$

10.

You want to join a gym. There are 3 gyms that are close to you. The following representations show the total monthly cost for each gym.

Which gym charges the most per month?

a)

Planet Fitness

b)

Gold’s Gym

c)

Locally Owned Gym

d)

All three gyms charge the same amount per month.

11.

Which integer CANNOT be the solution to the inequality $6x-4\le7x-3$ ?

a)

1

b)

0

c)

-1

d)

-2

12.

The area of a rectangular door is given by the trinomial $x^2-14x+45$ . The door’s width is $(x-9)$ . What is the door’s length?

a)

(x - 9)

b)

(x + 9)

c)

(x - 5)

d)

(x + 5)

13.

Carter is solving this equation by factoring. 10x² - 25x = -15 Which of the following expressions are factors of the equation? Select all that apply.

a)

2x + 1

b)

x + 3

c)

2x - 3

d)

x - 3

e)

x - 1

14.

Which of the following graphs would represent the greatest vertical stretch?

a)

A

b)

B

c)

C

d)

D

15.

A rectangle has a length of 2x - 5 units and a width of x - 3 units. What is the area, in square units, of the rectangle?

a)

2x² - 15

b)

2x² + 15

c)

2x² - 11x - 15

d)

2x² - 11x + 15

16.

Bryce wants to solve the system of equations below using substitution. What would be her best first step?

Equation 1: x - 4y = 10

Equation 2: 2x - 5y = 16

a)

Subtract 4y to both sides of Equation 1.

b)

Add 4y to both sides of Equation 1.

c)

Multiply Equation 1 by 2 and then subtract the equations.

d)

Add 5y to both sides of equation 2.

17.

Timmy has a rectangular backyard with a width of x. The length of the backyard is 2 yards more than 2 times the width. What is the area of the backyard?

a)

$2x^2+2x$

b)

$2x^2$

c)

$2x$

d)

$2x^2+4$

18.

The functions, f(x), g(x), and h(x) are represented below. Which function has the smallest minimum value?

a)

f(x)

b)

g(x)

c)

h(x)

d)

All minimum values are equal

19.

Identify ALL the true statements about the quadratic function $f(x)=-3x^2+6x-4$ .

a)

The increasing interval is $(-\infty,\ 1)$

b)

The vertex is at the point (1, -1)

c)

An equivalent form is $f(x)=-3(x-1)^2-1$

d)

An equivalent form is $f(x)=-3(x+1)^2-1$

e)

The vertex is at the point (-1, 1)

20.

Nesta took medication to help her headache. The amount, A, in milligrams, of the medication left in her body after t hours, is represented by the function $A(t)=200(0.63)^t$ .

Select all true statements about the function.

a)

Nesta initially took 200 mg of the medication.

b)

Nesta initially took 126 mg of the medication.

c)

The medication in Nesta’s body is decreasing by 37% per hour.

d)

After 4 hours there is 31.5 mg left in Nesta’s body.

e)

The medication in Nesta’s body is decreasing by 63% per hour.

21.

Simplify the following expression. The answer should contain only positive exponents.

a)

$\frac{1}{m^4}$

b)

$\frac{n^8}{m^4}$

c)

$\frac{2n^8}{m^4}$

d)

$\frac{n^9}{m^4}$

22.

Function A is represented with the equation -3x + 2y = 10.

The graph of function B has a slope of $\frac{3}{2}$ and a y-intercept of 6.

Select two statements that are true about function A and function B.

a)

C. The slope of function A is greater than the slope of function B.

b)

B. Functions A and B have the same y-intercept.

c)

A. Functions A and B have the same slope.

d)

F. The y-intercept of function B is greater than the y-intercept of function A.

e)

D. The slope of function B is greater than the slope of function A.

23.

In the inequality $2x+\text{10,000}\ge\text{70,000}$ where x represents the salary of an employee in a school district. Which phrase most accurately describes the employee’s salary?

a)

At least $30,000

b)

At most $30,000

c)

Less than $30,000

d)

More than $30,000

24.

Gavin is using the complete the square method to solve the quadratic below. $3x^2-18x=21$ .

Which of the following describes Gavin’s best first step?

a)

A. Take half of 18 and then square it.

b)

B. Divide all terms by 3.

c)

C. Add 81 to both sides.

d)

D. Subtract 21 to both sides.

25.

The height of a golfball hit upward from the ground is given by the quadratic function $h=120t-16t^2$ , where $h$ is in feet and $t$ is in seconds. What is a reasonable range in context of this scenario?

a)

$0\le y\le120$

b)

$0\le y\le225$

c)

$0\le y<\infty$

d)

$-\infty<y<\infty$

26.

What is the domain of the function below?

a)

0 ≤ x ≤ 5

b)

0 ≤ x ≤ 8

c)

0 ≤ y ≤ 1

d)

0 ≤ y ≤ 6

27.

Use the graph of the linear inequality below to answer the question. Identify which of the ordered pairs are solutions.

Select ALL that apply.

a)

(4, 5)

b)

(−4, −3)

c)

(0, 1)

d)

(2, 1)

e)

(−3, 0)

28.

Select the type of function that best represents the table.

Function A is:

a)

linear

b)

quadratic

c)

exponential

29.

Select the type of function that best represents the table.

Function B is:

a)

linear

b)

quadratic

c)

exponential

30.

Select the type of function that best represents each table. Function C is:

a)

linear

b)

quadratic

c)

exponential

31.

Graph the line of the equation $y-3=2(x+1)$ .

a)

b)

c)

d)

32.

Solve $-2\le-3x+10$ for x.

Select the graph that matches your solution.

a)

b)

c)

d)

33.

Given the system of equations compare their key characteristics to determine the type of solution.

Line 1: slope=3 y-intercept= -2

Line 2: 4x + 3y = 12

a)

The slopes and y-intercepts are both different. The system will create intersecting lines and therefore have one solution

b)

The slopes and y-intercepts are both the same. The system will create one line and therefore infinite number of solutions.

c)

The slopes are the same and the y-intercepts are different. The system will create parallel lines and therefore have no solutions.

d)

The slopes and y-intercepts are both different. The system will create intersecting lines and therefore have no solutions.

34.

The scatter plot shows babies’ ages and their weights. The y-intercept of the linear model shows that

a)

babies weigh about 2 lbs at birth

b)

babies weigh about 8 lbs at birth

c)

each baby gains about 2 lbs per month

d)

each baby gains about 8 lbs per month

35.

The value in dollars, v(x), of a certain car after x years is represented by the equation $v(x)=25,000(0.86)^x$ .

To the nearest dollar, how much more is the car worth after 2 years than after 3 years?

a)

2589

b)

6510

c)

15901

d)

18490

36.

Which statement is true based off the graph.

a)

10 minutes costs $20 for both companies.

b)

20 minutes costs $10 for both companies.

c)

Company Z is cheaper for minutes less than 10.

d)

Company S is more expensive for less than 10.

37.

Which sets of ordered pairs represent a function? Select all that apply.

a)

{(1, 0), (2, 1), (2, 3)}

b)

{(1, 3), (1, 4), (1, 5)}

c)

{(1, 5), (2, 5), (3, 5)}

d)

{(3, 1), (2, 2), (3, 3)}

e)

{(3, 2), (5, 1), (4, 0)}

38.

What is the range of the function graphed below?

a)

[-1, 6]

b)

(-1, 6)

c)

[-3, 2]

d)

(-3, 2)

39.

What is the complete factorization of $25x^2-36$ ?

a)

(5x + 6)(5x + 6)

b)

(5x - 6)(5x - 6)

c)

(5x + 6)(5x - 6)

d)

(6x + 5)(6x - 5)

40.

The table shows the time students spent practicing the day before the 100 meter sprint and the finishing time for the sprint.

a)

The correlation coefficient is 0.09, which suggests a weak positive correlation between the variables.

b)

The correlation coefficient is -0.99, which suggests a strong negative correlation between the variables.

c)

The correlation coefficient is 0.99, which suggests a strong positive correlation between the variables.

d)

The correlation coefficient is -0.01, which suggests a weak negative correlation between the variables.

41.

Look at the two expressions:

Expression 1: 3(y + 4)

Expression 2: 3y + 4

Which of the following statement is true?

a)

For any value of y the expressions are equivalent.

b)

The expressions are equivalent because both expressions have a value of 4 when y = 0.

c)

The expressions are not equivalent because they only have the same value when y = 0.

d)

For any value of y the expressions are not equivalent.

42.

For an algebra class, all students took a unit 5 test. The score and the amount of hours they studied are contained on the graph below. Each letter represents a student. If a student scores a 63 on test approximately how long did they study for?

a)

6 hours

b)

4.5 hours

c)

30 minutes

d)

3.5 hours

43.

Xander is solving the function below using the quadratic formula. His solution method is recorded below. Identify the step in which Xander made an error and then correct the mistake.

Given: $2x^2-13x-24=0$

Step 1: $\frac{13\pm\sqrt[]{\left(-13\right)^2-4\left(2\right)\left(-24\right)}}{2\left(2\right)}$

Step 2: $\frac{13\pm\sqrt{23}}{2\left(2\right)}$

Step 3: $\frac{13\pm\sqrt[]{23}}{4}$

a)

Step 1: 13 should be negative outside the square root.

b)

Step 1: 13 should be positive. The discriminant should be 361.

c)

Step 2: The discriminant should be 361.

d)

Xander did not make an error. The solution is correct.

44.

A student is factoring the problem 2n² + n – 15. The student has begun the factoring process and has gotten 2n(n + 3) – 5(n + 3). What is the final result that the student got when factoring the problem?

a)

(n – 3)(2n + 5)

b)

(n + 3)(2n + 5)

c)

(n + 3)(2n – 5)

d)

cannot be factored

45.

The graph of a quadratic function is shown below. An equation that represents the function could be:

a)

$q(x)=\frac{1}{2}(x+15)^2-25$

b)

$q(x)=-\frac{1}{2}(x+15)^2-25$

c)

$q(x)=\frac{1}{2}(x-15)^2+25$

d)

$q(x)=-\frac{1}{2}(x-15)^2+25$

46.

Using the table below, determine what type of function is represented.

a)

A. Linear

b)

B. Quadratic

c)

C. Exponential

d)

D. None

47.

A student tried to multiply two binomials. Their work is shown below:

Step 1: $(2x-3)(x-2)$

Step 2: $2x^2-4x-3x-6$

Step 3: $2x^2-7x-6$

In which step did the student make the first error?

a)

A. Step 1

b)

B. Step 2

c)

C. Step 3

48.

Solve P = 2(l + w) for l.

a)

$l=\frac{P}{2}+w$

b)

$l=\frac{P}{2}-w$

c)

$l=\frac{P-w}{2}$

d)

$l=\frac{P-w}{2}$

49.

Does the system of equations:

y = 3/2 x + 2

-2x + 3y = 6

have no solution, one solution, or infinitely many solutions?

a)

A) No solution

b)

B) One solution

c)

C) Infinitely many solutions

50.

Solve the system of equations.

a)

(10, 3)

b)

(6, 3)

c)

(15, 3)

d)

No solution

e)

Infinite Solution

51.

What is the solution to this system?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

52.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

53.

The table shows the values of an exponential function.

Select ALL true statements about the function modeled by the values shown in the table.

a)

The y-intercept of the functions is 2

b)

The x-intercept of the function is -5

c)

The function is decreasing in its domain

d)

The vertical asymptote of the function is x = 1.5

e)

The horizontal asymptote of the function is y = 0

54.

Identify the key features of the following quadratic function.

$f\left(x\right)=2\left(x-3\right)^2+5$

a)

The axis of symmetry is x = 3, the vertex is (3, 5), the function has a maximum value of 5.

b)

The axis of symmetry is x = -3, the vertex is (-3, 5), the function has a minimum value of 5.

c)

The axis of symmetry is x = 3, the vertex is (3, 5), the function has a minimum value of 5.

d)

The axis of symmetry is x = -3, the vertex is (-3, 5), the function has a maximum value of 5.

55.

Given $f\left(x\right)=x^3-2x^2-x$ what is f(-4)?

a)

-100

b)

-92

c)

-44

d)

-36

56.

Which equations represent a line that passes through the point (3, -1) and has a slope of 2.

Select ALL that apply.

a)

$y=2x-7$

b)

$y=2x+5$

c)

$2x-y=7$

d)

$y-1=2x+3$

e)

$y+1=2x-3$

57.

Choose the quadratic equation that has x-intercepts of $-\frac{1}{3}$ and $\frac{5}{2}$

a)

$f\left(x\right)=\left(x-3\right)\left(5x+2\right)$

b)

$f\left(x\right)=\left(x+3\right)\left(5x-2\right)$

c)

$f\left(x\right)=\left(3x-1\right)\left(2x+5\right)$

d)

$f\left(x\right)=\left(3x+1\right)\left(2x-5\right)$

58.

A coffee shop sells donuts for $2 and muffins for $3. On a very cold morning, the shop sold 10 more donuts than muffins and made $250. Which system of equations could be used to find the number of donuts, d, and muffins, m, that the shop sold that day?

a)

A

b)

B

c)

C

d)

D

Intermediate Algebra -- Practice EOC

Total questions: 58

Worksheet time: 38mins

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