A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03) x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

Each day after the first, the number of users is 3% greater than it was the day before.

The number of users increases by 3 each day.

The number of users increases by 103 each day.

Each day after the first, the number of users is 103% greater than it was the day before.

A quadratic expression is shown. x 2 - 100 Which statement best explains why the quadratic expression can be rewritten as (x + c)(x - c) for some integer value of c?

The quadratic expression is a difference of squares.

The quadratic expression does not have a linear term.

The coefficient of the x 2 term in the quadratic expression is 1.

The function $$f(x)=4(0.5)^x$$ gives the remaining amount, in grams, of a radioactive substance after the substance has been decaying for x minutes. What does the equation f(4) = 0.25 represent in this situation?

After decaying for 4 minutes, there is 0.25 gram of the substance remaining.

After decaying for 15 seconds, there are 4 grams of the substance remaining.

After decaying for 25 seconds, there are 4 grams of the substance remaining.

After decaying for 4 minutes, there is 0.25 of the original amount of the substance remaining.

Reggie carves and sells wooden sculptures online. He uses the function f(x) = 15x + 60 to determine the selling price, f(x), for a sculpture that took him x hours to make. Which statement explains the meaning of the value of f(7.5)?

The selling price of a sculpture that took Reggie 75 hours to make is $1,185.

The selling price of a sculpture that took Reggie 1 hour to make is $75.

The selling price of a sculpture that took Reggie 5 hours to make is $75.

The selling price of a sculpture that took Reggie 5 hours to make is $135.

Which situation can be modeled by an exponential function?

The population of a town increases by 3% each year.

The pay for an employee is $12.25 an hour plus 5% sales commission.

The number of gallons of water in a tank decreases by 52 gallons each day.

Victoria and Roberto are climbing stairs in a tall building to raise money for charity. They are raising money together as a team. Victoria and Roberto receive donations differently. - Victoria receives donations from people who give a fixed amount for each flight of stairs she climbs. - Roberto receives donations from people who give a fixed amount regardless of how many flights of stairs he climbs. Victoria and Roberto write an equation to represent the total amount of money their team raises, y, based on the number of flights of stairs Victoria climbs, x. Which statement best describes the equation Victoria and Roberto write?

The equation is linear because the amount Victoria and Roberto raise increases at a constant rate for each additional flight of stairs Victoria climbs.

The equation is linear because Victoria and Roberto raise some money that does not depend on how many flights of stairs Victoria climbs.

The equation is exponential because only part of the money that Victoria and Roberto raise depends on how many flights of stairs Victoria climbs.

The equation is exponential because the amount of money Victoria and Roberto raise for climbing each flight of stairs increases the more Victoria climbs.

Which of the following situations is best represented by a linear function?

The amount Jeremy tips at a restaurant is a function of the total bill. He tips 15% of the total bill.

The area of a square is a function of the length of the side of the square.

The distance a ball travels after being dropped is a function of acceleration and time. The distance is one-half of the acceleration multiplied by the square of the time.

The length of the side of a rectangle with an area of 48 is a function of the width of the rectangle.

Population A is 800. It grows by 5% each month. Population B is 500. It grows by 20 each month. Which set of statements correctly describes the growth of both populations?

B. Population A is exponential. Population B is linear.

A. Population A is linear. Population B is exponential.

C. Population A is exponential. Population B is exponential.

D. Population A is linear. Population B is linear.

The table shows some values for a linear function. A second linear function passes the y-axis at the point (0,4) and has a slope of $$\frac{1}{4}$$ . Where do the two functions intersect?

The two functions do not intersect.

The height (h), in meters, of an item in d days can be modeled using the equation $$h=3(\frac{5}{4})^d$$ . What does the fraction $$\frac{5}{4}$$ represent in this equation?

The height of the object is multiplied by $$\frac{5}{4}$$ each day.

The final height of the object is $$\frac{5}{4}$$ meters.

The starting height of the object is $$\frac{5}{4}$$ meters.

The height of the object increases by $$\frac{5}{4}$$ meters each day.

Larry’s Dairy sells butter to local grocery. The equation y = 2.4x can be used to model the relationship between the value of butter and the weight of the butter they sell. They can sell any amount of butter, up to 30 pounds. Which statement is true?

The equation has infinite solutions.

The equation has 2.4 solutions.

Two linear functions are created. The first linear function is represented by the graph shown. The second linear function has the equation y = 2x - 6. Which statement best describes the difference between the values of the two functions at x = 8?

The value of the second linear function is 4 greater than the value of the first linear function.

The value of the first linear function is 1 greater than the value of the second linear function.

The value of the first linear function is 14 greater than the value of the second linear function.

The value of the second linear function is 10 greater than the value of the first linear function.

A store is open from 10 a.m. to 6 p.m. At noon, the manager of the store begins tracking the total sales for the day. The graph models the linear relationship between the total sales, y, in dollars, and the number of hours, x, after noon. Which statement best describes the y-intercept of the graph?

The total sales at noon are $400.

The total sales are measured for 6 hours.

The total sales have a maximum of $1,600.

The total sales increase by $200 per hour.

The owner of an electronics store conducts a voluntary survey. The store owner notices that there is a linear relationship between the number of customers that enter the store, x, and the number of surveys taken, y. Which best represents the domain of the relationship?

C {1, 5, 9, 13, 17, 21, 25, 29, 33}

Algebra 1 Practice EOC

Quiz

•

Mathematics

•

9th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF.LE.B.5, HSA-REI.B.4B, HSA.REI.D.12

+20

Standards-aligned

Beth-Ann Reeves

Used 17+ times

FREE Resource

44 questions

Show all answers

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

V = d - m

V = dm

Answer explanation

To find the volume (V) from the density (d) and mass (m), rearrange the equation d = m/V. Multiplying both sides by V gives dV = m, then dividing by d results in V = m/d. Thus, the correct equation is V = m/d.

Tags

CCSS.HSA.CED.A.4

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Emilio is given the triangle shown below. Emilio represents the perimeter of the triangle with the equation (5w - 13) + (2w + 6) + 2(5w + 15) = P, where P is the perimeter of the triangle. Which equation is correctly solved for w?

Answer explanation

To solve for w, first simplify the perimeter equation: (5w - 13) + (2w + 6) + 2(5w + 15) = P. This simplifies to 17w + 7 = P. Rearranging gives w = (P - 7)/17. The correct choice is w = (P - 23)/17.

Tags

CCSS.7.EE.B.4A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Kaylee is building a rectangular enclosure with an area of 90 square yards. She wants the length of the enclosed area to be 6 yards longer than the width, x. To represent this, she writes the equation x² + 6x = 90. She then completes the square to help solve her equation for x. Which equation is equivalent to Kaylee’s equation after she completes the square?

(x + 3)² = 93

(x + 3)² = 99

(x + 6)² = 96

(x + 6)² = 126

Answer explanation

To complete the square for the equation x² + 6x = 90, we add (6/2)² = 9 to both sides, resulting in (x + 3)² = 99. Thus, the correct choice is (x + 3)² = 99.

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Amil is given the equation shown. x² + 14x + 37 = 0. He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

(x + 7)² - 12 = 0

(x - 7)² - 12 = 0

(x + 7)² + 12 = 0

(x - 7)²+ 12 = 0

Answer explanation

To complete the square for the equation x² + 14x + 37 = 0, we rewrite it as (x + 7)²= 0 by adding and subtracting 49. Thus, the equivalent equation is (x + 7)² = 0.

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Answer explanation

The inequality y > -2/3x + 2 represents a region above the line y = -2/3x + 2. The correct graph will show a dashed line (indicating 'greater than') and shade the area above this line.

Tags

CCSS.HSA.REI.D.12

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which graph represents the solutions to 5x – 2y ≥ 10?

Answer explanation

To solve 5x – 2y ≥ 10, rearrange to y ≤ (5/2)x - 5. Graph A correctly shows the shaded area below the line y = (5/2)x - 5, indicating all solutions satisfying the inequality.

Tags

CCSS.HSA.REI.D.12

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Mark hits a tennis ball into the air. He uses the equation shown to approximate the height, h, in feet, of the ball t seconds after he hits it. h = -16t² + 88t + 4 What does the 4 represent in Mark’s equation?

The ball was in the air for a total of 4 seconds.

The ball landed 4 feet away from where Mark hit it.

The ball was 4 feet above the ground when Mark hit it.

The ball reached its maximum height 4 seconds after Mark hit it.

Answer explanation

In the equation h = -16t² + 88t + 4, the constant 4 represents the initial height of the ball when Mark hits it, meaning the ball was 4 feet above the ground at that moment.

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Algebra 1 Practice EOC

44 questions

To find the volume (V) from the density (d) and mass (m), rearrange the equation d = m/V. Multiplying both sides by V gives dV = m, then dividing by d results in V = m/d. Thus, the correct equation is V = m/d.

Emilio is given the triangle shown below. Emilio represents the perimeter of the triangle with the equation (5w - 13) + (2w + 6) + 2(5w + 15) = P, where P is the perimeter of the triangle. Which equation is correctly solved for w?

To solve for w, first simplify the perimeter equation: (5w - 13) + (2w + 6) + 2(5w + 15) = P. This simplifies to 17w + 7 = P. Rearranging gives w = (P - 7)/17. The correct choice is w = (P - 23)/17.

To complete the square for the equation x² + 6x = 90, we add (6/2)² = 9 to both sides, resulting in (x + 3)² = 99. Thus, the correct choice is (x + 3)² = 99.

Amil is given the equation shown. x² + 14x + 37 = 0. He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

To complete the square for the equation x² + 14x + 37 = 0, we rewrite it as (x + 7)²= 0 by adding and subtracting 49. Thus, the equivalent equation is (x + 7)² = 0.

The inequality y > -2/3x + 2 represents a region above the line y = -2/3x + 2. The correct graph will show a dashed line (indicating 'greater than') and shade the area above this line.

Which graph represents the solutions to 5x – 2y ≥ 10?

To solve 5x – 2y ≥ 10, rearrange to y ≤ (5/2)x - 5. Graph A correctly shows the shaded area below the line y = (5/2)x - 5, indicating all solutions satisfying the inequality.

Mark hits a tennis ball into the air. He uses the equation shown to approximate the height, h, in feet, of the ball t seconds after he hits it. h = -16t² + 88t + 4 What does the 4 represent in Mark’s equation?

In the equation h = -16t² + 88t + 4, the constant 4 represents the initial height of the ball when Mark hits it, meaning the ball was 4 feet above the ground at that moment.

A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03)^x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

In the equation, 1.03 indicates that each day, the number of users increases by 3% compared to the previous day. This means the user count grows by a factor of 1.03 daily.

A quadratic expression is shown. x² - 100 Which statement best explains why the quadratic expression can be rewritten as (x + c)(x - c) for some integer value of c?

The quadratic expression x² - 100 can be rewritten as (x + c)(x - c) because it is a difference of squares, where c is 10. This form arises from the identity a² - b² = (a + b)(a - b).

The expression x⁴ + 6x² + 9 can be rewritten as (x² + 3)². However, it is also equivalent to (x + 3)⁴when expanded. Thus, the correct choice is (x + 3)⁴.

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Algebra 1 Practice EOC

44 questions

To find the volume (V) from the density (d) and mass (m), rearrange the equation d = m/V. Multiplying both sides by V gives dV = m, then dividing by d results in V = m/d. Thus, the correct equation is V = m/d.

Emilio is given the triangle shown below. Emilio represents the perimeter of the triangle with the equation (5w - 13) + (2w + 6) + 2(5w + 15) = P, where P is the perimeter of the triangle. Which equation is correctly solved for w?

To solve for w, first simplify the perimeter equation: (5w - 13) + (2w + 6) + 2(5w + 15) = P. This simplifies to 17w + 7 = P. Rearranging gives w = (P - 7)/17. The correct choice is w = (P - 23)/17.

To complete the square for the equation x2 + 6x = 90, we add (6/2)2 = 9 to both sides, resulting in (x + 3)2 = 99. Thus, the correct choice is (x + 3)2 = 99.

Amil is given the equation shown. x2 + 14x + 37 = 0. He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

To complete the square for the equation x2 + 14x + 37 = 0, we rewrite it as (x + 7)2 = 0 by adding and subtracting 49. Thus, the equivalent equation is (x + 7)2 = 0.

The inequality y > -2/3x + 2 represents a region above the line y = -2/3x + 2. The correct graph will show a dashed line (indicating 'greater than') and shade the area above this line.

Which graph represents the solutions to 5x – 2y ≥ 10?

To solve 5x – 2y ≥ 10, rearrange to y ≤ (5/2)x - 5. Graph A correctly shows the shaded area below the line y = (5/2)x - 5, indicating all solutions satisfying the inequality.

Mark hits a tennis ball into the air. He uses the equation shown to approximate the height, h, in feet, of the ball t seconds after he hits it. h = -16t² + 88t + 4 What does the 4 represent in Mark’s equation?

In the equation h = -16t² + 88t + 4, the constant 4 represents the initial height of the ball when Mark hits it, meaning the ball was 4 feet above the ground at that moment.

A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03)x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

In the equation, 1.03 indicates that each day, the number of users increases by 3% compared to the previous day. This means the user count grows by a factor of 1.03 daily.

A quadratic expression is shown. x2 - 100 Which statement best explains why the quadratic expression can be rewritten as (x + c)(x - c) for some integer value of c?

The quadratic expression x2 - 100 can be rewritten as (x + c)(x - c) because it is a difference of squares, where c is 10. This form arises from the identity a2 - b2 = (a + b)(a - b).

The expression x4 + 6x2 + 9 can be rewritten as (x2 + 3)2. However, it is also equivalent to (x + 3)4 when expanded. Thus, the correct choice is (x + 3)4.

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Discover more resources for Mathematics

To complete the square for the equation x² + 6x = 90, we add (6/2)² = 9 to both sides, resulting in (x + 3)² = 99. Thus, the correct choice is (x + 3)² = 99.

Amil is given the equation shown. x² + 14x + 37 = 0. He completes the square and rewrites the given equation. Which equation is equivalent to the given equation?

To complete the square for the equation x² + 14x + 37 = 0, we rewrite it as (x + 7)²= 0 by adding and subtracting 49. Thus, the equivalent equation is (x + 7)² = 0.

A website tracks the number of users it has at the end of each of its first 30 days since going online. The equation y = 15(1.03)^x shows the relationship between the number of days since the website went online, x, and the number of users it has, y. What does 1.03 represent in the equation?

A quadratic expression is shown. x² - 100 Which statement best explains why the quadratic expression can be rewritten as (x + c)(x - c) for some integer value of c?

The quadratic expression x² - 100 can be rewritten as (x + c)(x - c) because it is a difference of squares, where c is 10. This form arises from the identity a² - b² = (a + b)(a - b).

The expression x⁴ + 6x² + 9 can be rewritten as (x² + 3)². However, it is also equivalent to (x + 3)⁴when expanded. Thus, the correct choice is (x + 3)⁴.