Question 1

Solve the problem.
-Find all points on the line through (-1, 7) and (15, -1) that lie between these two points and have integral coordinates.

Accepted Answer

A)  (1, 7), (4, 5), (7, 3), (10, 1), and (13,0) 
B)  (1, 6), (3, 5), (5, 4), (7, 3), (9, 2), (11, 1), and (13, 0) 
C)  (0, 5), (1, 4), (2, 3) (3, 2), (4, 1), (5, 2), (6, 3), and (7, 4) 
D)  (3, 5), (7, 3), (11, 1) and (14, 0)

Question 2

Solve the problem.
-A chemist makes a mixture of concentrated hydrochloric acid and distilled water so that the ratio of acid to water is 7 : 3. If he starts with 28 L of acid, how much water is mixed with the acid?

Accepted Answer

A)  12 L 
B)  35 L 
C)  23 L 
D)  49 L

Question 3

Solve the problem.
-A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 28 ounces of water. After it has been filling for 13
Seconds, the gauge indicates the bottle contains 68 ounces of water. Let w be the amount of water in the bottle t
Seconds after the faucet was turned on. Write a linear equation that models the amount of water in the bottle in
Terms of x.

Accepted Answer

A)  w = 5t + 55 
B)   
C)  w = -5t + 53 
D)  w = 5t + 3

Question 4

Solve the problem using your calculator.
-The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters). Use linear regression to find a linear function that predicts a plant's growth as a
Function of temperature.

Accepted Answer

A)  y = 14.6 + 0.211x 
B)  y = -14.6 - 0.211x 
C)  y = 7.30 + 0.122x 
D)  y = 7.30 - 0.112x

Question 5

Change the equation to slope-intercept form and identify the slope and y-intercept.
--3x + 6y = 14

Accepted Answer

A)   
B)   
C)   
D)

Question 6

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation.
-

Accepted Answer

A)  Identity, {all real numbers} 
B)   
C)  Conditional, {5} 
D)  Conditional, {-6}

Question 7

Use a graphing calculator to estimate the solution of the equation to two decimal places.
-5.93x - 425 = 0

Accepted Answer

A)  {0.02} 
B)  {71.73} 
C)  {0.01} 
D)  {71.67}

Question 8

Find the slope of the line described.
-A line parallel to 3x + 8y = -4

Accepted Answer

A)   
B)   
C)   
D)

Question 9

Solve the equation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Solve the equation.
-

Accepted Answer

A)  {-3} 
B)  {3} 
C)   
D)

Question 11

Graph the equation.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Solve the problem.
-A driver wants to gauge the fuel efficiency of her vehicle at speeds of 30 mph and above. She notices that traveling at an average speed of 45 mph results in a rating of 35 mpg, whereas, at an average speed of 60 mph,
Her car rates 25 mpg. Find an equation to model the gas mileage, m, as a function of average speed s mph.

Accepted Answer

A)   
B)   
C)   
D)

Question 13

Find the solutions to the equation by reading the graph.
-

Accepted Answer

A)  {12, 6} 
B)  {12} 
C)  {-2, 6, 12} 
D)  {-2, 6}

Question 14

Find the perfect square trinomial whose first two terms are given.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 15

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers.
-

Accepted Answer

A)  16 
B)  7 + 81i 
C)  88 
D)  7 - 81i

Question 16

Find the equation of the line through the given pair of points. Solve it for y if possible.
-(-7, -6), (-4, 9)

Accepted Answer

A)  y = 15x + 99 
B)  x = -7 
C)  y = 5x + 29 
D)  y = 3x + 15

Question 17

Use the method of your choice to find all real solutions of the equation.
- - 4 = 0

Accepted Answer

A)  {2, 0} 
B)   
C)   
D)

Question 18

Change the equation to slope-intercept form and identify the slope and y-intercept.
-3y - 5x = 7

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Write the standard equation for the circle.
-Center (3, 22), passing through the origin

Accepted Answer

A)   
B)   
C)   
D)

Question 20

Solve the problem.
-Your company uses the quadratic model  to represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 18?

Accepted Answer

A)  9864 units 
B)  6498 units 
C)  2736 units 
D)  6102 units

Exam 1: Equations, Inequalities, and Modeling

Solve the problem. -Find all points on the line through (-1, 7) and (15, -1) that lie between these two points and have integral coordinates.

Solve the problem. -A chemist makes a mixture of concentrated hydrochloric acid and distilled water so that the ratio of acid to water is 7 : 3. If he starts with 28 L of acid, how much water is mixed with the acid?

Solve the problem using your calculator. -The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters) . Use linear regression to find a linear function that predicts a plant's growth as a Function of temperature.

Change the equation to slope-intercept form and identify the slope and y-intercept. --3x + 6y = 14

Solve the equation. Identify the equation as an identity, an inconsistent equation, or a conditional equation. -

Use a graphing calculator to estimate the solution of the equation to two decimal places. -5.93x - 425 = 0

Find the slope of the line described. -A line parallel to 3x + 8y = -4

Solve the equation. -

Solve the equation. -

Graph the equation. -

Find the solutions to the equation by reading the graph. -

Find the perfect square trinomial whose first two terms are given. -

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. -

Find the equation of the line through the given pair of points. Solve it for y if possible. -(-7, -6) , (-4, 9)

Use the method of your choice to find all real solutions of the equation. - - 4 = 0

Change the equation to slope-intercept form and identify the slope and y-intercept. -3y - 5x = 7

Write the standard equation for the circle. -Center (3, 22) , passing through the origin

Solve the problem. -Your company uses the quadratic model to represent how many units (y) of a new product will be sold (x) weeks after its release . How many units can you expect to sell in week 18?