Math 107 Quiz 2 - Foundations of Mathematics: Problems and Solutions

This document presents the complete solutions for Math 107 Quiz 2, a comprehensive assessment in Foundations of Mathematics. The quiz consists of 30 problems, each worth 4 points, covering a range of mathematical concepts. The solutions include detailed explanations and answers for questions involving finding the slope of a line, solving systems of equations, determining the center and radius of a circle, identifying perpendicular lines, working with linear functions, interpreting scatter plots and trend lines, graphing equations, finding equations of graphs, calculating slopes, using point-slope equations, graphing absolute value functions, evaluating functions, determining equations of circles, applying the Pythagorean theorem, finding slopes between points, calculating slopes of roofs, determining parallel and perpendicular lines, solving inequalities, solving quadratic equations, and solving for variables in various expressions. This resource is designed to aid students in understanding and mastering the key concepts covered in the quiz.

Math 107 Quiz 2 – Each question is worth 4 points for a total of 120 points.
Quiz 2: Instructions:
 The quiz is worth 120 points. There are 30 problems, each worth 4 points. Your score
on the quiz will be converted to a percentage and posted in your assignment folder with
comments.
 This quiz is open book and open notes, and you may take as long as you like on it
provided that you submit the quiz no later than the due date posted in our course schedule
of the syllabus. You may refer to your textbook, notes, and online classroom materials,
but you may not consult anyone.
 Please type your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is also acceptable. Be sure to include your name in
the document. Please make your responses easy to see.
There are 30 problems with each problem being worth 4 points. A total of 120 points.
1. Given the points (-6, 1) and (2, 4) find the slope of the line that connects these points
a) -3/8
b) 8/3
c) -4/3
d) 3/8
e) -5/4
SOLUTION: (d) 3/8
2. Solve the system
a) The value of y = -5
b) The value of y is 30
c) The value of y is 5
d) The value of y is -10

SOLUTION: (b) the value of y is 30
3. Find the center and radius of the circle given this equation:
(x – 1)² + (y – 5)² = 36
Center = ______________ and Radius = _________________
SOLUTION: Center: (1, 5) and radius: 6
4. Given the equations of the lines
(I) 2y + 3x = 3
(II) -3y - 2x = 5
(III) -6y + 4x = 9,
(IV) 2y + 6x = 9
which two lines are perpendicular?
A) (I) and (II)
B) (II) and (III)
C) (III) and (IV)
D) (I) and (III)
E) (IV) and (II)
SOLUTION: (D) (I) and (III)
5. If f(x) is a linear function such that f(-1) = 11 and f(2) = 5,
then f(0) =
A) 5
B) 6
C) 7
D) 8
E) 9
SOLUTION: (E) 9

6. The scatter plot below shows the weights in ounces of several kittens at various ages. What is
the best equation of the trend line through these points?
A) y = 10x
B) y = 4x
C) y = 1/4x + 10
D) y = 4x + 10
SOLUTION: (D) y = 4x + 10
7. What is the graph of the equation 5x – 2y = 6?
A)
B)

C)
D)
SOLUTION: (D)
8. What is the equation of the graph?
A) y = -|x| - 5
B) y = -|x -5|
C) y = |x + 5|
D) y = |x - 5|
SOLUTION: (C) y = |x + 5|
9. What is the slope of the line through the points P(–5, –6) and Q(–12, 5)?
A) -11/7

B) 17/11
C) - 11/17
D) 11/17
SOLUTION: (A) -11/7
10. What is the point-slope equation of the line through the point (–5, 5) that is perpendicular to
the line whose equation is 5x = 3y?
A) y – 5 = 5/3(x + 5)
B) y – 5 = -3/5(x + 5)
C) y – 5 = 3/5(x + 5)
D) y – 5 = -5/3(x + 5)
SOLUTION: (B) y – 5 = -3/5(x + 5)
11. What is the graph of y = |3x + 6|?
A)
B)

C)
D)
SOLUTION: (D)
12. Find f(–5) if f(x) = –8x – 1
A) 39
B) -41
C) -39
D) 12
SOLUTION: (A)
13. Evaluate the following functions: Given f(x) = 3x + 20, find f(- 4)
SOLUTION: f(- 4)=8
14. What is the equation of a circle of radius 6 units centered at (3, 2)?
A. x2 + y2 + 6x – 4y = 23
B. x2 + y2 - 6x + 4y = 23

C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x – 4y = - 23
E. x2 + y2 - 6x – 4y = 23
SOLUTION: (E) x2 + y2 - 6x – 4y = 23
15. If you have a right triangle that has one leg being 21 units and the other leg being 72 units,
what would be the number of units for the hypotenuse?
SOLUTION: 75 units
16. What is the slope of the line that contains the given pairs of points (-11, 7) and (15, -3)?
SOLUTION: -5/13
17. What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of
the top floor to the top of the pitch and a length of 8.2 feet from the center to the edge of the
house?
SOLUTION: -8.54 ft.
18. Determine whether the graphs of the equations are parallel? y = 2x + 7 and 5y + 10x = 20
A) Yes
B) No
SOLUTION: (B) NO, It’s not parallel
19. Determine whether the graphs of the equations are perpendicular lines?
y = -8 + x and x – y = -1
A) Yes
B) No
SOLUTION: (B) NO, it’s not perpendicular
20. Determine whether the graphs of the equations are parallel, perpendicular or neither? 5y +
50 = 4x and 4y + 5x = 12

A) Parallel
B) Perpendicular
C) Neither
SOLUTION: (B) Perpendicular
21. Solve
a) x
5
b) x – 3
12
c) x² - 3
5x + 7
d) x + 3
5
SOLUTION: (C) X +3
5
22. Solve 4(x - 1) - (5x + 1) > 2x + 1
a)
b) x > -2
c) x < -2
d) x > -1
e) x < -1
SOLUTION: (C) x < -2

23.
a)
b)
c)
d)
SOLUTION: (A)
24. Solve for x: 3x2 - 5x > 2
a) x > 2 or x <
b)
c) or x < -2
d)
e)
SOLUTION: (A) x > 2 or x <

25. Solve
a)
b)
c)
d)
SOLUTION: (C)
26. Solve for x:
a) x = 3/2
b) x = 1/4
c) x = 1
d) x = 3
e) x = -1
SOLUTION: (C) x = 3
27. If x2 - 8x - 4 = - 5 then
a) x = -11, 19
b)
c)

d) No real roots.
SOLUTION: (C)
28. Solve for x:
a)
b)
c)
d)
e) None of these
SOLUTION: (C)
29. Which of the following correctly completes the problem?
Solve for x: 2(x – 1) + 3 = 5
a) x = 3
b) x = 3/2
c) x = 5
d) x = 2
SOLUTION: (D) x = 2
30. Which of the following expressions represents the product of two less than a number and
three more than twice the number?
a) 2x² - x - 6

b) -2x² + x + 6
c) 2x² + x – 6
d) 2x² - x + 3
e) -2x² + x – 3
SOLUTION: (A) 2x² - x - 6