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Spring MAT 140 Worksheets for Mathematics Course - Prof. Dubravko Ivansic, Exams of Algebra

Murray State UniversityAlgebra
Prof. Dubravko Ivansic

A series of worksheets for the spring 2006 mat 140 mathematics course, covering topics such as number systems, algebraic expressions, inequalities, functions, and logarithms. Each worksheet includes a set of problems with instructions for students to show their work and find solutions.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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koofers-user-8eg ๐Ÿ‡บ๐Ÿ‡ธ

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Spring โ€™06/MAT 140/Worksheet 1 Name: Show all your work.
1. (4pts) Write two examples of each kind of number:
natural integer rational irrational
2. (12pts) Simplify:
a) 3 โˆ’ยต4ยท2+4ยท2
3ยถ=
b) 3
20 โˆ’7
15 =
c)
3
14
18
7
=
d) (โˆ’4)3=
e) โˆ’2โˆ’4=
f) p(โˆ’5)2=
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14

Partial preview of the text

Download Spring MAT 140 Worksheets for Mathematics Course - Prof. Dubravko Ivansic and more Exams Algebra in PDF only on Docsity!

Spring โ€™06/MAT 140/Worksheet 1 Name: Show all your work.

  1. (4pts) Write two examples of each kind of number:

natural integer rational irrational

  1. (12pts) Simplify:

a) 3 โˆ’

b)

c)

d) (โˆ’4)^3 =

e) โˆ’ 2 โˆ’^4 =

f)

(โˆ’5)^2 =

  1. (2pts) Draw the numbers โˆ’5 an 4 on the number line and find the distance between them.
  2. (8pts) Simplify and write the answer so all exponents are positive:

a)

(2x)^2 (x^3 y)^4 x^5 (4y)^3

b)

3 xโˆ’^3 (5y)^2 (5xโˆ’^2 y^3 )^4

  1. (2pts) Convert to scientific notation:

34745 = 0 .000000893 =

  1. (2pts) Convert to a decimal number:

  2. 486 ร— 107 = 2. 5417 ร— 10 โˆ’^3 =

  1. (8pts) Factor the following. Use either a known formula or a factoring method.

a) x^2 โˆ’ 2 x โˆ’ 35 =

b) 6x^2 โˆ’ 7 x โˆ’ 10 =

c) x^3 + 125 =

  1. (8pts) Simplify.

a)

x + 1 x^2 โˆ’ 64

2 x โˆ’ 3 x^2 + 7x โˆ’ 8

b)

3 x x^2 โˆ’ 4 x + 1 x + 2

Spring โ€™06/MAT 140/Worksheet 3 Name: Show all your work.

  1. (6pts) Let A = (2, โˆ’3), B = (7, 2), C = (1, 1). a) Find the distance between A and the midpoint of B and C. b) Is the triangle ABC a right triangle?
  2. (6pts) Use your calculator to sketch the graph of y = x^4 โˆ’ 3 x^3 + 5x โˆ’ 17. Make sure all the features of the graph are visible and indicate your viewing window. Find the all the x-intercepts and the y-intercept to two decimal places.

Spring โ€™06/MAT 140/Worksheet 4 Name: Show all your work.

  1. (15pts) Solve the following quadratic equations:

2 x^2 โˆ’ 39 = 11 x^2 + 2x = 24

18 x^2 โˆ’ x = 8x + 2 2 x^2 โˆ’ 8 x = x^2 + 6x โˆ’ 3

  1. (8pts) Solve the following equations:

| 3 x โˆ’ 1 | = 7 x + 2 =

5 x + 24

  1. (7pts) You have a rectangular plot of length 7 feet and width 4 feet and would like to enlarge it so its area is 35 square feet. To this end, you increase the length by x feet and increase the width by 2x feet. By how much did you need to increase the length and width of the rectangle to achieve the desired area?
  1. (5pts) Let A = (2, โˆ’3), B = (7, 2), C = (1, 1). Without using the Pythagorean theorem, determine whether the triangle ABC is a right triangle. (Hint: check for perpendicular lines.)
  2. (5pts) The line 3x + 2y = 5 is given. a) Find the equation of the line that passes through (3, 2) and is parallel to the given line. b) Sketch the picture.
  3. (5pts) Find the equation of the circle whose diameter is the line segment connecting (โˆ’ 1 , 3) and (5, โˆ’3). Draw the picture.

Spring โ€™06/MAT 140/Worksheet 6 Name: Show all your work.

  1. (6pts) Let f be given by f (x) =

3 x โˆ’ 5 x^2 + 3x

. Find the f (3), f (โˆ’x), f (x + 2) and (Simplify

where possible).

  1. (4pts) Find the domain of f (x) =

x + 1 x + 2x โˆ’ 15

  1. (10pts) Use the graph of the function f at right to answer the following questions.

a) What is the domain of f?

b) What is the range of f?

c) Find f (โˆ’4) and f (2).

d) List the x-intercepts of the graph.

e) Where is the function decreasing?

f) What are the solutions of the equation f (x) = 2?

g) For which x is f (x) > 0?

Spring โ€™06/MAT 140/Worksheet 7 Name: Show all your work.

  1. (6pts) Suppose a cab company charges $2.50 per ride plus 55 cents for every mile traveled. a) Write the linear function that expresses the cost of a ride as a function of miles traveled. b) What is the cost of a ride that takes you 13 miles? c) What is the farthest you can reach with $20 in your pocket?
  2. (6pts) In an effort to relate a childโ€™s height H to their head circumference C, a pedia- trician has measured nine children. a) Draw the scatterplot of the data on paper. Does the relationship look linear? b) Use the calculator to find the โ€œline of best fitโ€ to the data. Draw the line on paper. c) What does the equation from b) predict about the head circumference of a child whose height is 26in?

H C 25.25 16. 25.75 16. 25 16. 27.75 17. 26.5 17. 27 17. 26.75 17. 26.75 17. 27.5 17.

  1. (4pts) Use the basic graph of y =

x and transformations to help you sketch the graph of y = 2

x + 3. Explain how you transform the original graph.

  1. (8pts) The graph of the function f is given below. On three separate graphs, sketch the graphs of the functions f (x โˆ’ 1), 12 f (x) and f (โˆ’x) + 3. Label all the relevant points.
  2. (6pts) The function f is given below. a) Sketch the graph of f. b) Find the domain and range of f.

f (x) =

โˆ’ 3 x + 2, if โˆ’ 5 โ‰ค x < 2 โˆ’x + 7, if 2 โ‰ค x < 6.

  1. (11pts) Consider the rational function Q(x) = 2 x^2 โˆ’ 5 x^2 โˆ’ x โˆ’ 12 . Answer the following (decimal

answers should have accuracy to two decimal places). a) Find the domain of the function and where the vertical asymptotes are. b) Find the x-intercepts of the graph and the y-intercept. c) Find the horizontal asymptote, if any. d) Sketch the graph of the function on paper. Make sure scale is marked and all features you found in a)-c) are indicated. e) Find the intervals where the function is decreasing.

Spring โ€™06/MAT 140/Worksheet 9 Name: Show all your work.

  1. (5pts) The table gives values of f and g for some xโ€™s. Find the following:

x 1 2 3 4 f (x) 1 3 4 2 g(x) 4 3 1 2

f โˆ’^1 (3) =

gโˆ’^1 (2) =

(f โ—ฆ gโˆ’^1 )(1) =

(gโˆ’^1 โ—ฆ f โˆ’^1 )(3) =

  1. (4pts) The graph of a function f is given. Use it to find the graph of f โˆ’^1 , la- beling the relevant points.
  2. (5pts) Let f (x) =

4 x 3 x โˆ’ 2

a) Find f โˆ’^1 (x). b) Find the domain and range of f โˆ’^1.

Spring โ€™06/MAT 140/Worksheet 10 Name: Show all your work.

  1. (4pts) Evaluate without using the calculator:

log 3 81 = log 7 491 = log 5 8

53 = loga 3

a =

  1. (7pts) Solve the equations:

log 4 x = 5 ln x = 7

103 xโˆ’^1 = 32 log 2 (2x + 8) = 5

  1. (4pts) If A represents the area of a wound, then normal healing of a wound that is 120mm^2 in size is represented by A = 120eโˆ’^0.^35 t, where t is the number of days following the injury. How long is it before the wound is 1/3 of the original size?
  1. (5pts) Write as a sum and/or difference of logarithms. Express powers as factors. Simplify if possible.

log 3

x^7 โˆš x โˆ’ 1

ln(ex(ex^ โˆ’ 4)^5 ) =

  1. (6pts) Write each the following as a single logarithm. Simplify if possible.

1 3 log^ v

(^6) + 2 log v (^2) =

ln(x^2 โˆ’ x + 2) โˆ’ 2 ln(x + 1) =

  1. (4pts) Solve the equation:

3 x+1^ = 7^2 xโˆ’^3