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Prerequisite Material: Practice Exercises - Lecture Notes | MATH 116, Assignments of Algebra

University of Wisconsin (UW) - MilwaukeeAlgebra

Material Type: Assignment; Class: College Algebra; Subject: Mathematical Sciences; University: University of Wisconsin - Milwaukee; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 09/02/2009

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Math 116 Prerequisite Material
Practice Exercises
We summarize below that post-arithmetic material students need to be expert in
if they are to be successful in Math 116. If any of this material is unfamiliar to you,
the student, consult your instructor or the Math 116 coordinator, Professor Key,
during office hours for help in mastering this material. This is pre-requisite
material and its mastery will be presumed. This material will not be
covered during class meetings.
1 Respect for definitions
1. Define circle.
2. Define straight angle.
3. Define right angle.
4. Define square.
5. Define quadratic equation.
6. Define isosceles triangle.
7. Define right triangle.
8. Define hypotenuse.
2 Check your work!
In each case check the answer to see if it is correct or not.
1. x= 3 is a solution of 2x+ 4 = 3x+ 1.
2. x=โˆ’3 is a solution of x2+ 4 = โˆ’x+ 10.
3. x= 3 is a solution of x2+ 4 = โˆ’x+ 10.
4. x= 2, y= 1 is a solution of 2x+ 4y= 8, 3x+ 2y= 9.
5. x= 2, y= 1 is a solution of 2x+ 4y= 8, 3x+ 2y= 8.
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Download Prerequisite Material: Practice Exercises - Lecture Notes | MATH 116 and more Assignments Algebra in PDF only on Docsity!

Math 116 Prerequisite Material

Practice Exercises

We summarize below that post-arithmetic material students need to be expert in if they are to be successful in Math 116. If any of this material is unfamiliar to you, the student, consult your instructor or the Math 116 coordinator, Professor Key, during office hours for help in mastering this material. This is pre-requisite material and its mastery will be presumed. This material will not be covered during class meetings.

1 Respect for definitions

  1. Define circle.
  2. Define straight angle.
  3. Define right angle.
  4. Define square.
  5. Define quadratic equation.
  6. Define isosceles triangle.
  7. Define right triangle.
  8. Define hypotenuse.

2 Check your work!

In each case check the answer to see if it is correct or not.

  1. x = 3 is a solution of 2x + 4 = 3x + 1.
  2. x = โˆ’3 is a solution of x^2 + 4 = โˆ’x + 10.
  3. x = 3 is a solution of x^2 + 4 = โˆ’x + 10.
  4. x = 2, y = 1 is a solution of 2x + 4y = 8, 3x + 2y = 9.
  5. x = 2, y = 1 is a solution of 2x + 4y = 8, 3x + 2y = 8.

3 Some concepts from geometry

  1. A triangle has sides of length 5, 12 and 13. Is it a right triangle?
  2. A triangle has sides of length 7, 24 and 25. Is it a right triangle?
  3. Two sides of a triangle measure 3 and 5. What possible lengths can the third side have so that this is a right triangle?
  4. An equilateral triangle has side length 6. How long is its altitude? What is its area?
  5. The diameter of a circle is 6 units. How long is its radius?

4 Absolute value

  1. Which real numbers are 6 units from 0?
  2. Which real numbers are more that 5 units from 0?
  3. Which real numbers are negative and no more than 3 units from 0?
  4. Solve |x| = 6 for x.
  5. Solve |x| > 6 for x.
  6. Solve |x| โ‰ค 3 and x < 0 for x.
  7. Solve | 2 x โˆ’ 3 | < 8 for x.
  8. Solve | โˆ’ 3 x + 11| > 9 for x.

4.1 Quadrants

Identify the quadrant containing each point below, and give the distance from the point to the horizontal axis, to the vertical axis, and to (0, 0).

  1. (3, 4).
  2. (โˆ’ 3 , 13).
  3. (13, โˆ’12).
  4. (2, โˆ’9).
  5. (โˆ’ 3 , โˆ’8).
  6. (6, โˆ’8). Graph each triple of points, determine if they form the vertices of a triangle. If so, determine if the triangle is an isosceles triangle, an equilateral triangle or a right triangle.
  1. 3(x โˆ’ 2) + 6(y + 1) = 0, (โˆš 2 , โˆš5). Find a line perpendicular to the given line and passing through the given point:
  2. 2x + 4y = 3, (3, 5).
  3. 3(x โˆ’ 4) + 5(y โˆ’ 1) =, (2, 5).
  4. 3(x โˆ’ 2) + 6(y โˆ’ 1) = 2, (โˆ’ 3 , 2).
  5. โˆ’ 2 x + 4y = 3, (4, โˆ’5).
  6. 4x + 2y = 8, (โˆ’ 11 , โˆ’12).
  7. 3(x โˆ’ 2) + 6(y โˆ’ 1) = 2, (โˆš 2 , โˆš5).

6 Graphing absolute value equations

Graph each of the following equations.

  1. y = 3|x โˆ’ 2 | + 4.
  2. y = | 3 x โˆ’ 2 | + 4.
  3. y = โˆ’ 3 |x + 2| โˆ’ 4.
  4. y = 4|x + 7| + 2.
  5. x = 3|y โˆ’ 2 | + 4.
  6. x = โˆ’ 3 |y + 2| + 2.

7 Two factor patterns, completing the square, quadratic

formula

Factor the following into the product of two binomials.

  1. x^2 โˆ’ 4.
  2. 4x^2 โˆ’ 25.
  3. 9y^2 โˆ’ 16 w^2.
  4. 3x^2 โˆ’ 2.
  5. 9x^4 โˆ’ 16 s^6.
  6. x โˆ’ 1 assuming x โ‰ฅ 0. Factor each perfect square:
  7. x^2 + 4x + 4.
  1. x^2 โˆ’ 6 x + 9.
  2. x^2 + 2โˆš 2 x + 2.
  3. y^4 + 6y^2 + 9.
  4. x + 2โˆšx + 1.
  5. 4x^2 + 4x + 1. Complete the square in each expression. Example: x^2 + 2x + 2 = (x + 1)^2 + 1.
  6. x^2 + 4x = ยท ยท ยท.
  7. x^2 โˆ’ 4 x โˆ’ 1 = ยท ยท ยท.
  8. 9x^2 โˆ’ 4 x = ยท ยท ยท.
  9. x^2 + 3x + 2 = ยท ยท ยท.
  10. 3x^2 + 2x + 1 = ยท ยท ยท. Solve each of the following equations two ways: first by completing the square and second by using the quadratic formula. If there are no real solutions, state why this is the case.
  11. x^2 โˆ’ 4 x โˆ’ 2 = 0
  12. x^2 + 2x โˆ’ 1 = 0
  13. x^2 + 12x โˆ’ 4 = 0
  14. x^2 โˆ’ 12 x โˆ’ 4 = 0
  15. 3x^2 โˆ’ 12 x โˆ’ 4 = 0
  16. x^4 โˆ’ 12 x^2 โˆ’ 4 = 0

8 Graphing quadratic equations

Graph each of the following quadratic equations:

  1. y = x^2.
  2. y = x^2 + 2x + 1.
  3. y = x^2 + 2x + 2.
  4. y = 4x^2 + 4x + 2.
  5. y = x^2 โˆ’ 6 x โˆ’ 3.
  6. y = 3x^2 + 12x โˆ’ 4.