Alg2a

ALG 2A Algebra II, First Semester Box 42191, Lubbock, TX 79409 (806) 742-7200 FAX (806) 742-7222 www.ode.ttu.edu

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To the Student: After your registration is complete and your proctor has been approved, you may take the Credit by Examination for Algebra 2A. WHAT TO BRING • sharpened No. 2 pencils • graphing calculator • paper ABOUT THE EXAM The exam will consist of 40 questions. It is based on the Essential Knowledge and Skills for this subject. Since questions are not taken from any one source, you can prepare by reviewing any of the state-adopted textbooks that are used at your school. You must review all of the concepts of algebra. If you do not have a textbook or any other study material available locally, you may contact the Outreach & Distance Education Bookstore. The bookstore carries the textbook used with our Algebra 2A Distance Education course. The textbook is Glencoe Algebra II by Glencoe/McGraw-Hill (1998). There is also a sample examination included with this letter. The sample exam will give you a model of the types of questions that will be asked on your examination. It is not a duplicate of the actual examination. It is provided to illustrate the format of the exam, not to serve as a review sheet. The formulas included with the sample exam will also be provided with the CBE. For more information about CBE policies, visit http://www.ode.ttu.edu/takeacbe/ or see your course Policies & Forms Guide. Good luck on your examination!

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Preparing for the CBE For successful completion of the CBE, you should be able to do the following. • Use the order of operations to evaluate expressions • Use the properties of real numbers to simplify expressions • Find and use the mean, median, and mode to interpret data • Solve equations by using the properties of equality • Solve equations for specific variables • Solve equations containing absolute value • Solve inequalities and graph the solution sets • Solve compound inequalities using “and” and “or” • Solve inequalities involving absolute value and graph the solutions • State a relation’s domain, range and determine if it is a function • Find the value of functions for given elements of the domain • Identify equations that are linear and graph them • Write linear equations in standard form • Determine the slope of a line • Write and equation of a line in slope-intercept form given the slope and one or two points • Write an equation of a line that is parallel or perpendicular to the graph of a given line • Draw graphs or inequalities in two variables • Solve systems of equations by graphing • Use the substitution and elimination methods to solve systems of equations • Solve systems of equations by using Cramer’s rule • Solve systems of inequalities by graphing • Solve systems of three equations in three variables

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• Perform scalar multiplication on a matrix • Solve matrices for variables • Add, subtract, and multiply matrices • Add, subtract, multiply and divide polynomials (including synthetic division) • Represent numbers in scientific notation • Factor polynomials • Add, subtract, multiply, and divide radical expressions (including simplifying radicals) • Solve equations containing radicals You should review these subjects to prepare yourself for the exam.

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Sample CBE Exam 1. Simplify: 5 – 8 (3 – 6) ÷ 22 + 10 2. Simplify: 2a (5.4 – 4b) – 4a (3.1 + 8b) 3. Find the mean, median and mode of the following data: 66, 67, 68, 69, 70, 73, 74, 76, 78, 78, 84 4. Solve: 2(a –1) = 8a – 6 5. Solve for x: 3(x – 2) = y 6. Solve: |r + 14| = 23 7. Solve and graph: 3 – 4x ≤ 6x – 2 8. Solve: -2 ≤ x – 4 < 3 9. Solve: |3x + 7| ≥ 26 10. State the following relation’s domain and range and determine if it is a function: {(-5, 6), (-2, -4), (-1, -6), (2, 6)} 11. Find f (-3) if f (x) = x3 – 5. 12. Graph 2x + y = 11. 13. Write 2x – 6 = y + 8 in standard form. 14. Determine the slope of the line that passes through (-5, 3) and (7, 9). 15. Given the slope of a line is

3 and passes through (-6, 9), write the equation of the 4

line in slope-intercept form 16. Write the slope-intercept form of a line that passes through (1, 2) and is parallel to the graph of y = -3x + 7.

17. Graph x > y – 1. 18. Solve by graphing:

y+x=3 3x − y = 1

19. Solve by substitution or elimination method:

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x+ y =4 x − y = 8.5

20. Solve using Cramer’s rule:

21. Solve by graphing:

4 x + 7 y = −1 2x + y = 7

y−x≤2 .5 x + y ≥ −4 2x + y − z = 2

22. Solve the system: x + 3 y + 2 z = 1 x+ y+z =2 2 −3 23. Multiply: 4 4 1 0 3

24. Solve:

2x 32 + 6 y = 7−x y

25. Subtract: 2

8 −1 1 6 −3 − 2 −3 3 4

26. Multiply the following: (x4y 6) • (8x3y) 27. Write 31000 in scientific notion. 28. Subtract: (5x2 + 4x) – (3x2 + 6x – 7) 29. Divide (4x4 – x3 – 19x2 + 11x – 2) by (x – 2). 30. Factor: 4x3 – 6x2 + 10x – 15 31. Simplify:

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2187x14 y 35

32. Multiply: 6 5 32m3 • 5 5 1024m 2

33. Solve:

3x − 8 + 1 = 3

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Sample CBE Exam Answers

1. 21 2. -1.6a – 40ab 3. mean is 73, mode is 78; median is 73 4. a = 2/3 5. x =

y+6 3

6. r = 9 or r = -37 7. 1/2 ≤ x 8. 2 ≤ x < 7 9. x ≥

19 or x ≤ -11 3

10. domain is {-5, -2, -1, 2}; range is {6, -4, -6}; the relation is a function. 11. f (-3) = -32 12. Graph should have a negative slope; crossing the x-axis at 5.5 and the y-axis at 11. 13. 2x – y = 14 14. The slope is 1/2. 15. y = .75x + 13.5 16. y = -3x + 5 17. Graph should have a positive slope with a broken line crossing the x-axis at -1 and the y-axis at 1 and shaded below. 18. The solution is (1, 2). 19. x = 6.25 and y = -2.25 20. The solution is (5, -3). 21. See graph. 22. The solution is (2, -1, 1).

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23.

8 −12 16 4 0 12

24. The solution is (9.25, -2.25) 25.

13 −20 12 17

26. 8x7y7 27. 3.1 x 104 28. 2x2 – 2x + 7 29. 4x3 + 7x2 – 5x + 1 30. (2x2 + 5)(2x – 3) 31. 3x2y5 32. 240m 33. x = 4

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FORMULAS

Value of a Second Order Determinant:

a b = ad – bc c d

Cramer’s Rule: The solution to the system

e b f d ⎧ ax + by = e is (x, y), where x = ,y= ⎨ a b ⎩cx + dy = f c d

a e a b c f ≠0 , and a b c d c d

Scalar Multiplication of a Matrix:

⎡ a b c ⎤ ⎡ ka kb kc ⎤ k⎢ ⎥=⎢ ⎥ ⎣ d e f ⎦ ⎣ kd ke kf ⎦ Expansion of a Third-Order Determinant:

a b d e g h

c e f =a h i

f d −b i g

f d +c i g

e h

Area of Triangles: The area of a triangle having vertices at (a, b), (c, d), a b 1 1 c d 1 and (e, f) is |A|, where A = 2 e f 1 Negative Exponents: For any real number a, and any integer n, where a ≠ 0, 1 1 a − n = n and − n = a n a a Degree of a Constant: The degree of a constant is always zero Multiplying Powers: For any real number a and integers m and n, a m • a n = a m+ n Dividing Powers: For any real number a, except a = 0, and integers m and n, am = a m−n n a

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Properties of Powers:

Suppose m and n are integers and a and b are real numbers. Then the following properties hold. Power of a Product:

( ab )

m

= a mb m

n

an ⎛a⎞ Power of a Quotient: ⎜ ⎟ = n , b ≠ 0 and ⎝b⎠ b

⎛a⎞ ⎜ ⎟ ⎝b⎠

−n

n

bn ⎛b⎞ = ⎜ ⎟ or n , a ≠ 0, b ≠ 0 ⎝a⎠ a

Factoring:

ANY NUMBER OF TERMS Greatest Common Factor (GCF): a3b 2 + 2a 2b − 4ab 2 = ab ( a 2b + 2a − 4b )

TWO TERMS Difference of Two Squares

a 2 − b 2 = ( a + b )( a − b )

Sum of Two Cubes

a 3 + b3 = ( a + b ) ( a 2 − ab + b 2 )

Difference of Two Cubes

a 3 − b3 = ( a − b ) ( a 2 + ab + b 2 ) THREE TERMS

Perfect Square Trinomials

General Trinomials

a 2 + 2ab + b 2 = ( a + b ) a 2 − 2ab + b 2 = ( a − b )

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2

acx 2 + ( ad + bc ) x + bd = ( ax + b )( cx + d ) FOUR OR MORE TERMS

Grouping

ra + rb + sa + sb = r(a + b) + s(a + b) = (r + s)(a + b)

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