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NAME ______________________________ DUE: FRIDAY, SEPTEMBER 11, 2009 BASIC ALGEBRA PRELIMINARY ASSESSMENT Students entering Basic Algebra are expected to recall mathematics skills taught in their middle school math classes. To review these basic concepts prior to beginning the course, the mathematics department has prepared the following packet to review those skills. For each skill, the packet contains several examples, links to online tutorials, and practice problems for you to complete. The packet is also divided into two parts: one part without a calculator and one part using a calculator. SINCE THIS MATERIAL IS A REVIEW, YOU ARE RESPONSIBLE FOR COMPLETING THIS PACKET ON YOUR OWN. IF YOU NEED ASSISTANCE, YOU MUST COME FOR EXTRA HELP. There will be an in-class assessment within the first few weeks of school. Prior to taking the test, this packet will be collected and graded by the teacher to evaluate your efforts to recall this information. Be sure to SHOW ALL WORK to receive credit. NO WORK = NO CREDIT!! PART I – NO CALCULATOR Complete all the problems in the PRACTICE sections without using a calculator. SHOW ALL WORK!! I. THE NUMBER LINE Practice – Plot the given set of numbers on the number line. 1) { -3, -1.3, 0, 1.5, 4 } 2) { -2.3, 5 4 , 1, 4.03 } Basic Algebra Preliminary Assessment QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. 1 II. GRAPHING INEQUALITIES Tutorials: http://www.sparknotes.com/math/algebra1/inequalities/section4.rhtml http://www.onlinemathlearning.com/algebra-inequalities.html Practice - Graph each of the following inequalities on a number line. RECALL: Use an open OR closed circle and then shade correctly. 1) x3 QuickTime™ and a decompressor are needed to see this picture. 2) x > -1 QuickTime™ and a decompressor are needed to see this picture. III. PLOTTING Tutorial: ON THE COORDINATE PLANE http://www.math.com/school/subject2/lessons/S2U4L1GL.html Practice - Plot each of the following points on the coordinate plane below. Be sure to label the grid and label the points with the correct letter after you plot them. A (3, 6) B (-2, 5) C (-4, -2) D (5, -3) E (0, 5) F (2, 0) G (-3, 0) H (0, -4) Basic Algebra Preliminary Assessment 2 IV. OPERATIONS WITH INTEGERS Tutorials: http://www.regentsprep.org/Regents/math/ALGEBRA/AOP3/indexAOP3.htm http://www.aaamath.com/g65-add-3-negative.html Practice - Evaluate the following using your knowledge of positive and negative numbers. SHOW WORK AND DO NOT USE A CALCULATOR!! 1) -13 + 18 = _________ 2) (-6)(-2)(3) = _________ 3) 8 – (-4) – 19 = _________ 4) 6 + -12 = _________ 5) 3(-2)(-1)(-1)(4) = _________ 6) -3 – 12 + (-8) = _________ 7) -8 – 3 + 10 = _________ 8) -28 -2 = _________ V. ABSOLUTE VALUE Tutorials: http://www.regentsprep.org/Regents/math/ALGEBRA/AO7/indexAO7.htm http://www.coolmath.com/algebra/Algebra1/05AbsValueEq/01_review.htm Practice - Evaluate the following absolute value problems. 1) | -16.5 | 2) |5| 4) - | - 13 | 5) | 8 – 17 | Basic Algebra Preliminary Assessment 3) - | 18 | 3 VI. EXPONENTS Tutorial: http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/LExp.htm Practice - Evaluate each of the following. SHOW WORK AND DO NOT USE A CALCULATOR!! 1) VII. 43 2) 62 3) 104 4) 91 SIMPLIFYING VARIABLE EXPRESSIONS Tutorials: http://www.classbrain.com/artteensb/publish/distributive_property.shtml http://www.algebrahelp.com/lessons/simplifying/distribution/ http://www.algebrahelp.com/lessons/simplifying/combiningliketerms/ Examples 1) 6x + 9y – 2x – 12y 6x + 9y – 2x – 12y Combine the terms with x’s and combine the terms with y’s. 4x – 3y 2) 7 (8x + 3) 7(8x) + 7(3) 56x + 21 Distribute the 7 to both terms in the parentheses. Practice - Simplify each expression by distributing and/or combining like terms. 1) 4x + 7y – 14x + 2y 2) 5 (x + 3) 3) -3 (2x – 5y) 4) -13 – 4y – 5z + 15 – (-4z) + 11y 5) 7 (4y – 8m) 6) 20xy + 3x2y – 10x2y – 30xy Basic Algebra Preliminary Assessment 4 PART II – WITH CALCULATOR Complete each of the following questions. You may use a calculator. Show all work!! VIII. FRACTION OPERATIONS Examples Adding & Subtracting Fractions – To add and subtract fractions, you must have a common denominator – preferably a least common denominator (LCD). Example 1 1 2 7 The least common denominator for 2 and 8 is 8. 8 1 (4) 2 (4) 7 Multiply the denominator of the first fraction by 4 to 8 create the common denominator of 8 and multiply the numerator by 4 also. 4 8 Example 2 4 5 7 8 = 11 Add the numerators. 8 2 The least common denominator for 5 and 3 is 15. 3 4 (3) 5 (3) 2 (5) 3 (5) Multiply the numerator and denominator of the first fraction by 3 to create the common denominator. Multiply the numerator and denominator of the second fraction by 5 to create the common denominator. 12 15 10 15 = 2 15 Add the numerators. Basic Algebra Preliminary Assessment 5 Multiplying Fractions – To multiply two fractions, multiply the numerators and multiply the denominators. Then simplify the result. Example 1 Example 2 1 8 4 2 5 4 10 Multiply the numerators and the denominators. 9 6 8 6 9 1 Simplify the fraction. 48 2 9 5 Rewrite 6 as 6 1 . Multiply the numerators and the denominators. Simplify the fraction. 16 3 Dividing Fractions – To divide two fractions, rewrite the problem as multiplication by the reciprocal. Follow the rules for the multiplying fractions. Example 7 10 7 5 6 6 10 5 42 50 Rewrite the problem as first fraction being multiplied by the reciprocal of the second fraction. Multiply the numerators and the denominators. Simplify the fraction. 21 25 Mixed Numbers – Rewrite mixed numbers as improper fractions and proceed with the operations as described above. Basic Algebra Preliminary Assessment 6 Practice - Perform the indicated operation. 1) 3) 5) 7) 2 7 3 4 3 2 8 7 16 3 8 1 5 3 2 8 Basic Algebra Preliminary Assessment 2) 4) 5 12 3 14 1 5 6 7 6) 1 4 2 5 3 5 8) 2 3 2 4 3 7 IX. CONVERSIONS Tutorial: BETWEEN FRACTIONS, DECIMALS, AND PERCENTS http://www.purplemath.com/modules/percents.htm Examples Fraction Decimal Percent GIVEN: Divide the numerator by the denominator. Move the decimal point two places to the right (multiply by 100). 1 2 0.5 Since 5 is the last digit in the thousandths place, put 875 over 1000 and simplify the fraction. GIVEN: 0.875 875 1000 100 Move the decimal point two places to the right (multiply by 100). 87.5% 7 8 Since 2 is the last digit in the hundredths place, put 2 over 100 and simplify the fraction. 2 50% Move the decimal two places to the left (divide by 100). 1 0.02 GIVEN: 2% 50 Basic Algebra Preliminary Assessment 8 Practice - Complete the following table. Convert fractions, decimals, and percents. Fraction Decimal Percent 5 1 8 2 0.8 3 70% 8 4 3 5 3.5% 6 0.04 7 4 1 5 8 0.9% Practice - Compare each of the following pairs of numbers using >, <, or =. 9) 12) 3.398 ______ 3.349 5 8 ______ 4 6 10) 13) Basic Algebra Preliminary Assessment 1 5 3 2 ______ ______ 1 11) 6 2 8 ______ 1 4 4 6 9 X. ORDER OF OPERATIONS (PEMDAS) Tutorials: http://www.regentsprep.org/Regents/math/ALGEBRA/AOP2/indexAOP2.htm http://www.math.com/school/subject2/lessons/S2U1L2GL.html Parentheses Exponents Multiplication Done from left to right Division Addition Done from left to right Subtraction Practice – Simplify using the order of operations. Show all work!! 1) 24 4 + 32 2) 14 7 5 - 32 3) 13 + ( 3 2 )2 – 8 4) 5 + [ 30 – ( 6 – 1 )2 ] 5) [82–(3+9)]+[823] Basic Algebra Preliminary Assessment 10 XI. EQUATIONS Tutorials: http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/LSolvEq.htm http://www.regentsprep.org/Regents/math/ALGEBRA/AE2/PSolvEq.htm http://www.coolmath.com/algebra/algebra-practice-solving.html Practice – Solve each of the following equations. Show all work!! 1) x–4=2 4) w+ 7) 5x + 2 = 2 2 3 = 5 6 2) 11 + b = 18 3) 5) -7a = -49 6) 8) 4x – 3 = 17 9) Basic Algebra Preliminary Assessment 4x = 48 m 6 = -3 -7 = 47 – 6k 11