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1247140116496300Pre-Algebra Review for Students taking Algebra 1 Regents Level CourseName: ______________________________________Date: _______________________________________DIRECTIONSThis packet contains practice problems and examples for all the pre-requisite skills you need to be successful in Algebra 1 at the Regents level. The skills are listed below and do not have to be practiced in order. It is very important that you show all your work. There is a list of websites that may help you as you work through the packet. This packet is due the first day of school in September, 2017. Although this packet is not mandatory, it will count as a BONUS classwork assignment. NO CREDIT WILL BE TAKEN AWAY ONLY ADDED.TABLE of CONTENTSMultiplication Drills Division DrillsWorking with FractionsPractice Percents and DecimalsGreater than or Less ThanIntegers ExponentsPerfect SquaresThe Pesky X – One and Two-Step EquationsGraphingMultiplication and Division DrillsFor each section, set a timer for 1 minute and solve all the problems you can WITHOUT a calculator. If you do not finish all the problems IT IS OKAY. Record how many you solved and then go back and finish the rest. If you finish early, record how long it took you to finish. Example:1) 6 x 7 = __42_ 2) 5 x 8 = _40_ 3)4 x 9 = _36_ 4) 9 x 6 = _54_ 5) 5 x 4 = _20_ 6)2 x 7 = _14_Time Completed: 1 minute# Completed: 5 Multiplication1) 4 x 7 = ____ 2) 5 x 8 = ___ 3) 3 x 9 = ___ 4) 9 x 8 = ___ 5) 5 x 6 = ___ 6) 8 x 6 = ____Time Completed: __ min / sec# Completed: 1) 8 x 8 = ____ 2) 9 x 9 = ___ 3) 7 x 7 = ___ 4) 5 x 5 = ___ 5) 6 x 6 = ___ 6) 4 x 4 = ____Time Completed: __ min / sec# Completed: 1) 4 x 10 = ____ 2) 11 x 8 = ___ 3) 10 x 9 = ___ 4) 9 x 12 = ___ 5) 5 x 12 = ___ 6) 11 x 6 = ____Time Completed: __ min / sec# Completed: Division1) 10/5 = ____ 2) 12/6 = ___ 3) 21/7 = ___ 4) 45/9 = ___ 5) 64/8 = ___ 6) 36/2 = ____Time Completed: __ min / sec# Completed: 1) 60/6 = ____ 2) 35/7 = ___ 3) 48/12 = ___ 4) 9/3 = ___ 5) 15/3 = ___ 6) 121/11 = ____Time Completed: __ min / sec# Completed: Working with FractionsAdding Fractions and Subtracting Fractions 5/6 = 5 is Numerator and 6 is DenominatorFind a common denominator. Then add or subtract the numerators. Simplify.5/6 – 2/3 = common denominator of 6 = 5/6 – 4/6 = 1/65/6 + 2/3 = common denominator of 6 = 5/6 + 4/6 = 9/6 = 1 3/6 = 1 ?1) 7/8 + 3/4 = 2) 2/5 + 1/6 = 3) 1/2 + 3/5 = 4) 3/9 + 1/2 =Ans._________Ans. ___________ Ans. _________Ans. __________1) 5/6 – 3/4 = 2) 4/5 - 1/6 = 3) 7/8 - 3/5 = 4) 6/9 - 1/2 =Ans._________Ans. ___________ Ans. _________Ans. __________Multiplying FractionsMultiply straight across both the numerator and the denominator. Simplify.4/8 * 2/6 = 8/48 = 1/6 * means to Multiply1) 7/8 * 3/4 = 2) 2/5 * 1/6 = 3) 1/2 * 3/5 = 4) 3/9 * 1/2 =Ans._________Ans. ___________ Ans. _________Ans. __________Dividing FractionsFlip the second fraction (take the reciprocal) and multiply. Simplify4/8 / 2/6 = 4/8 * 6/2 = 24/16 = 3/21) 7/8 / 3/4 = 2) 2/5 / 1/6 = 3) 1/2 / 3/5 = 4) 3/9 / 1/2 =Ans._________Ans. ___________ Ans. _________Ans. __________Practice Converting Percents and DecimalsPercent to a DecimalTake the percent and move the decimal two places to the left. 3.6% = 0.036 36% = 0.36Take the percent and divide by 100. 3.6% = 3.6/100 = 0.036 or 36%= 36/100 = 0.361) 45% = 2) 2.3% = 3) 72% = 4) 8.5% =Ans._________Ans. ___________ Ans. _________Ans. __________Decimal to a PercentTake the decimal and move the decimal two places to the right. 0.036 = 3.6% or 0.36 = 36%Take the decimal and multiply it by 100. 0.036 = 0.036 * 100 = 3.6% or 0.36 = 0.36 * 100 = 36%1) 0.04 = 2) 0.22 = 3) 0.38 = 4) 0.42 = Ans._________Ans. ___________ Ans. _________Ans. __________Greater Than and Less Than> = Greater Than≥ = Greater Than or Equal To 7 > 4 and 7 ≥ 7< = less Than ≤ = Less Than or Equal To 4 < 7 and 4 ≤ 4Place the appropriate sign in the box below.36 □ 4 ? 812 □ 2 ? 915 □ 45-1518 □ 36 / 3 Write a number in the space that will make the equation true. ____ ? 10 ≤ 4030 ≥ _____ / 2 12 / _____ ≤ 3 78 ≥ 12 ? _____ IntegersAdding If the signs are the SAME - ADD - Keep the Sign. -3 + -6 = -9 and 3 + 6 = 9If the signs are DIFFERENT – SUBTRACT – take the sign of the larger number. -3 + 6 = 6 -3 = -3SubtractingWhen SUBTRACTING a POSITIVE change it to ADDING a NEGATIVE -3 – 6 = -3 + -6 = -9When SUBTRACTING a NEGATIVE change it to a ADDING a POSITIVE -3 – (-6) = -3 + 6 = -31) 7 + (-5) = 2) -4 + -6 = 3) -8 + 5 = 4) -6 + (-8) =Ans._________Ans. ___________ Ans. _________Ans. __________ 1) 9 – (-3) = 2) -4 – (-3) = 3) -6 – 7 = 4) 5 – (-5) =Ans._________Ans. ___________ Ans. _________Ans. __________Multiplying and DividingIf the signs are the SAME = POSITIVE answer.If the signs are DIFFERENT = NEGATIVE answer.1) -8 ? -2 = 2) 7 ? -8 = 3) -3 ? 9 = 4) -2 ? - 12 =Ans._________Ans. ___________ Ans. _________Ans. __________ 1) -35 / 7 = 2) -60 / -6 = 3) 56 / -8 = 4) 12 / -4 =Ans._________Ans. ___________ Ans. _________Ans. __________Exponents Calculating Positive Exponents 24 where 2 = Base Number 4 = ExponentThe Base number multiplied by itself repeated the number of the exponent. 24 = 2 ? 2 ? 2 ? 2 = 16 so 24 = 16Calculating Negative Exponents The base number placed under 1 in a fraction with the exponent made positive. 2-4 = 1/24 = 1/161) 35 = 2) 43 = 3) 5-2 = 4) 3-5 =Ans._________Ans. ___________ Ans. _________Ans. __________Adding and Subtracting Exponents with Variables 3x2 where 3 is the Coefficent and x2 is the VariableAdd or subtract the coefficients and KEEP the variable the SAME 3x2 - 2x2 = x2 and 3x2 + 2x2 = 5x2 1) -8x2 + 2 x2 = 2) 7 x2 - 3 x2 = 3) 3 x5 + 9 x5 = 4) -4 x3 - 12 x3 =Ans._________Ans. ___________ Ans. _________Ans. __________Multiplying Exponents with Variables Multiply the coefficients and ADD the Exponents 3x2 ? 2x2 = 6x4 and 3x2 ? 2x = 6x3 1) -8x3 ? 3 x2 = 2) 5 x3 ? 3 x2 = 3) 2x ? 9 x5 = 4) -5 x3 ? 6x =Ans._________Ans. ___________ Ans. _________Ans. __________Perfect Squares – The product of a number multiplied by itself. MEMORIZE them!!!!!Fill in the missing number.1) 1 = 1 ?____ 2) 4 = 2 ? _____3) 9 = 3 ? ___ 4) 16 = 4 ? ___ 5) 25 = 5 ?____ 6) 36 = 6 ? ____ 7) 49 = 7 ? _____ 8) 64 = 8 ? ___ 9) 81 = 9 ? ____ 10) 100 = 10 ? _____The Pesky X – One and Two Step EquationsUse inverse operations to solve each equation for the variable. 1) -5h = 502) -6 = 2 + x3) 65 = 5x4) f + 3 = -85) 9 – 4x = 16) 5x + 4 = 49 7) 4x – 9 = 238) 3x – 8 = -329) 6 + 4x = 6x + 1410) -5 = x + x – 511) 16 = 6x – 7x +812) 3x – 1 – 7x = -2113) 7(4x -1) = 4914) 2(3 –x) = -16 GraphingGraphing Continued ................
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