Summer PacketWilliamsburg School for Architecture and DesignMr . Leverenz and
Ms. Spaziani
Pre-Algebra Review Summer 2017
Pre-Algebra Review for Students taking Algebra 1 Regents Level Course
Name: ______
Date: ______
DIRECTIONS
This 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.
www.purplemath.com
www.khanacademy.org
www.mathway.com
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 CONTENTS
1. Multiplication Drills
2. Division Drills
3. Working with Fractions
4. Practice Percents and Decimals
5. Greater than or Less Than
6. Integers
7. Exponents
8. Perfect Squares
9. The Pesky X – One and Two-Step Equations
10. Graphing
Multiplication and Division Drills
For 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
Multiplication
1) 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:
Division
1) 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 Fractions
Adding Fractions and Subtracting Fractions 5/6 = 5 is Numerator and 6 is Denominator
- Find a common denominator. Then add or subtract the numerators. Simplify.
- 5/6 – 2/3 = common denominator of 6 = 5/6 – 4/6 = 1/6
- 5/6 + 2/3 = common denominator of 6 = 5/6 + 4/6 = 9/6 = 1 3/6 = 1 ½
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 Fractions
- Multiply straight across both the numerator and the denominator. Simplify.
- 4/8 * 2/6 = 8/48 = 1/6 * means to Multiply
1) 7/8 * 3/4 = 2) 2/5 * 1/6 = 3) 1/2 * 3/5 = 4) 3/9 * 1/2 =
Ans.______Ans. ______Ans. ______Ans. ______
Dividing Fractions
- Flip the second fraction (take the reciprocal) and multiply. Simplify
- 4/8 / 2/6 = 4/8 * 6/2 = 24/16 = 3/2
1) 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 Decimals
Percent to a Decimal
- Take the percent and move the decimal two places to the left. 3.6% = 0.036 36% = 0.36
- Take the percent and divide by 100. 3.6% = 3.6/100 = 0.036 or 36%= 36/100 = 0.36
1) 45% = 2) 2.3% = 3) 72% = 4) 8.5% =
Ans.______Ans. ______Ans. ______Ans. ______
Decimal to a Percent
- Take 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 ≤ 4
Place the appropriate sign in the box below.
36 □ 4 ∙ 8 12 □ 2 ∙ 9 15 □ 45-15 18 □ 36 / 3
Write a number in the space that will make the equation true.
____ ∙ 10 ≤ 40 30 ≥ _____ / 2 12 / _____ ≤ 3 78 ≥ 12 ∙ _____
Integers
Adding
- If the signs are the SAME - ADD - Keep the Sign. -3 + -6 = -9 and 3 + 6 = 9
- If the signs are DIFFERENT – SUBTRACT – take the sign of the larger number. -3 + 6 = 6 -3 = -3
Subtracting
- When SUBTRACTING a POSITIVE change it to ADDING a NEGATIVE -3 – 6 = -3 + -6 = -9
- When SUBTRACTING a NEGATIVE change it to a ADDING a POSITIVE -3 – (-6) = -3 + 6 = -3
1) 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 Dividing
- If 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 = Exponent
- The Base number multiplied by itself repeated the number of the exponent. 24 = 2 ∙ 2 ∙ 2 ∙ 2 = 16 so 24 = 16
Calculating Negative Exponents
- The base number placed under 1 in a fraction with the exponent made positive. 2-4 = 1/24 = 1/16
1) 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 Variable
- Add 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 Equations
- Use inverse operations to solve each equation for the variable.
1) -5h = 50 2) -6 = 2 + x 3) 65 = 5x 4) f + 3 = -8
5) 9 – 4x = 1 6) 5x + 4 = 49 7) 4x – 9 = 23 8) 3x – 8 = -32
9) 6 + 4x = 6x + 14 10) -5 = x + x – 5 11) 16 = 6x – 7x +8 12) 3x – 1 – 7x = -21
13) 7(4x -1) = 49 14) 2(3 –x) = -16
Graphing
Graphing Continued
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