Name: _______________________________________________________________
Abraham Clark High School ALGEBRA 2 SUMMER PACKET PART 1 Due: September 9 – 10, 2013 (The day your class meets A or B day) INFORMATION/DIRECTIONS: All questions marked “Practice” must be complete and correct. You must return in September knowing how to do all the material in this packet. If you do not understand the material, you must use on-line resources or get a tutor to help you. The main objective of the packet is that you have mastered these skills before entering Algebra 2. You will be given a series of quizzes in September to verify your mastery of these skills.
You will turn in PART 2 with complete work and answers along with its cover page. You will keep PART 1 (the tutorial section) and should have the work and answers on those pages as well. This is for your reference as you need to use these skills next school year. This will be the first test grade for marking period 1. This is mandatory.
Summer contact for assistance: Mrs. Fischer
[email protected] **** Emails may take a few days for a response. Please be specific in your email what you need assistance with.
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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ORDERING AND COMPARING NUMBERS Example: Graph the numbers on a number line, then write the numbers in increasing order. Given: 5,
3 2 , –2, – , 3 2
10
ORDERING AND COMPARING NUMBERS Practice: Graph the numbers on a number line, then write the numbers in increasing order. 1.
2,
3 1 , –4, – , 3 2
12
Step 1: Rewrite the numbers as decimals. When necessary, round the numbers to two decimal places. 5, 2.5, –2, –0.66, 3.16 Step 2: Plot the numbers on the number line. –2
–
2 3
3 2
10
5
______, ______, ______, ______, ______
Step 3: Write the numbers in increasing order.
2 3 –2, – , , 3 2
10 , 5 2.
,
40 7 , –4.5, – , 8 4
2
______, ______, ______, ______, ______
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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OPERATIONS WITH SIGNED NUMBERS EXAMPLE ADDITION OF SIGNED NUMBERS: 4+5
–4 + (–5)
4 + (–5)
–4 + 5
OPERATIONS WITH SIGNED NUMBERS Practice: Add or subtract as indicated. 1. 5.3 + 11.8 =
Step 1: Check if the numbers have the same sign.
2. 11.8 – 5.3 =
Step 2: Depends on the signs. If yes, find the sum and keep the sign. –4 + (–5) = –9
4+5=9
If no, find the difference and keep the sign of the larger digit. 4 + (–5) = –1
–4 + 5 = 1
EXAMPLE SUBTRACTION OF SIGNED NUMBERS: 4–5
–4 – (–5)
4 – (–5)
–4 – 5
Step 1: Rewrite the subtraction problem as an addition problem.
4. –5.3 – (–11.8) =
5. –5.3 + 11.8 =
6. –11.8 – (–5.3) =
–4 + 5
4 + (–5) 4+5
3. –5.3 + (–11.8) =
–4 + (–5)
Step 2: Add the numbers as above. 4 + (–5) = – 1
–4 + 5 = 1
4+5=9
–4 + (–5) = –9
These rules work with real numbers.
7. 5.3 + (–11.8) =
8. –11.8 – 5.3 =
3 4 1 7 + – = – = – 8 8 2 8 9. 5.3 – 11.8 =
–
3 7 4 1 + = = 8 8 8 2
3.8 – (–4.5) = 8.3
10. 11.8 – (–5.3) =
–3.8 – 4.5 = –8.3
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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OPERATIONS WITH SIGNED NUMBERS MULTIPLICATION OF SIGNED NUMBERS: 8(4)
–8(–4)
8(–4)
–8(4)
OPERATIONS WITH SIGNED NUMBERS Practice: Multiply or divide as indicated. 1. 24.8(1.6) =
Step 1: Check if the numbers have the same sign. Step 2: Depends on the signs.
2. 24.8 ÷ 1.6 =
If yes, multiply the numbers and make the sign positive. 8(4) = 32
–8(–4) = 32
If no, multiply the numbers and make the sign negative. 8(–4) = –32
3. –24.8(–1.6) =
–8(4) = –32
DIVISION OF SIGNED NUMBERS: 8÷4
–8 ÷ (–4)
8 ÷ (–4)
–8 ÷ (4)
Step 1: Check if the numbers have the same sign.
4. –24.8 ÷ (–1.6) =
5. –24.8(1.6) =
Step 2: Divide by following the same rules as multiplication. 8÷4=2
–8 ÷ (–4) = 2
8 ÷ (–4) = –2
–8 ÷ (4) = –2
6. –24.8
÷ 1.6 =
These rules work with real numbers. 4.5(–2.5) = –11.25
7. 24.8(–1.6) =
4.5(2.5) = 11.25 8. 24.8
÷ (–1.6) =
–4.5 ÷ (–2.5) = 1.8
–4.5 ÷ 2.5 = –1.8
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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OPERATIONS WITH FRACTIONS
OPERATIONS WITH FRACTIONS
Equivalent Fractions are fractions that are
Hint: Use factor trees to prime factor.
equal in value.
Example: Prime factor 36.
25 1 2 10 Example: = = = 4 8 40 100
36 = 22(32)
36
Examples: 2 = 2(1)
18
2
A prime number is a number whose only factors are one and itself. The smallest and only even prime number is 2. 1 is not a prime number.
2
9 3
3
17 = 17(1)
A composite number is a number which has additional factors besides one and itself.
Practice: Prime factor each number. 1. 11 =
2. 52 =
3. 124 =
4. 96 =
5. 140 =
6. 495 =
Example: 12 = 2(6) = 3(4) = 12(1) A factor is one of two or more expressions that are multiplied together to get a product. A product is the result of multiplication. Prime Factorization means finding all the prime factors of a number. You do not need the factor 1 when doing prime factorization. Examples: 6 = 2(3)
12 = 2(2)(3) = 22(3)
2
28 = 2(2)(7) = 2 (7)
2
98 = 2(7)(7) = 2(7 )
Simplified Fraction is a fraction in which the numerators and denominators do not have any common factors except 1. Examples:
14 7 = 4 2
25 5 = 35 6
Simplify a Fraction Using Prime Factorization Example: Simplify
Practice: Simplify each fraction. Show the prime factorization and canceling. 1.
30 = 252
35 90
Step 1: Write the numerator and denominator as a product of prime factors. 5( 7) 35 = 2(3)(3)(5) 90
2. –
36 = 60
Step 2: Cancel out all the common factors. 5( 7) 35 7 = = 2(3)(3)(5) 18 90 ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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OPERATIONS WITH FRACTIONS ADDING AND SUBTRACTING FRACTIONS
ADDING AND SUBTRACTING FRACTIONS Practice: Add or subtract the fractions as indicated.
1 2 + 5 10
Adding Example:
OPERATIONS WITH FRACTIONS
Step 1: Make sure that both fractions have the same denominator.
1.
2 1 + = 3 2
2.
2 1 – = 3 2
3.
3 2 + = 7 3
4.
3 2 – = 7 4
6.
3 2 – = 4 3
The lowest common denominator is 10. Multiply:
2 4 = 10 2
2 5
Step 2: Add the numerators together. DO NOT add the denominators. Add:
1 5 4 + = 10 10 10
Step 3: Reduce the answer if possible.
1 5 = 2 10 . Subtracting Example:
2 1 – 5 3
This is the same instructions as above except subtract in step 2 instead of adding.
5. –
3 2 + = 4 3
Step 1: Make sure that both fractions have the same denominator. The lowest common denominator is 15. Multiply:
1 3
5 5 = 5 15
2 5
3 6 = 15 3
7.
2 3 + – = 5 3
8. –
3 2 – = 5 3
Step 2: Subtract the numerators. DO NOT subtract the denominators. Subtract:
6 1 5 – = – 10 15 15
Step 3: Reduce the answer if possible. –
1 is in simplest form. 10
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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OPERATIONS WITH FRACTIONS MULTIPLYING AND DIVIDING FRACTIONS Multiplying Example:
1 2 x 2 3
Step 1: Multiply the numerators together and the denominators together.
OPERATIONS WITH FRACTIONS MULTIPLYING AND DIVIDING FRACTIONS Practice: Multiply or divide the fractions as indicated. 1. –
1 2 x = 2 3
1(2) 2(3)
Step 2: Write the fraction. 2.
3 2 x = 4 7
3.
3 2 x = 5 3
2 6 Step 3: Reduce the answer if possible.
2 1 = 3 6 NOTE: Multiplication and division do NOT need to have common denominators. You can cancel before you multiply so you do not have to reduce at the end.
4. –
1 2 x = 3 9
1(2) 1(2) 1 2 1 x = = = 3 3 2 2(3) 2(3)
1 Dividing Example: ÷ 2 3 2
5.
3 2 = 7 4
6.
1 2 = 3 3
Step 1: Convert to multiplication by KCF (Keep-Change-Flip).
1 3 x 2 2 Step 2: Multiply as per previous section. 1(3) 2(2) Step 3: Write the fraction and reduce if possible.
3 4
This is in simplest form.
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
7. –
8.
1 2 = 5 3
3 – 2 = 2 3
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RATIO – PROPORTION – PERCENT RATIO A ratio is a direct comparison of two different quantities. When writing a ratio, unless told otherwise in the problem, the quantity listed first in the problem is the first one in the ratio and the quantity listed second is the second one in the ratio. Example: If there are 4 boys and 6 girls in the room, what is the ratio of boys to the total number of students? Ratios can be written in several forms. The chart shows the different ways to answer the example. RATIO 4 to 10
SIMPLIFIED 2 to 5
4 : 10 4 10 0.4
2:5 2 5 0.4
RATIO – PROPORTION – PERCENT Ratio Practice: Find the ratio for each of the questions. Reduce when possible. 1. Find the ratio of two meshed gears if one gear has 48 teeth and the other has 36 teeth. ANSWER: ________
2. An auto dealership has the following annual break-down of vehicles sold: Sedans Sports Cars Minivans Trucks Total Vehicles
360 150 215 125 850
Find the following ratios. a) Sedans to sports cars. ANSWER: ________
b) Minivans to trucks. Example: What is the ratio of a nickel to a quarter?
1 5 = 5 25
or
ANSWER: ________
5 : 25 is 1 : 5
Example: On a triangle, each side measures 5 cm, 10 cm, and 30 cm, respectively. In lowest terms, find the ratios of the lengths of the sides. The ratio is 5 : 10 : 30. Each number can be divided by 5. Simplified: 1 : 2 : 6.
c) Trucks to total vehicles. ANSWER: ________
3. Adam, Bob, and Carl share a job. Adam works 3 hours, Bob works 9 hours, and Carl works 12 hours. What is the ratio of the hours worked in simplest form? ANSWER: ________
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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RATIO – PROPORTION – PERCENT PROPORTION A proportion is an equation showing two ratios are equal.
RATIO – PROPORTION – PERCENT Proportion Practice: Find the proportion for each of the questions. 1.
8 x = 12 15
ANSWER: ________
2.
65 5 = x 4
ANSWER: ________
Extreme is another way of saying at the ends. Mean is another way of saying in the middle. extreme
mean
c a = d b extreme
mean
Note: This is not the same mean as used in taking an average. Cross product: The product of the extremes is equal to the product of the means. Example: Check to see if the proportion is a real proportion. Cross multiply to find the products.
3 12 = 16 4
4(12) = 3(16)
A proportion can be used to find missing information.
Set up the proportion using a variable for the missing information.
Make sure the set up is correct. If the proportion is set up incorrectly, the result will be incorrect.
Cross multiply.
Examples: On a map, 1 inch represents 5 miles. Find the distance two cities are from each other if they are 4 inches apart on the map.
1 4 = 5 x
1(x) = 5(4)
ANSWER: ________
48 = 48
Since both sides are equal, it is a proportion.
inches miles
3. A certain factory produces 80 good motors for every 3 defective motors. At this defect rate, how many defective motors will result with a production of 480 good motors?
4. The scale on a map of Europe states: 1 cm = 62 miles. If Rome is 11.2 cm from Paris on this map, find the distance in miles between these two cities. ANSWER: ________
5. A community college has a student to faculty ratio of 21 to 2. If this college has 234 faculty members, how many students are enrolled there? ANSWER: ________
x = 20 miles
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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RATIO – PROPORTION – PERCENT
Example (find the base):
PERCENT
7 is 70% of what number?
A percent is out of 100. It is part of 100. The symbol used is %.
70z = 100(7)
Percent is a ratio or fraction where the denominator is 100.
This can also be set up as a proportion. part percent y x = 100 z whole base Example (find the percent): What percent of 10 is 7? 10x = 100(7)
70z = 100(7)
RATIO – PROPORTION – PERCENT Percent Practice: Find the missing information using either method. Percent Practice: Find the missing information using either method.
ANSWER: ________
2. 28 is what percent of 280?
x 7 = 100 10
ANSWER: ________ x = 70%
3. What is 6% of 75? ANSWER: ________
Example (find the part):
10(70) = 100y
y is 70% of 10
700 100y = 10 100
Using proportion: 10(70) = 100y
z = 10
x = 70%
10x 700 = 10 10
What is 70% of 10?
70 7 = 100 z
70z 700 = 70 70
7 is x% of 10
Using proportion:
z = 10
1. What percent of 129 is 86?
10x 700 = 10 10
10x = 100(7)
70z 700 = 70 70
Using proportion:
General percent equation: y is x% of z, where: y = the part of the whole x = the percent z = the base.
7 is 70% of z
4. Find 5.5% of 128. y=7
ANSWER: ________
y 70 = 100 10
700 100y = 10 100
5. 18 is 25% of what number? y=7
ANSWER: ________
6. 349 is 106% of what number? ANSWER: ________
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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PERCENT – DECIMAL – FRACTION CONVERSIONS FRACTION TO…
PERCENT TO… Convert from percent to decimal:
Convert from fraction to decimal:
1 8 = 0.125 Convert from fraction to percent:
Example: Convert 12.5% to a decimal.
Divide the denominator into the numerator. 1 Example: Convert to a decimal. 8
Divide the denominator into the numerator. Then multiply by 100. Example: Convert
12.5% = 0.125 Convert from percent to a fraction:
Percent is over 100.
Remove the percent sign and place over 100. Do not remove the decimal yet.
Look at how many places there are after the decimal. Remove the decimal and put add a zero to the denominator for each decimal place.
Simplify if possible.
1 to a percent. 8
(1 8)100 = 0.125(100) = 12.5%
Remove the percent sign and move the decimal place 2 units to the left.
DECIMAL TO…
Example: Convert 12.5% to a fraction.
Convert from decimal to fraction:
125 1 12.5 = = 1000 8 100
Determine the place value of the last number on the right that is not a zero.
Remove the decimal point.
Use the numbers from the decimal as the numerator.
Use the place value found as the denominator.
Simplify if possible.
RATIO – PROPORTION – PERCENT Conversion Practice: Fill in the table. Fraction
Decimal 0.17
Example: Convert 0.12 to a fraction. The place value of the 5 is the thousandths place.
62%
3 12 = 25 100 Convert from decimal to percent:
1.2 7 20
Move the decimal place 2 units to the right and put a percent sign after it. Example: Convert 0.125 to a percent. 0.125 = 12.5%
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
Percent
80%
1 3
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ORDER OF OPERATIONS
ORDER OF OPERATIONS Practice: Use order of operations to simplify the following problems. Show each step.
When solving math problems with more than one operation, you must follow the correct order of operations.
1. 5(7 – 3)2 ÷ 8 • 2 + 5 =
Go through the operations in the following order. Parenthesis (in order from inner to outer) Exponents (including radicals) Multiplication/Division (in order from left to right) Addition/Subtraction (in order from left to right) Ignoring these rules will give different answers.
Notice the difference the parenthesis makes in the two examples below. 8–7+3=1+3=4 8 – (7 + 3) = 8 – 10 = –2
Notice the difference the order of operations makes in the two examples below. 16 ÷ 2 • 4 = 8 • 4 = 32
2. 20 + 16 ÷ 4 = 18 ÷ 9 + 6
16 • 2 ÷ 4 = 32 ÷ 4 = 8 Example: Simplify 3(2 + 5)2 ÷ 7 +
9
Step 1: Parenthesis 3(7)2 ÷ 7 +
2+5=7
9
Step 2: Exponents (radicals) 72 = 49
9 =3
3(49) ÷ 7 + 3
Step 3: Multiplication/Division 3(49) = 147
147 ÷ 7 = 21
21 + 3
Step 6: Addition 21 + 3 = 24 NOTE: When you have a fraction, simplify the numerator and denominator first, then simplify the fraction.
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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LAWS OF EXPONENTS
NEGATIVE POWER RULE:
PRODUCT RULE: am · an = am + n
1 and n a
a–n =
(when multiplying like bases, add the powers)
1 = an –n a
(take the reciprocal of the variable to the negative power) NOTE: Apply the negative power
Examples:
1. x4 · x5 = x4 + 5 = x9
rule to only negative POWERS.
2. a7 · a · a12 = a7 + 1 + 12 = a20
Examples:
3. (3x6)(2x4) = (3)(2)x6 + 4 = 6x10
1. 3x
–4
1 3 = 4 4 x x
= 3 –8 2
POWER RULE: (ambm)n = amnbmn
2.
(when taking a monomial to a power, multiply the powers including the coefficient)
2 5
–5n y –5m n = 10 –5 8 10 x y mx
Examples:
LAWS OF EXPONENTS
1. (a4b3)2 = a8b6 2. (3m2n5)4 = 34m8n20 = 81m8n20 9 6 2
3.
2
18 12
(6a b ) 6 a b = = 4 2 5 5 20 10 (–c d ) (–1) c d
QUOTIENT RULE: am an
18 12
36a b 20 10 –1c d
Practice: Simplify each expression using the laws of exponents. Write the answers as positive exponents.
1. 15-4(158) = 154 =
= am - n
(when dividing with like bases, subtract the powers) Note: it is always the numerator's power minus the denominator's power.
2. a7(a8)(a) = a7 + 8 + 1 =
Examples: 6
1.
x = x6 – 4 = x2 4 x
2.
mn = m5 – 4n7 – 2 = mn5 4 2 mn
3. (3m4n6)(2m2n) =
5 7
6
–3 5
–28a b c 4. 11 –5 5 7a b c
=
ZERO POWER RULE: a0 = 1 (any term to the zero power is one) Examples:
5. (–x5y6)10 =
1. (m5 n7)0 = 1 2. (4m8n2)(–2mn4)0 = (4m8n2)(1) = 4m8n2 ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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LITERAL EQUATIONS
LITERAL EQUATIONS
Formulas are equations that state a fact or rule relating two or more variables. You can solve a formula for any of its variables using the rules for solving equations.
Practice: Solve each equation for the variable required. Show all work.
Some common formulas:
Temperature
9 F = C + 32 5
Distance
d = rt
1. Simple interest formula:
I=
1 pt 20
Evaluate for p. p = _____________
Circumference of a circle C = d Area of a triangle
A=
1 bh 2
Density
d=
m v
At times it is necessary to move the
variables around in the formula without solving the formula. Use the rules of algebra to do this.
2. Perimeter of a rectangle formula: P = 2L + 2W
Evaluate for L. L = _____________
Example: Formula: A =
1 bh 2
Solve for b
Multiply both sides by 2
2A = bh
Divide both sides by h
2A =b h
Note: When solving literal equations, the result will be an algebraic expression, not a number.
V = r2h
Evaluate for r.
Example: Formula: a2 + b2 = c2
3. Volume of a cylinder:
Solve for a
Subtract b2 from both sides a2 = c2 – b2 Take the square root of both sides a=
c2 – b2
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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SLOPE OF A LINE The slope of a line measures the steepness of the line. This is usually referred to as “rise over run.” Run means how far left or right you move from point to point. On the graph, that would mean a change of x values.
SLOPE OF A LINE Practice: Find the slope of the line through the given points. 1. (–7, 10 ) and (1, 10)
m = ____________
2. (3, 7) and (3, –8)
m = ____________
Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. The direction of the line will refer to the type of slope it has. Look at the diagram below.
Positive Slope
Negative Slope
3. (100, 10) and (–3, 50) m = ____________
Zero Slope
Undefined Slope
Numerator = 0
Denominator = 0
Slope Formula Given Two Points Given two points (x1, y1) and (x2, y2) m=
4. (4, 6) and (7, 7)
m = ____________
y – y1 change in y rise = = 2 run changein x x 2 – x1
Example: Find the slope of the line that passes through the points (–5, 2) and (4, –7). m=
–9 –9 –7 – 2 = = = –1 4+5 9 4 – (–5)
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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WRITE THE EQUATION OF A LINE IN SLOPE-INTERCEPT FORM GIVEN TWO POINTS
WRITE THE EQUATION OF A LINE IN SLOPE-INTERCEPT FORM GIVEN TWO POINTS
The slope-intercept form of the equation of a line is y = mx + b, where (x, y) is any point on the line, m is the slope, and b is the y-intercept.
Practice: Write the equation of the line that passes through the given points. Show all work.
Example: Write the equation of the line that passes through the points (–2, 3) and (1, –6).
1. (2, 7) and (0, 1)
Step 1: Find the slope of the line. m=
–9 –9 –6 – 3 = = = –3 3 1– (–2) 1+ 2
Step 2: Plug the slope and either on of the points into the formula.
2. (2, 0) and (0, 3)
y = mx + b 3 = –3(–2) + b Step 3: Solve for b. 3 = –3(–2) + b 3=6+b
3. (2, 6) and (–2, 4)
–3 = b Step 4: Write the equation of the line by plugging in the values of m and b into the slope-intercept form. y = mx + b y = –3x – 3 4. (2, 13) and (1, 8)
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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GRAPH THE EQUATION OF A LINE The equation of a line can be graphed in several ways. One method is to use the slope and y-intercept of the line to draw the graph. Example: Graph the equation y = –3x – 3. Step 1: Find the values of m and b.
GRAPH THE EQUATION OF A LINE Practice: The equation of a line can be graphed in several ways. One method is to use the 1. Graph y =
1 x–1 4
m = –3 and b = –3 Step 2: Plot b on the graph. This is the yintercept which means (0, –3). Step 3: Use the slope to find a second point. m=–
3 1
This means move up 3 units and left 1 unit from the slope intercept. Step 4: Draw a line using the two points.
2. Graph y = –4x + 3 Left 1
Up 3
ACHS – ENTERING ALGEBRA 2 – SUMMER 2013 WORK
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WEBSITES ORDERING AND COMPARING NUMBERS http://www.ck12.org/arithmetic/Order-of-Real-Numbers/ http://www.virtualnerd.com/pre-algebra/real-numbers-right-triangles/real-and-irrational/compare-classify-numbers/orderreal-numbers-example OPERATIONS WITH SIGNED NUMBERS http://www.epcc.edu/tutorialservices/valleverde/Documents/SignsOOPS.pdf http://amby.com/educate/math/integer.html http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut4_operations.htm OPERATIONS WITH FRACTIONS http://www.aaamath.com/fra.html http://www.ck12.org/arithmetic/Equivalent-Fractions/ http://www.ck12.org/arithmetic/Fractions-in-Simplest-Form/ http://www.ck12.org/arithmetic/Sums-of-Fractions-with-Like-Denominators/ http://www.ck12.org/arithmetic/Differences-of-Fractions-with-Different-Denominators/ http://www.ck12.org/arithmetic/Products-of-Two-Fractions/ http://www.ck12.org/arithmetic/Quotients-of-Fractions/ RATIO – PROPORTION – PERCENT http://www.ck12.org/arithmetic/Ratios/ http://www.ck12.org/arithmetic/Proportions/ http://www.ck12.org/arithmetic/Percents/ ORDER OF OPERATIONS http://www.ck12.org/algebra/PEMDAS/ LAWS OF EXPONENTS http://www.mathsisfun.com/algebra/exponent-laws.html http://www.algebralab.org/practice/practice.aspx Go to exponents and exponential functions LITERAL EQUATIONS http://www.ck12.org/algebra/Linear-Equations/enrichment/Solving-Literal-Equations---Overview/ http://www.ck12.org/user:sccmath101/section/Literal-Equations/ SLOPE OF A LINE http://www.ck12.org/algebra/Slope-of-a-Line-Using-Two-Points/ WRITE THE EQUATION OF A LINE IN SLOPE-INTERCEPT FORM GIVEN TWO POINTS http://www.ck12.org/algebra/Standard-Form-of-Linear-Equations/ GRAPH THE EQUATION OF A LINE http://www.ck12.org/algebra/Graphs-Using-Slope-Intercept-Form/
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