Download Gr 7 Unit Study Guides #1-6 - 2012 Midterm Topics - Blank

Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Rounding, Sets of Real Numbers, Rational vs. Irrational, Perfect Squares & Square Roots, Placing Real
Numbers on a Number Line, Absolute Value, Signed Numbers
I. Rounding
Examples:
Steps:
1) Look to the number in the decimal place to the right
of whatever decimal place you are rounding to...
2) Round up or Stay the same?
1) Round 123.45cm to the nearest cm.
2) Round $123.45678 appropriately.
0 - 4 Stays the Same
*3) Round 1.299 to the nearest hundredth.
5 - 9 Round Up
II. Exact Values vs. Rounding
Exact Values: Fractions and Decimals that terminate (stop) or
have a bar over the last digit(s)
III. Sets of Real Numbers
1) Counting/Natural Numbers:
2) Whole Numbers:
3) Integers:
4) Rational Numbers:
5) Irrational Numbers:
1
IV. Rational vs. Irrational
Rational or
Irrational?
Real Number
1)
Explanation
16
100
2) 12.77
3) – 123. 4
4)
81
5)
83
6) 0.121221222…
7)

8
V. Perfect Squares & Square Roots
Square Root
1 2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Perfect
Square
VI. Placing Real Numbers on a Number Line
Directions: Use your estimation skills to place each of the following real numbers on the number line below.
1) – 5
2)
4
3)
18
4) – 2.75
5) 0.8
6) 
2
3
7)
27
VII. Absolute Value
Directions: Simplify the following expressions below.
1)  4  10
Steps:
1) Operation inside bars
2) Absolute Value
2)  6  5
Steps:
1) Absolute Value
2) Operation outside bars
2
VIII. Signed Numbers
1) Addition: SADS = _S___________ _A__________, _D_________________ _S_______________
1) SAME signs, ____________ the common sign and ____________ the numbers.
2) DIFFERENT signs, ___________ the sign of the ____________ and _____________ the smaller.
3) Additive Inverse Property: a number added to it’s opposite (inverse) equals _________________.
–3 + (–9)
3 7

2 3
–9 + 4
4 + (–4)
2) Subtraction
1) __________________ the sign of the first number.
2) __________________ the subtraction sign to an __________________ sign.
3) __________________ the sign of the __________________ number.
4) Apply addition rules (SADS)
3–7
–1 – 7
–2 – (–6)
3) Multiplication & Division
1) Find the product (answer to a multiplication problem) or quotient (answer to a division problem).
2) Odd number of negatives, the answer is _____________________ (positive or negative).
3) Even number of negatives, the answer is ______________________(positive or negative).
(7) (–4)
–42 ÷ 6
(2)( –5)( –3)
(1) (–1) (1)( –1)(1)( –1)(1)
3
Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Properties, Exponents, Order of Operations, and Scientific Notation
I. Properties
Directions: Match the property on the left hand side with the correct example of the property on the right hand side. Place the
corresponding letter on the given line. Each property will only be used once.
________1) 5  0 = 0
A) Additive Identity
________2) 5  4 = 4  5
B) Additive Inverse
________3) (7+8) + 9 = 7 + (8+9)
C) Associative Property of Addition
________4) 5(6 + 9) = 56 + 59
D) Associative Property of Multiplication
________ 5) 7  1 = 7
E) Commutative Property of Addition
________6) 12 + 13 = 13 + 12
F) Commutative Property of Multiplication
________7) 29 + 0 = 29
G) Distributive Property
________8) 5 + (-5) = 0
H) Multiplication Property of Zero
________9) 2 (54) = (25)  4
I) Multiplicative Identity
________10) 6 
1
=1
6
J) Multiplicative Inverse
________ 11) 4 = y so y = 4
K) Symmetric Property
II. Exponent Rules (no variables)
all
Directions: Simplify the following expressions. Leave your answers in exponential form unless the answer is -1, 0, or 1. Express
final answers with a positive exponent.
1) Product Rule:
a) 4 5  4  4 2  __________
2) Power to a Power Rule:
4 
3) Quotient Rule:
158  15 2  _____________
4) Zero Exponents:
a)  4   _______
5) Negative Exponents:
3 2
b) 2 3  3 4  ___________
 _____________
0
b)  4 0  ________
4 2  _______
4
III. Order of Operations
PE
MA
DS
Steps:
1) Operation inside parentheses
2) Exponents
3) Multiplication or Division (whichever comes first when reading L to R)
4) Addition or Subtraction (whichever comes first when reading L to R)
Example #1: 30  2  4  3  2 2
Example #2: 75  68  6  3
IV. Scientific Notation
a) Convert 8.2  10 6 to standard form.
b) Convert 8.2  10 6 to standard form.
c) Convert 8,200,000 to scientific notation.
d) Convert 0.0000082 to scientific notation.
e) Express the quotient of 6.3  10 8 and 3 10 4
in scientific notation.
f) Express the product of 2.3  10 4 and 3.5  10 2 in
scientific notation.
5
Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Algebraic Expressions
I. Translating
1) Operations:
 The sum of x and 5  __________
 The difference of x and 5  __________
 The quotient of x and 5  __________
 The product of x and 5  __________
2) Hebrew Rule  ________________
 5 less than x  __________
 5 subtracted from x  __________
 5 more than x  __________
3) Parentheses

1
time the quantity of x plus 4  _______________
2

1
the sum of x and 4  _______________
2

1
the difference of x and 4  _______________
2
4) Let Statements: are needed when the problem doesn't provide you with variables to use for
unknowns.
 Five more than n  _______________
 The quotient of five and a number  _______________
6
II. Evaluating Expressions
1) If x = -3 and y = 5, what is the value of 5x2 – 2y + 2 ?
x2  4 y
2) What is the value of
, if x= 6 and y = -2 ?
2
III. Evaluating Formulas
5
F  32
9
 Convert 86oF to Celsius.
1) Celsius Formula: C 
9
2) Fahrenheit Formula: F  C  32
5
Convert 15oC to Fahrenheit.
7
Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Solving Linear Equations, Literal Equations, & Inequalities
I. Solving Linear Equations
Steps:
* Only do steps 1, 2, or 3 if possible, if not start at step 4!
1) “Clear” Parentheses (by Distributing when necessary)
 Multiply the term on outside of the
7 x  4  5x  1  35
2) Combine Like Terms
 Add or Subtract terms that have the
same variable AND the same exponent
3) Variables on Both Sides of the Equal Sign
 “Undo” smaller term with variable on one side of the
equal sign from the larger term with variable on the
other side of the equal sign.
 By the Inverse (opposite) Addition or Subtraction
4) “Undo” the Constant
 By the Inverse (opposite) Addition or Subtraction
 Constant number alone (stays the same)
5) “Undo” the Coefficient
 By the Inverse (opposite) Division or Multiplication
 Coefficient number with variable
6) Check (your solution)
7 x  4  5x  1  35
1) Rewrite
2) Replace
3) Recalculate
 No Distributing, Combining Like Terms, or Inverse
operations in Check.
 Simply plug in value to determine if both sides of the
equation are equal.
Reminder:
 Negative (-) is the same as Subtraction (-)
 Positive (+) is the same as Addition (+)
Ex. 5 – x = 12 is the same as – x + 5 = 12
Ex. 5 + x = 12 is the same as x + 5 = 12
 An equation is like a scale…whatever you do to one side, must also be done to the other side
8
II. Literal Equations: equations with multiple variables
1) c = 2m + d, solve for m.
*Need help?
Solve 10 = 2x + 4 to help you with the steps.
2) 3ax  b  c , solve for x.
III. Solving & Graphing Inequalities: you start off solving inequalities the same way you solve linear
equations...
1) x + 5 < 10
2)  5  x  10
3)
4 x  5x  6
9
Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Ratio, Rate, Proportion, & Percent
I. Ratio: a comparison of two numbers by division, written as boys : girls or boys to girls or
boys
.
girls
II. Rate: a fraction that compares two numbers of different units
ie. You drive 246 miles after 4 hours
II. Unit Rate: rate with a denominator of 1  great way to compare rates to see which is better
ie. You drive 246 miles after 4 hours. What was your average speed in miles per hour?
 Option #1: Divide: If you are going to use this method, the placement of the numbers in the numerator
(top) and denominator (bottom) matter. Make sure the denominator is whatever
you was one of, so in this problem: the hours must be in the denominator because
you was miles per hour.
 Option #2: Proportion: two equal ratios (fractions)
* remember units on left of proportion to keep you organized!
* make sure both numerators are the same unit and that both denominators are the same unit
 Option #3: Distance Formula: Distance = (rate) (time)
10
III. Unit Price/Cost: great was to compare the prices of two store items to see which is the better buy.
ie. Which is a better deal for cereal? Large size: 15 ounces for $2.50 or Small size: 9 ounces for $1.70.
IV. Proportions
 Determining Whether two Ratios are in Proportion
,
 Algebraic Proportions
Directions: Solve algebraically for x.
1)
=
2)
3x  3 7 x  1

3
5
11
IV. Direct Variation
ie. Julio's wages vary directly as the number of hours that he works. If his wages for 5 hours are $29.75,
how much will he earn for 30 hours?
VII. Converting between Fractions, Decimals and Percents
1) Fraction to Decimal - divide numerator by denominator
7
28
2) Fraction/Decimal to Percent - multiply by 100
7
28
3) Percent to a Fraction/Decimal - divide by 100
25%
VIII. Percent
1) 64.2% of 84 is what number?
2) 4 of what number is 25%?
3) What percent of 49 is 7?
12
IX. Percent of Change
In NY the average price for a gallon of regular gas in December of 2007 was $3.26. In one year's time the
price per gallon dropped to $2.08. What is the percent of change to the nearest hundredth of a percent?
X. Tax - multiply subtotal by 8.625% or 0.08625 (tax varies depending on location)
ie. How much will a $25 hat cost plus 8.625% tax?
XI. Tip - multiply bill by (15% - 20%), then add amount to bill. Pre-tax or post-tax depending on preference.
ie. You go out to dinner and your bill comes to $37.42 (tax included). How much should you pay in total if
you want to tip 15%?
XII. Discount - multiply percent discount by original price, then subtract from original price to get sales price.
ie. A soccer ball costs $123. The ball is discounted 20%. Tax on the ball is 8%. What did the soccer ball cost
you?
XIII. Simple Interest
1) Loan = $550. Rate = 4.5%. 3 years. How much interest is owed after 3 years?
2) Investment = $1,500. Rate = 4%. Interest = $300. How long was the investment in years?
13
Name: ______________________________
Mr. Art
Date: _______________
Period: ______________
Converting Measurements (Metric & Customary) & Relative Error
I. Metric is the system of measurement used in most countries around the world.
Reference
Sheet:
3) Jose fills his fish tank with water. The tank holds 250 liters of water. How many milliliters does the
tank hold?
F 25
G 2,500
H 25,000
J
250,000
14
II. Customary is the system of measurement used in the US.
Reference
Sheet:
1) At the doctor's office the man's height measurement was 72 inches.
What would the man's height be in feet?
2) Jennifer makes fruit punch for her family. She prepares a total of two gallons of fruit punch. How many cups
of fruit punch does she make?
III. Relative Error
ie. A soccer player walks the length of the soccer field for his coach and measures 95 yards. The soccer
field is actually 110 yards long. What was the soccer players relative error?
15