Transcript Course 2 Nine Weeks Review

Course 2 Nine Weeks (1)
Review
SOLs 7.3, 7.1, 7.16, 7.2, 7.13
SOL 7.3
The student will
a) model addition, subtraction, multiplication and division of integers; and
b) add, subtract, multiply, and divide integers.
• The set of integers is the set of whole numbers and their
opposites (e.g., … –3, –2, –1, 0, 1, 2, 3, …).
• Integers are used in practical situations, such as temperature
changes (above/below zero), balance in a checking account
(deposits/withdrawals), and changes in altitude (above/below
sea level).
• The sums, differences, products and quotients of integers are
either positive, zero, or negative.
SOL 7.3
Question 1
Jasmine’s bank account was in the red $15. She
deposited $28. Then, she wrote a check for $6.
What is the balance of Jasmine’s bank account?
Jasmine’s account balance is in the red $9; so, -9.
Jasmine’s account balance is $7; so, 7.
Jasmine’s account balance is $19; so 19.
Jasmine’s account is in the red $7; so, -7.
Correct
WOW!
You’re a Math Star!
SOL 7.3
-
Question 2
-
-
-
3
11
-3
-11
+
+
+
+
Correct
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You’re a Math Star!
SOL 7.3
Question 3
-7 – (-9) =
2
-2
-16
16
Correct
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You’re a Math Star!
SOL 7.3
Question 4
Over the past week, the temperature dropped a total of
28 degrees. Write an integer to represent the average
drop in temperature per day.
4
28
-4
7
Correct
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I think you’re ready to move on!
SOL 7.1
The student will
a) investigate and describe the concept of negative exponents for powers of ten;
b) determine scientific notation for numbers greater than zero;
c) compare and order fractions, decimals, percents and numbers written in
scientific notation;
d) determine square roots; and
e) identify and describe absolute value for rational numbers.
SOL 7.1
Question 5
Which is the equivalent of 10−4 .
-0.0001
-40
0.0001
0.4
Correct
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SOL 7.1
Question 6
Which is the equivalent of
10−2
10−1
102
101
1
.
100
Correct
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SOL 7.1
Question 7
Over a lifetime, the average corporate CEO grosses
$205,000,000. Write this number in scientific notation.
2.5 × 108
2.05 × 106
2.05 × 108
2.5 × 106
Correct
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SOL 7.1
Question 8
Which selection below is placed in
descending order?
2.5 ×
101 ,
1
, 44%, 0.043
5
1
, 0.043, 2.5 × 101 , 44%
5
1
0.043, ,44%, 2.5 × 101
5
2.5 ×
101 , 44%,
1
, 0.043
5
Correct
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SOL 7.1
Question 9
Place the following in order from least to greatest.
Letter
A
B
C
D
Scientific Notation
9.9 × 106
1.1 × 108
9.056 × 101
5.98 × 104
A, B,C, D
D, C, B, A
B, A, D, C
A, C, D, B
Correct
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SOL 7.1
Question 10
What is
12.5
5
625
50
25 ?
Correct
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SOL 7.1
Question 10
What is the value of 19 ?
-19
9.5
1
19
19
Correct
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I think you’re ready to move on!
SOL 7.16
The student will apply the following properties of operations with real numbers:
a) the commutative and associative properties for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity properties;
d) the additive and multiplicative inverse properties; and
e) the multiplicative property of zero.
• Subtraction and division are neither commutative nor associative.
• Identity elements are numbers that combine with other numbers without changing the
other numbers.
• Inverses are numbers that combine with other numbers and result in identity elements
[e.g., 5 + (–5) = 0;
1
∙5
5
= 1]
• Zero has no multiplicative inverse.
• Division by zero is not a possible arithmetic operation. Division by zero is undefined.
SOL 7.16
Question 11
If the distributive property is applied
to 5(7+3) , which is the result?
5(3+7)
5+7+3
5(3) + 5(7)
5+3+5+7
Correct
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SOL 7.16
Question 12
What property is displayed shown?
5 + (8 + 4)= 5 + (4 + 8)
Associative
Commutative
Distributive
Additive Inverse
Correct
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SOL 7.16
Question 13
If 5 • a = 1, then a must be…
One
Multiplicative Identity
Zero
Multiplicative Inverse
Correct
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I think you’re ready to move on!
SOL 7.2
The student will describe and represent arithmetic
and geometric sequences using variable
expressions.
• In the numeric pattern of an arithmetic sequence, students must determine the
difference, called the common difference.
• In geometric sequences, students must determine what each number is multiplied by
in order to obtain the next number in the geometric sequence, called the common
ratio.
• A variable expression can be written to express the relationship between two
consecutive terms of a sequence.
SOL 7.2
Question 14
Which variable expression was used to find the
common difference in the sequence below?
2, 4, 6, 8, 10, 12…
2n
n+2
nx2
2+2
Correct
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SOL 7.2
Question 15
Find the 7th term in the sequence below,
2, 4, 8, 16,…
32
128
64
112
Correct
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SOL 7.2
Question 16
3n represents the relationship between two
consecutive terms in which sequence?
3, 9, 15, 21…
3, 9, 27, 81…
1, 3, 6, 9…
-3, 0, 3, 6…
Correct
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I think you’re ready to move on!
SOL 7.13
The student will
a) write verbal expressions as algebraic expressions and sentences as equations
and vice versa; and
b) evaluate algebraic expressions for given replacement values of the variables.
•
•
•
•
•
An expression is a name for a number.
An expression that contains a variable is a variable expression.
An expression that contains only numbers is a numerical expression.
A verbal expression is a word phrase (e.g., “the sum of two consecutive integers”).
A verbal sentence is a complete word statement (e.g., “The sum of two consecutive
integers is five.”).
• An algebraic expression is a variable expression that contains at least one variable
(e.g., 2x – 5).
• An algebraic equation is a mathematical statement that says that two expressions are
equal (e.g., 2x + 1 = 5).
• To evaluate an algebraic expression, substitute a given replacement value for a
variable and apply the order of operations.
SOL 7.13a
Question 17
8 more than the quotient of 42 and r is which
expression?
42
8+
𝑟
42𝑟 + 8
42
+8
𝑟
8 + 42𝑟
Correct
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SOL 7.13a
Question 18
Which phrase best represents the following?
2𝑥 − 8
Twice a number less than 8
8 minus half a number
8 less than double a number
Two times 8 minus a number
Correct
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SOL 7.13b
Question 19
Evaluate the following expression
𝑚2 − 7 + 6𝑚, when m = 4.
33
25
60
28
Correct
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SOL 7.13b
Question 20
Evaluate the following expression
3 − 𝑟 − 𝑟(2𝑟 + 1), when r = 5.
57
31
-77
-57
Correct
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I think you’re ready to ace your test!
7.16
Sorry, Wrong Answer!
Commutative Property: The ORDER of the numbers changes.
Associative Property: The order of the numbers stays the same,
but the numbers inside of the PARENTHESES change.
Distributive Property: The number on the outside of the
parentheses is PASSED OUT to the numbers inside of the
parentheses.
Identity Properties: An operation (+ 0 or x 1) is performed and
NOTHING CHANGED with the original number.
Inverse Properties: The OPPOSITE was added or the RECIPROCAL
was multiplied to give a sum of zero or a product of one.
Zero Property: Any number TIMES ZERO, EQUALS ZERO.
7.2
Sorry, Wrong Answer!
• Arithmetic sequence, use the common difference, between to determine
what is added to each previous number to obtain the next number.
• Geometric sequences, use the common ratio to determine what each
number is multiplied by in order to obtain the next number. This
• A variable expression can be written to express the relationship between two
consecutive terms of a sequence- If n represents a number in the sequence
3, 6, 9, 12…, the next term in the sequence can be determined using the
variable expression n + 3. If n represents a number in the sequence
• 1, 5, 25, 125…, the next term in the sequence can be determined by using
the variable expression 5n.
7.13a
Sorry, Wrong Answer!
Remember
the rules of
“than”, “from”
and “to”.
Read,
STOP,
Think,
then
Answer!
7.13b
Sorry, Wrong Answer!
7.1a
Sorry, Wrong Answer!
Use the pattern we discovered in class, shown below,
and what you know about place value to help you
answer the question!
3
10
1,000
1000
1
2
10
100
100
1
10
10
10
1
0.1
10
1
1
1
1
10
1
10
0
−1
7.1b
Sorry, Wrong Answer!
1. Place a decimal point after the first natural number
(counting numbers).
2. Count the number of spaces you moved the decimal point!
3. Write your “x 10”.
4. Tack on your exponent (step 2).
7.1c
Sorry, Wrong Answer!
7.1d
Sorry, Wrong Answer!
The square root of a number can be
represented geometrically as the
length of a side of the square.
9=3
There are 9 small
squares that make
the larger square.
The side of the large
square is 3 units.
Draw a picture or think about what number times itself will give you the same product as
the number under the radical sign to help you figure out the answer!
7.1e
Sorry, Wrong Answer!
The absolute value of a number is the distance
from 0 on the number line regardless of direction.
Use the number line to help you answer the question!
7.3
Sorry, Wrong Answer!
Use your number
line, these rules, or
draw counters to
help you solve the
problem!