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Math Review
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Math Concept Review (7th)
Number Sense and Operations.
Classify numbers. Counting numbers
(also called natural numbers): 1, 2, 3, etc.
Whole numbers: 0, 1, 2, 3, etc.
Integers: positive and negative whole
numbers, and 0: …-3, -2, -1, 0, 1, 2, 3…,
etc.
Write the prime factorization of a number.
A number in prime factorization form is
written as the product of prime numbers.
Example the prime factorization of the
number 20 is 2 x 2 x 5 = 22 x 5.
Write 28 in prime factorization form.
How is the number -7 classified?
Understand exponents. An exponent
represents repeated multiplication.
Example base →43←exponent
43 means 4 x 4 x 4 = 64
Example 4 squared = 4 x 4 = 42
The base 4 is multiplied 3 times, indicated
by the exponent 3.
3
What is the value of 2 ?
Use scientific notation. In scientific
notation, a number is written as the product
of:
 A number that is greater than 0 and
less than 10
 And a number that is a power of 10
Example 5,280 = 5.28 x 10
Write the square of a number. The square
of a number is the product of a number
times itself, usually written with an
exponent.
3
Write 460 in scientific notation.
Identify prime numbers. A prime number
is a whole number greater than 1 that has
only two factors: itself and the number 1.
Example the number 7 is a prime number.
The only factors of 7 are 1 and 7. 7 = 1 x 7
Name all prime numbers that are less
than 10.
What is the value of 62?
Find the square root of a number.
The square root of a number is one of its
two equal factors. To find the square root,
ask, “What number times itself equals this
number?” the symbol for square root is √.
Example √36 = 6 because 6 x 6 = 36.
What is the square root of 25?
Write a ratio. A ratio compares two
numbers by division.
Example in a group of 6 girls and 8 boys,
the ratio of girls to boys is six to eight:
which reduces to .
What is the ratio of boys to girls?
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Math Review
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Understand the concept of rate.
A rate is a ratio that compares quantities of
different units.
Example miles per hour, price per pound,
and beats per minute.
What two units are compared in the rate
feet per second?
Solve a simple proportion.
A proportion says that two ratios are equal.
A proportion is written as two equivalent
fractions.
Example
Determine absolute value.
Absolute Value is a number’s value when
the sign of the number (positive or
negative) is ignored. The symbol for
absolute value is ││. Absolute value is the
distance from 0 to the number on the
number line.
Example │+7│ = 7 and │-7│ = 7
What is the │-8│?
Understand decimal forms of a fraction.
A terminating decimal has digits that do
not repeat indefinitely.
Examples ½ = 0.5; ¼ = 0.25.
=
In the proportion = , what is the value
of x?
A repeating decimal has digits that repeat
without end.
Examples 1/3 = 0.333…; 2/3 = 0.666…,
and so on.
Identify percent as part of a whole.
Percent (%) means parts out of each 100
equal parts.
Written as a decimal, is 1/6 terminating
or repeating?
Example 5% is 5 parts out of each 100
equal parts. 5% of $1.00 is $0.05.
What is 65% of $1.00?
Order numbers on a number line.
Positive number any number greater than
zero, located to the right of zero on a
number line.
Negative number any number less than
zero, located to the left of zero on a number
line.
Negative numbers │ Positive numbers
•---•---•---•---•---•---•---•---•---•---•
-5
-1 0 1
5
Place -2 and 4 on the number line.
Understand order of operations. The
order of operations is the order in which
an expression is evaluated:
1st
Find the value of the number within
parentheses.
nd
2
Find the value of the numbers with
exponents.
rd
3
Perform multiplication or division,
working left to right.
th
4
Perform addition or subtraction,
working left to right.
Example 2(8 – 5)2 + 3 = 2(3)2 + 3
=2(9) + 3
=18 + 3
=21
Find the value of 3(6 – 4)2 – 9
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Math Review
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Algebra
Represent a number by a variable.
A variable is a letter that stands for a
number.
Example x + 7
The value of an expression is known only
when the value of each variable is given.
Solve a one-step equation.
A one-step equation is solved in one
inverse operation.
Example x + 5 = 9
To find x, subtract 5 from each side:
x+5–5=9–5
x=4
Solve for x: x – 8 = 10
Find the value of x + 7 when x = 4.
Use substitution to evaluate an algebraic
expression. An algebraic expression
contains one or more variables and
constants (numbers).
To evaluate an expression, substitute a
number for each variable.
Example 3x – 9; When x = 5, the value of
3x – 9 is 3(5) – 9 = 15 – 9 = 6.
If n = 3, what is the value of 2n + 6?
Evaluate a formula. A formula is a rule
that shows a relationship.
Example P = 3s (The perimeter P of an
equilateral triangle equals 3 times s, the
length of each side.)
Using A = πr2, find the value of A when
r = 6ft, and π = 3.14.
Understand inverse operations.
An inverse operation undoes another
operation.
Addition and subtraction are inverses:
4–2+2=4
Multiplication and division are inverses:
4x2÷2=4
What is the inverse operation of
multiplying by 9?
Solve a one-step inequality.
An inequality compares two numbers.
Examples n > 4 says that n is greater than
4; x + 3 < 8 says that x plus 3 is less than 8
To solve a one-step inequality, perform the
inverse operation on each side of the
inequality.
Example to solve x + 3 < 8, subtract 3 from
each side:
x+3–3<8–3
x<5
Solve the inequality x – 3 > 2.
Geometry
Identify parts of a circle. The parts of a
circle are indicated below. A chord is a
line segment that connects any two points
on the circle.
radius
diameter
chord
What is the ratio of the diameter of a
circle to its radius?
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Use circle formulas to find unknowns.
Example If the circumference = 6, what is
the diameter, d? Use C = πd
First solve for d: C ÷ π = πd ÷ π
C÷π=d
Substitute 6 for C. 6 ÷ 3.14 ≈ 1.9
Calculate volume. The volume (V) of a
rectangular prism is given by the formula
V = lwh (length x width x height)
The volume (V) of a cylinder is given by
the formula V = πr2h (area of circular base
x height)
r
Example
h
V= lwh
V = πr2h
Find the volume of the rectangular prism
shown above.
Identify the faces and bases of 3dimensional shapes.
base
↓
Find the area and surface area. The
surface area of a figure is the sum of the
area of each surface of a figure.
Rectangular Prism.
Surface area = 2lh + 2lw + 2hw
Cylinder
r
h
Surface area = 2πr2 + 2πrh
What is the surface area of a rectangular
prism that is 8 feet long, 3 feet wide and 2
feet high?
Understand similar figures. Similar
figures have the same shape but may not
have the same size. Corresponding sides
are in proportion, and corresponding angles
are equal.
Vertex→
←face
Example.
Edge→
6 faces
B
Y
↑ base
How many faces does the pyramid have?
(Be sure to count any faces you cannot
see!)
X
Z
A
C
∆XYZ is similar to ∆ABC
Which side of triangle ABC corresponds
to side YZ of triangle XYZ?
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Math Review
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Statistics and Probability
Identify coordinates of a point.
A coordinate plane uses two axes to locate
a point. The point (x,y) is an ordered pair
in which the x-coordinate is written first,
followed by the y-coordinate.
Example point A has coordinates (-4,3)
name the coordinates of point B.
Find the mean, median, mode, and range
of a set of data.
Consider the set: {1, 1, 5, and 9}
To find the mean, add the numbers and
then divide the sum by the number of
addends (numbers added).
Example mean: (1 + 1 + 5 + 9) ÷ 4 =
16 ÷ 4 = 4
The median is the middle value, or the
average of two middle values.
Example median: (1 + 5) ÷ 2 = 3
Name the coordinates of point B.
Measurement
Understand weight/mass units.
Customary units of Weight
1pound (lb) = 16 ounces (oz)
1 ton (t) = 2,000 pounds
Metric Units of Mass
1 gram (g) = 1,000 milligrams (mg)
1 kilogram (kg) = 1,000 grams
Comparing Units
1 pound ≈ 450 grams
1 kilogram ≈ 2.2 pounds
Understand central angle.
A central angle has its vertex at the center
of a circle; its sides are radii.
←central angle
The mode is the number t hat occurs most
frequently in a set of numbers
Example mode: 1
The range is the difference between the
greatest and least values.
Example range 9 – 1 = 8
For the set {3, 4, 6, 7, 7, 9} find:
mean _____ median _____
mode _____ range _____
List all outcomes (sample space) in a
probability experiment. An outcome is a
possible event. The sample space is a list of
all possible outcomes.
Example the sample space for tossing two
coins is:
(H, H), (H, T), (T, H), (T, T).
List the sample space for tossing three
coins.