8th Grade Study Guide
Quarter 1
M8D3.a Find the probability of simply independent events
1. What is the probability of landing on heads if you flip one coin?
2. Kyle is one of 7 actors trying out for a part in a production at a community theater
center. If each actor is equally likely to get the part, what is the probability that Kyle will
NOT be selected?
3. What is the probability of getting a four on one roll of a number cube?
M8D3.b Find the probability of compound independent events
1. Suppose a number cube labeled from 1 to 6 is rolled and the spinner below is spun one
time. What is the probability of rolling a number less than 4 and spinning a B?
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2. Chad does a magic trick involving a deck of ten cards. The cards are numbered one
through ten. Chad asks Kristina to draw a card, look at it, and replace it in the deck. He
then asks her to draw again. What is the probability that Kristina will draw a seven both
times?
3. If you flip three coins what is the probability of landing all three coins on tails?
Squares and Square Roots
M8N1a, b: Find square roots of perfect squares and recognize the positive square
root of a number as a length of a side of a square with a given area.
1. Jack’s backyard is in the shape of a square with an area of 100 square yards.
What are the dimensions of Jack’s backyard?
2. The area of a square rug is 39 square feet. Estimate the length of each side of
the field.
3. Elizabeth would like to make a square wool rug with the area of 68 square
feet. What is the least amount of wool that she would need to use?
M8N1c: Recognize square roots as points and as lengths on a number line.
1. The
75 is between what two integers?
2. Between what two numbers is 125 ?

3. Between what two numbers is
18 ?

M8N1d: Understand that the square root of 0 is 0 and that every positive number
 opposite in sign.
has two square roots that are
1. What are the square roots of 49?
2. What are the square roots of 256?
3. What are the square roots of 0?
M8N1e: Recognize and use the radical symbol to denote the positive square root of
a positive number.
1. Simplify
64 .
2. Simplify

1
.
25
3. Simplify

9
.
36
M8N1f: Estimate square roots of positive numbers.

Round the square root to the nearest tenth.
1. 11
2. 20

3.
43
M8N1g: Simplify, add, subtract, multiply, and divide expressions containing square
roots.


Evaluate the expressions.
10 40
1.
2. 2 5 x 10
4

3. - 5
M8N1h: Distinguish between rational and irrational.



Rational or Irrational?
1. 156
2. 81
3. 
4. 28.326451982…
M8N1i: Simplify expressions containing integer exponents.



Write the following in Standard Form.
1.
54
2.
9-2
3.
(-5)2
61
4. 4
6
M8N1j: Express and use numbers in Scientific Notation.
1. Jupiter is 460,100,000 miles from the sun. What is the number written in

scientific notation?
2. Find the quotient:
8.82x105
3.6x103

3. Write 0.000096
using scientific notation.
M8G2.a Apply properties of right triangles, including the Pythagorean theorem.
1. How long is the hypotenuse of this right triangle?
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2. What is the missing side of his right triangle?
12in., 35in., ________
3. 53 is the length of the hypotenuse of a triangle with a side length of 2, what is the
length of the other side?

M8G2.b Recognize and interpret the Pythagorean theorem as a statement about areas
of squares on the sides of a right triangle.
1. The gate of a fence is 8ft tall and 15ft wide. How long is the diagonal strip used to brace
the gate?
2. A rectangular park measures 30 meters by 40 meters. How long does the diagonal path
from one corner of the park to the other corner measure?
3. Mike’s TV screen is 20 inches in length and 15 inches in width. The length of the
diagonal measures the size of a TV. What is the size of Mike’s TV?
M8D1a - Demonstrate relationships among sets through the use of Venn diagrams
M8D1b - Determine subsets, complements, intersection, and union of sets.
M8D1c - Use set notation to denote elements of a
set.
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M8D2a - Use tree diagrams to find the number of outcomes.
M8D2b - Apply the addition and multiplication principles of counting.
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3.
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5.
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