6th Grade Pre-Algebra
Chapter 9
Are You Ready?
Calculators Allowed
Name:
Date:
Block:
Vocabulary
1.) Draw a right triangle and label the legs and hypotenuse:
2.) Pythagorean Theorem: ___________________________________________________________________
3.) Rational Number: ________________________________________________________________________
4.) Irrational Number: _______________________________________________________________________
5.) Midpoint Formula: ____________________
6.) Distance Formula: ____________________________
Skills
Find the square ROOTS of the numbers.
7.) 256
8.) 400
9.) What two perfect squares are closest to √86?
Use a calculator to approximate to the nearest tenth.
10.) √97
-
11.) −√17
Evaluate the following expressions for when a = 12 and b = 4, round to the nearest tenth if
necessary.
12.) √𝑎2 − (𝑏 + 15)
13.) √𝑏 2 − 𝑎
14.) 3√𝑎𝑏 + 1
Solve each equation, round to the nearest tenth if necessary.
15.) 𝑥 2 = 196
16.) 3𝑥 2 = 675
17.) 3𝑥 2 + 5 = 30
18.) 1.5𝑛2 + 7 = 20
19.) (𝑥 − 2)2 + 1 = 37
Simplify the expression.
11
36
20.) √
21.) √
28𝑓2
9
Find the unknown length, round to the nearest tenth if necessary.
22.) 𝑎 = 6, 𝑏 = ______, 𝑐 = 10
23.) 𝑎 = 20, 𝑏 = 31, 𝑐 = _____
24.)
Circle whether the number is rational or irrational.
25.) √45
rational
irrational
26.)
2
7
Complete using <, >, 𝑜𝑟 =.
4
4
27.) √5 ____ 5
28.)
rational
irrational
Order from least to greatest.
7
− 2 _____ − √16
29.) 6.7,
√40,
40
3
,
169
√
4
_______ _______ _______ ______
Find the DISTANCE between the given points. Round to the nearest tenth if necessary.
30.) (2, 7) (9, 8)
31.)
Find the MIDPOINT of the segment with the given endpoints.
32.) (3, −9) (−4, 3)
33.)
Applications
Answer the following questions showing ALL WORK necessary! Be sure to label
your answer when necessary.
34.) A chipmunk drops a nut from the deck
of a house 24 feet above the ground. Use
the equation 𝑑 = 16𝑡 2 to determine the time
𝑡, in seconds, that it takes the nut to fall to
the ground.
36.) The diagram shows how a post was
broken. What was the original height of the
post?
35.) Bobby left his house riding his bike 20
miles south then 15 miles east to get to his
friend’s house. What is the shortest distance
between Bobby’s house and his friend’s
house?
37.) A builder needs to add diagonal braces
to a wall. The wall is 16 feet wide by 12 feet
high. What is the length of each brace?
24 inches
18 inches
̅̅̅̅ has endpoint A(-3, -4) and B(-7, -8) . 𝑃𝑄
̅̅̅̅ has endpoints P(3,2) and Q(9, 8). Which segment is
38.) 𝐴𝐵
longer?
39.) Draw the right triangle with vertices X (-3, 2), Y (-3, -7), and Z (5, 2).
Then find the coordinates of the midpoint of the hypotenuse.
y
x
Writing
Answer the following question in complete sentences. Be sure to USE EXAMPLES and correct math
terminology when possible.
40.) Explain why √3 is an irrational number. Give an example of a rational number.
41.) The area of a square is 7 square meters. Is the perimeter of the square a rational or irrational
number of meters? Explain.