MATH 8 UNIT 6 PRACTICE TEST NAME _____________________________PER.
_____
Show all your work. Circle your final answers so they are easy to identify.
LEAVE ALL DECIMALS ROUNDED TO THE NEAREST TENTH!
Solve for the variable (HINT: To solve an equation, un-do the operation.)
1. x2 = 16 2. √𝑥 = 3 3. x3 = 125 4. √𝑥 = 4
3
5. x2 = 225 6. √𝑥 = 17 7. x3 = 729 8. √𝑥 = 11
3
9. Label the sides of the triangle (a, b & c). ALSO, label which side is the hypotenuse and
which are legs.
State the Pythagorean Theorem:
10. If ____________________________ then _____________________________.
State the Converse of the Pythagorean Theorem:
11. If ____________________________ then _____________________________.
Find the missing side length on each right triangle.
12. ______________ 13. _______________ 14. ________________
X X 74 70
9
41
12 X
15. _______________ 16. _________________ 17. ________________
12 4
X
17 6 X 3
X
3
The side lengths for a right triangle are given. Which length on each problem represents the
hypotenuse? Circle the correct answer.
18. 20, 29, 21 19. 25, 144, 13
Tell whether the triangle with the given side lengths is a right triangle. Show your Work.
20. 8, 15, 17 21. 10, 12, 21 22. 1, 3, 6
23. 24. 25. 21
20 101 12 220
10 221
99
5
26. Mitch needs to wash the windows on the second floor of a building. He knows the windows
are 12 feet above the ground. Because of dense shrubbery, he has to put the base of the ladder
5 feet from the building. What ladder length does he need?
27. Tyler is framing a house. The length of the house is 45 ft. The width is 20 feet. Once the
outside walls are framed, Tyler measures the diagonal. It measures 51.5 ft. to the nearest
tenth. Draw a Picture and determine if Tyler has a perfect rectangular house?
Determine the distance between each pair of points by graphing and connecting the points,
creating a right triangle, and applying the Pythagorean Theorem.
28. (-1,1) and (4, 5) 29. (-3, 4) and (2, -5) (first graph the points)
30. Given the rectangle inscribed in a Circle. Find the following lengths and Areas.
(Hint Area of a Circle = 𝝅𝒓𝟐 , the radius (r) is half the diameter, Area of a Rectangle = lw)
Diameter: _________
Radius: __________
16m
Area of the Circle: _______
30m
Area of the Rectangle: ______
Area of the Shaded Region: _____
UNIT 6 HONORS PRACTICE QUES. NAME _____________________________PER. _____
1. Is 15, 20,25 a Pythagorean triple? Explain why or why not.
2. Solve for x: √𝑥 = 10.3 _____ 3. Solve for x: 𝑥 4 = 625 ______
4. Use the Pythagorean Theorem and find the missing side
X
1/8
6.576
5. A 24-ft cable is stretched from the top of an antenna to an anchor point on the ground 14
feet from the base of the antenna. Draw a Picture and determine the height of the
antenna?
6 & 7 Use the Pythagorean Theorem to find the missing lengths.
a = _____
b = _____
The figure is composed of a right triangle and a semi- 10. Find the length of the diagonal of
circle. The hypotenuse of the right triangle is the the 3-dimentional Rectangular Figure.
same length as the diameter of the semi-circle.
8.Find the area of the triangle
(Hint Area = 1/2bh)
10m
9. Find the area of the whole
Shape (Hint: Area of a
6 in 5 in. Semi-Circle = 1/2 𝝅𝒓𝟐 ) 3.5 m
5m
