Rational and Irrational Numbers
1. What numbers listed below are rational?
1
1
√3 − √2 −
3
2
𝜋 .555555 …
2
9
2. Using the numbers listed in question 1, which of the numbers are irrational?
3. Determine the fraction equivalent for 0.8333333……….
4. Draw a number line and place the following numbers on it.
√4 √2 √42 √23 𝜋 √62 − 20
5. Which of the following equations are correct?
1
√81
√9
=9
=
92 − 32 = 3
√9 = 3
3
√9
√81
6. Evaluate:
44
− √81 = −9
Properties of Exponents
4
7. Evaluate: 2−3
8. Evaluate: (2𝑥 2 )3
9. Evaluate: 3−2 ∙ 34
10.Replace a, b, c to make a true statement.
(2𝑎 )𝑏 ∙ 2𝑐 = 22
32 = 9
− 92 = 81
Functions and Function Rules
11.Does the data in the table represent a function? Explain.
input
3
output -3
3
2
5
4
5
5
6
9
12.Using the table of values below - write the rule for y in terms of x.
X
y
0
-1
1
2
2
5
3
8
13.Select all below that mean the same as, “three times a number increased by 2”
 (0,0), (3,3), (5,5)
 𝑦 = 3x + 2
 (0,2), (−1, −1), (2,8)
 Output 0 input -1
 Input -1 output 0
14.You want to use the data from a function to make a prediction. Would a functions
generated by a mathematical rule or a function lacking a mathematical rule lead to a
more accurate prediction? Justify your answer.
15. Each molecule of water contains 2 hydrogen atoms and 1 oxygen atom. Is the number
of hydrogen atoms a function of the number of oxygen atoms? Explain.
Square and Cube Roots
16. If x2 = 0.64, what does x =?
17. A cube has a volume of 27 cubic units. What is the length of the side of the cube?
18.Circle all of the integers from the list below that are perfect squares.
49 75 50 81 -100 9 121 145 144
19. The area of a square is 2.25 m2. What is the length of each side of the square?
20. The square root of 151 is between which two integers?
Scientific Notation
21. Evaluate:
( 4.1 × 107 ) × (1.9 × 10−3)
22. Evaluate:
(4.1 × 108 ) ÷ (2 × 105 )
23. The Great White Shark can detect 1 part of blood in 100 million parts of water. Express
this ratio in scientific notation.
24.Write the expression below as one scientific number.
(3 × 103 )(2 × 105 +2 × 105 )
6 × 107
2
25. Is 8 × 103 written in scientific notation. Explain your reasoning.
Slope
Given these two equations:
𝑦 = 2𝑥
𝑦 = 2𝑥 + 3
26. Make a table for each equation.
27. Graph each equation on the same grid.
28.Use the equations, the graph and table, explain the role of b in the equation
𝑦 = 𝑚𝑥 + 𝑏
29. How is slope used? What does it mean?
30. Write an equation of a line that has 0 slope. Write an equation of a line that has an
undefined slope. How are these equations similar and how are they different?
Solving Linear Equations
31. Solve: 4𝑥 + 5 = 2𝑥 + 11
32. Solve: 2(𝑎 + 1) =
1
2
(4𝑎 − 2)
33. Given 3𝑥 = 𝑎𝑥 + 𝑏 What values of a and b will result in infinitely many solutions?
34. Solve: 2(3𝑥 − 8) = 32
35. A square and an equilateral triangle have the same perimeter. Each side of the triangle
is 4 inches longer that each side of the square. What is the perimeter of the square?
Solving Systems of Equations
36.What is the solution to a system of equations?
37. Two numbers have a sum of 10. If you add the first number to twice the second
number, the result is 8. What are the two numbers? Write equations then solve.
38.Find the solution for the system given: 𝑦 = 𝑥 − 1
39.Find the solution for the system given: 3𝑥 + 2𝑦 = −10
1
3𝑥 − 4𝑦 = 8
2𝑥 + 3𝑦 = 0
40.Mrs. Jones spent $30 to buy 9 pounds of ground beef and chicken for a family cook2
out. If the price of ground beef was $3.50 per pound and chicken was $3.00 per pound,
how many pounds of each did she buy?
Proportional Relationships
41. Liz’s car traveled 420 miles and used 9 gallons of gasoline.
How many miles did Liz drive on one gallon of gas?
42. A tub fills with 2 quarts of water every 1.5 minutes. What is the rate at which the
sink is being filled in an hour? Construct a graph to represent the situation.
43.Compare the table below and the equation 3𝑥 + 4𝑦 = 5.
Which has a greater rate of change?
x
y
-2
2
0
3
2
4
4
5
44. Which of the following is the fastest unit rate? Justify your answer.
2,200 feet per minute
30 miles per hour
700 yards per minute
40 feet per second
45. Compare the two functions give. Explain which function has the greater rate of change.
How did you determine your answer?
2𝑦 = 5𝑥 + 4
2𝑥 − 𝑦 = 5
Volume of cylinders, cones, and spheres
46. Nicole is on a softball team at school. The regulation size of a softball is 3.75 inch
diameter. What is the volume of the softball? Use π = 3.14
47. Jenny want to have a waffle cone at the pudding shop. The diameter of the cone is 3
inches and the height is 7 inches. How much pudding can fill the waffle cone? Use
π=3.14
1
1
48.A 5 quart pail of ice cream has a diameter of 8 inches and a height of 7 inches. Find
8
2
the volume of the pail of ice cream to the nearest cubic inch. Use π = 3.14
49. John has 2 containers to store spaghetti sauce. One is in the shape of a rectangular
prism with dimension of 5 inches by 5 inches and 8 inches tall. The other is in the shape
of a cylinder with a diameter of 6 inches and a height of 8 inches. Which of the two
containers will hold the most sauce? Explain your reasoning.
50.Stephanie has a cone vase that is 12 inches across and 24 inches tall. She also has a
cylinder shape vase that is 12 inches across and 8 inches high. What will be the ratio of
the volume of the cone to the volume of the cylinder? Explain your reasoning.
Initial Value and Rate of Change
Use the graph below to answer questions 1-3.
This graph represents the money Sara has in her savings account.
51. What is the rate of change for this relationship?
52.What is the initial value?
53.Write the equation to represent Sarah’s savings account.
54.Jim sells lemonade for $0.50 per glass. Create a table representing 0 – 3 glasses of
lemonade sold.
55.Draw the graph for the relationship in problem 4. What is the rate of change?
Function Models
56. Draw the graph of a person on a bicycle traveling at a constant speed and then slowing
down to a complete stop.
57.Draw a graph to represent a person’s height from the ground when swinging on a swing.
58.Draw a graph to represent a person’s distance from the ground while riding a Ferris
wheel.
59.Draw a graph to represent the speed of a car approaching a stop sign.
Transformations
Plot triangle ABC with coordinate A (2,2), B (6,5), C (8,2)
For questions 61-65 plot each transformation on the same graph.
60.Translate left 3, down 2.
61. Reflect over the y-axis
62.Reflect over the x axis.
63.Rotate 90 degrees counter clockwise about the origin.
64.Dilate the triangle by a factor of 2.
Angles
In the figure below angle 1 = 65° and angle 2 = 50°.
65 Find the measure of angle 6.
66.Find the measure of angle 3.
Use the figure below to answer question 67-69.
Lines A and B are parallel and cut by transversal t.
67. If the measure of angle 4 is 92°, what are the measures of angles 1 and 5? Explain your
reasoning.
68.If the measure of angle 8 is 108°, what are the measures of angles 2 and 7? Explain your
reasoning.
69.If the measure of angle 3 is 35°, what are the measures of angles 6 and 7? Explain your
reasoning.
Pythagorean Theorem
70. A triangle has side lengths of 8, 15, 25. Is it a right triangle?
Explain.
71. What is the length of the diagonal of a flat screen monitor if the length is 18 inches and
the height is 10 inches?
72.The diagonal of a rectangular picture frame is 12 inches and its length is 9 inches.
What is the width of the picture frame?
73.Use the coordinate plane to find the exact distance between points (3,3) and (-2,-2).
Distance =
74. The handsome prince is planning to recue Rapunzel from a window in a tower 70 feet
above the ground. If he places a 75 foot ladder 5 feet from the base of the tower, will
the ladder reach Rapunzel’s window for her safe escape? Explain.