Circles and Ratios
Proportional Relationships
Transformations
Line & Angle Relationships
Linear Functions
Probability
The Real Number System & Exponents
1
How much fencing is needed to enclose a circular pond with diameter 12.5 feet? Use 3.14 for π.
12.5 * 3.14 = 39.25 feet
1
A company spends 13% of its monthly budget on rent, which totals $2600. Write a proportion that can be used to calculate the company’s total monthly budget.
13 = 2600
100 x
1
Regina drew a triangle with vertices at (1, 2), (3, 3), and (4, 1). She slid the triangle 2 units down to create an image. What are the vertices of the image?
(1, 0), (3, 1), and (4, − 1)
1
Which angles are supplements of ∠1?
∠2, ∠3, ∠6, and ∠8
1
Find the domain and range. Is this a function? Why or why not?
Domain: –3, 1, 2, 10
Range: -12, 3, 4, 5, 9
Not a function because 2 has two outputs.
1
Ilana drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that she picked a marble that is NOT red?
P(NOT red) = 11/14
1
Which statement is false?
A. All natural numbers are integers.
B. All whole numbers are natural numbers.
C. All integers are rational numbers.
D. All whole numbers are integers.
B. All whole numbers are natural numbers (Not 0).
2
The circumference of a circle is 32 centimeters. What is the length of the radius to the nearest tenth?
C = 2πr
32 ÷ (2π) = r
5.1 ≈ r
2
Your restaurant bill is $72.34. You want to leave about a 20% tip. How much is the tip?
$72.34 * 0.2 ≈ $14.47
2
Samantha drew ∆ JKL with the coordinates
(2, 3), (4, 3), and (5, 2). She
reflected this triangle across the x-axis to
create an image. What are the coordinates
of the image?
(2, − 3), (4, − 3), and (5, − 2)
2
A triangle has angle measures 23° and 35°. What is the measure of the third angle?
180º – (23º + 35º) = 180º – 58º = 122º
2
Find the domain and range. Is this a function? Discrete or continous? Linear or nonlinear?
Domain: –3 < x ≤ 1
Range: –4 ≤ y ≤ 0
It is a continuous, nonlinear function.
2
Breanna is conducting an experiment with a number cube. She rolled the cube 24 times. How many times could she expect the cube to land on 6?
P(6) = 1/6
24 * 1/6 = 4 times
2
What decimal is equivalent to 7/22? Show work using long division and write your answer using bar notation.
0.318
3
The circumference of a circle is 18π feet. What is the area in terms of π?
C = 2πr
C ÷ (2π) = r
18π ÷ (2π) = 9
A = πr2
A = 92π
A = 81π
3
Karen deposits $375 into a savings account that earns simple interest at a rate of 4% per year. She wants to use the interest to buy a new camera. How much will Karen have by the end of 5 years?
Simple interest: I = Prt
I = $375 * 0.04 * 5
I = $75
3
Blake drew Triangle ABC with coordinates A (7, 9), B(8, 4), and C (7, 6). He drew an image of the triangle ΔDEF with coordinates D (− 9, 7), E (− 4, 8), and
F (− 6, 7). How did he make the image?
He rotated ∆ABC 90° counterclockwise about the origin to create ΔDEF.
3
List the side lengths in order from
shortest to longest.
m∠P = 180º – (23º + 77º) = 180º – 100º = 80º
m∠W < m∠T < m∠P, so the side lengths in order from shortest to longest are:
Segment PT, Segment PW, Segment TW
3
Find the slope of the line that passes through the points (0, 6) and (3, –3).
m = y2 – y1
x2 – x1
m = –3 – 6
3 – 0
m = –9
3
m = –3
3
Adeline sets her music player to randomly select songs from her collection. She has 9 country songs, 11 jazz songs, 3 rap songs, and 6 pop songs. What is the probability that the next song is a rap song or a pop song?
P (rap song or pop song) = 9/29
3
Simplify − (32 ∙ 33)3.
− (32 ∙ 33)3
–(35)3
–315
4
A circular marble tabletop has a diameter of 42 inches. If the tabletop costs $280, what is the price per square inch?
Price per square inch
Price ÷ area
$280 ÷ (πr2)
$280 ÷ [(42/2)2π]
$280 ÷ (212π)
$280 ÷ (441π)
$0.20
4
The $199.99 digital camera Anne purchased was on sale for 15% off. How much will Anne need to pay?
$199.99 * (100% – 15%)
$199.99 * 85%
$199.99 * 0.85
$169.99
4
Triangle EFG is dilated with a scale factor of 1/2 to create ΔE′F′G′. The measure of ∠F′ is 36°. What is m∠F?
36º (dilations preserve angle measures)
4
What is the measure of each angle?
3x + 14 = 7x – 46
60 = 4x
15 = x
Each angle is 3(15) + 14 = 45 + 14 = 59º.
4
Graph the linear equation: y = –2x + 4
4
Which experiment has a non-uniform probability model? Select all that apply.
A. Tossing a fair coin one time
B. Spinning a spinner with sections that are different sizes
C. Spinning a spinner on which all sections are the same size
D. Tossing a pair of number cubes and determining the sum of the numbers that land up
E. Pulling a red marble out of a bag with 6 red marbles, 3 green marbles, and 1 yellow marble
B, D, and E
4
What fraction is equivalent to 0.757575... or 0.75?
100x = 75.757575...
– x = 0.757575...
99x = 75
x = 75/99
x = 25/33
5
One medium circle and one small circle touch each other, and each circle touches the larger circle.
What is the area of the shaded region? Express your answer in terms of π.
Largest circle area – (areas of two smaller circles)
132π – (92π + 42π)
169π – (81π + 16π)
169π – 97π
72π cm2
5
At Outdoor Adventures Clothing Company, all items are marked up to maximize profit. Life preservers costs $23 to buy from the manufacturer. They sell for $35. What is the percent increase on life preservers, to the nearest whole percent?
Percent change formula =
(New value – original value) * 100
original value
($35 – $23) * 100
$23
($12) * 100
$23
52%
5
Triangle FUN, with vertices F (− 2, 4), U (0, − 5), and N (− 3, − 8), was dilated to form ΔPET with vertices
P (− 1.6, 3.2), E (0, − 4), and
T (− 2.4, − 6.4). Which scale factor was used?
k = Image / Preimage
k = 0.8 or 4/5
5
Find the measures of ∠A and ∠B.
3x – 13 + 2x + 4 = 116
5x – 9 = 116
5x = 125
x = 25
m∠B = 2(25) + 4 = 54º
m∠A = 116º – 54º = 62º
5
Explain why it's nonlinear — don't write just the letter!
D because the rates are not constant.
12/2 = 6
48/4 = 12
36/2 = 18
5
You spin the spinner twice and record the sum of the numbers you get. What is the probability that the sum is 5?
P(sum of 5) = 2/9
5
How can you use the Properties of Powers to evaluate the expression
(32 ∙ 3−2 )2 ?
33
(32 ∙ 3−2 )2
33
(30 )2
33
30
33
1
27