Real Numbers & Expressions 1
Order the following from least to greatest:
7%, 1/3, 0.2, 0.26, 1/12, 2/9
7%, 1/12, 0.2, 2/9, 0.26, 1/3
Jodie is painting a room. The room consists of four walls measuring 17 feet in length and 11 feet tall. If 1 gallon of paint covers about 432 square feet, approximately how many cans of paint does Jodie need?
square footage = 17•11•4 = 748 ft2
# of cans = 748 ÷ 432 = 1.73 cans (round up to 2 cans)
What is the shape of a linear function?
straight line
What is the slope of the line that passes through the points (-6, 1) and (4, -4)?
m = (-4 - 1) / (4 - -6) = -5 / 10
m = -1/2
Jackie is 12, Sam is 15, and Kayla is 16. Find the range of their ages.
4
Which symbol goes in the blank to make the statement true?
√28 ___ 29/5
<
Rewrite the expression using the distributive property:
3x(x - 4)
3x2 - 12x
Which equations represents a line that is parallel to the x-axis?
A. x = 5
B. y = 10
C. y = 1/2x + 3
D. y = 4x
B. y = 10 (horizontal line)
What is the y-intercept of 4x + 2y = 12?
6 or (0, 6)
substitute x = 0:
4(0) + 2y = 12
2y = 12
y = 6
What is the interquartile range of the data set listed below?
4, 5, 8, 11, 14, 17, 20
12
upper quartile = 17
lower quartile = 5
IQR = 17 - 5 = 12
Simplify the expression (2x3)2.
4x6
Which ordered pair is in the solution set of the system of equations?
y = -x + 1
y = x2 + 5x + 6?
A. (-5, -1)
B. (5, -4)
C. (-5, 6)
D. (5, 2)
B. (-5, 6)
6 = -(-5) + 1 is TRUE
6 = (-5)2 + 5(-5) + 6 is TRUE
Which equation represents a line that is parallel to the line y = -4x + 5?
A. y = -4x + 3
B. y = -1/4x + 5
C. y = 1/4x + 3
D. y = 4x + 5
A. y = -4x + 3 (same slope)
What is the x-intercept of y = -2x + 6?
3 or (3, 0)
substitute y = 0:
0 = -2x + 6
2x = 6
x = 3
Which statement is true about the data set below?
3, 4, 5, 6, 7, 7, 10
A. Mean = Mode
B. Mean > Mode
C. Mean = Median
D. Mean < Median
C. Mean = Median
Median = 6 (middle number)
Mean = 6 (42 ÷ 7)
Rewrite as a simplified radical:
√18 + √8
√18 = 3√2
√8 = 2√2
3√2 + 2√2 = 5√2
Simplify:
(9x2 - 3x - 6) + (-3x2 - 7x - 3)
6x2 - 10x - 9
Pam is playing with red and black marbles. The number of red marbles she has is three more than twice the number of black marbles she has. She has 42 marbles in all. How many red marbles does Pam have?
29 red marbles
x + y = 42
x = 3 + 2y
3 + 2y + y = 42 -> y = 13
x = 3 + 2(13) -> x = 29
What is the equation of the line with a slope of 4 that passes through the point (3, -10)?
y = 4x - 22
y = 4x + b
-10 = 4(3) + b
-10 = 12 + b
b = -22
A scatter plot compares shoe size (s) to height (h), in cm. The equation for its line of best fit is s = 2/9(h - 140).
Use the equation to predict the shoe size of a person who is 7 feet tall (about 213 cm).
size 16
s = 2/9(213 - 140)
s = 2/9(73)
s = 16.2
Find the GCF and LCM of the following monomials:
18x3y2z and 12x4y4
GCF = 6x3y2
LCM = 36x4y4z
Jim likes to go fishing on Lake Chippewa every Saturday. He usually catches between 12 and 20 fish. If only half of those fish are big enough to keep, then about how many fish does Jim take home in 7 weeks?
56 fish
He catches about 16 per week and keeps half, which is 8. Over 7 weeks, he keeps 8•7 = 56.
Jack bought 3 slices of cheese pizza and 4 slices of mushroom pizza for a total cost of $12.50. Grace bought 3 slices of cheese pizza and 2 slices of mushroom pizza for a total cost of $8.50. What is the cost of one slice of mushroom pizza?
$2
3c + 4m = 12.50
3c + 2m = 8.50
2m = 4
m = 2
What is the equation of the line perpendicular to y = 3x + 5 and that passes through the origin?
y = -1/3x + 0 or y = -1/3x
slopes are opposite reciprocals (3/1 -> -1/3)
y-intercept (b) = 0
Enrique played 4 rounds of golf and ended up with scores of 80, 77, 89, and 84. What does he need in his next round to have a mean score of 80?
70
(80+77+89+84+x) / 5 = 80
(330+x) / 5 = 80
330 + x = 400
x = 70