Ratios & Unit Rates
A recipe uses 2 cups of rice for 6 servings. What is the unit rate (cups per serving)?
Answer: 1/3 cup per serving
Simplify:
6x + 2x + 15 + 7
8x + 22
Solve:
x − 3 = 9
X = 12
Find the mean:
2, 4, 6, 12, 15, 20, 25
X = 12
Find area: rectangle (l=9, w=3)
Area = 27
Plot (3, 2). Which quadrant?
Answer: Quadrant I
Find the median of the data:
2, 4, 6, 8, 10
Median = 6
A store sells 8 pencils for $4. What is the cost per pencil?
Answer: $0.50 per pencil
Are these equivalent?
3(x + 4) and 3x + 4
No
Solve:
4x = 20
X = 5
Find the median:
5, 8, 12, 15, 18, 21, 24, 27, 30
Median = 18
Find area: triangle (base=8, height=5)
Area = 20
Plot (-2, -5). Which quadrant?
Answer: Quadrant III
Find the range of the data:
5, 7, 9, 12, 15
Range = 10
Compare:
Answer: Same rate (5 mph)
Simplify:
4(3x − 2)
12x - 8
Solve:
x + 6 ≥ 10
Answer: x ≥ 4
Find the range:
3, 9, 11, 14, 17, 19, 21, 24
Range = 21
Find volume: 2 × 6 × 5
Volume = 60
Distance between (4,1) and (4,6)
Answer: 5
A data set has:
Min = 2, Q1 = 5, Median = 8, Q3 = 10, Max = 14
What is the interquartile range (IQR)?
IQR = 5
Solve: X/5 = 12/15
X = 4
Write an expression:
“5 less than three times a number”
3x - 5
Graph:
x > 2
Answer: Open circle at 2, shade right
Which measure is least affected by outliers?
Median
Find surface area of a cube with side length 2
Surface Area = 24
Plot points (0,0), (4,0), (4,4). What shape?
Answer: Right triangle
Data: 4, 6, 8
Mean = 6
Find the Mean Absolute Deviation (MAD)
MAD = 4/3 or 1.33
A school uses 24 bottles of water for 8 classrooms. How many bottles are needed for 15 classrooms?
Answer: 45 bottles
Simplify:
2x + 3 + 4x − 7 + x
7x -4
A number increased by 8 is 21. What is the number?
Answer: 13
Data Set A: 10, 10, 10, 10
Data Set B: 5, 10, 15, 20
Which has more variability?
Data Set B
Volume with fractional edges: 1/2 × 1/2 × 1/2
Volume = 1/8
Missing point:
(2,2), (2,6), (7,6), (?)
Answer: (7,2)
Two data sets:
A: 3, 5, 7, 9
B: 2, 6, 6, 10
Which has greater variability using MAD?
Answer: Data Set B
A student says: “If 5 shirts cost $25, then 10 shirts cost $40.”
Is this correct? Explain.
Answer: No, unit rate is $5 per shirt → 10 shirts = $50
Explain why:
5(x + 2) = 5x + 10
Answer: Distributive property
Solve and explain:
3x + 5 = 35
X = 10
Explain why mean might be misleading with extreme values.
Answer: Outliers pull the mean higher/lower
A prism is 4 × 3 × 2. If width doubles, what is new volume?
Volume = 48
Point moves from (1,1) to (5,4). Describe change.
Answer: +4 in x, +3 in y
A box plot shows:
Which section has the greatest spread?
Answer: Q3 to Max (9 to 15)