Ratios & Unit Rates
A pack has 6 juice boxes for $3. What is the cost per juice box?
Answer: $0.50
Simplify:
7x + 3x
10x
Solve:
x + 9 = 14
X = 5
Find the mean:
6, 8, 10, 15, 20, 25
Mean = 14
Find area: rectangle (l=14, w=15)
Area = 210
Plot (4, 1). Which quadrant?
Quadrant I
Find the median:
1, 3, 5, 7, 9
Answer: 5
A runner travels 12 miles in 3 hours. What is the unit rate?
Answer: 4 miles per hour
Are these equivalent?
2(x + 5) and 2x + 5
Answer: No
Solve:
5x = 35
X = 7
Find the median:
2, 5, 7, 9
Median = 6
Find area: triangle (base=12, height=4)
Area = 24
Plot (-3, 2). Which quadrant?
Answer: Quadrant II
Find the IQR:
Q1 = 4, Q3 = 12
Answer: 8
Compare:
Answer: 8 for $4 ($0.50 each is cheaper than $0.75)
Simplify:
3(4x + 2)
Answer: 12x + 6
Solve:
x − 2 ≤ 6
Answer: x ≤ 8
Find the range:
4, 10, 12, 20
Range = 16
Find volume: 15 × 30 × 20
Volume = 9000
Distance between (2,3) and (2,9)
Answer: 6
Data: 2, 4, 6, 8
Mean = 4
Find MAD
MAD = 2
Solve: 7/x = 21/9
X = 3
Write an expression:
“4 times a number decreased by 3”
Answer: 4x − 3
Graph:
x ≥ 1
Answer: Closed circle at 1, shade right
Which is most affected by outliers?
The Mean
Surface area of cube with side 4
Answer: 96
Plot (0,0), (3,0), (3,3). What shape?
Answer: Right triangle
Which has greater spread:
IQR of 6 or IQR of 10?
Answer: IQR of 10
A recipe uses 5 cups of flour for 20 cookies. How many cups are needed for 50 cookies?
Answer: 12.5 cups
Simplify:
5x + 6 − 2x + 4 + x
Answer: 4x + 10
A number multiplied by 3 equals 27. What is the number?
Answer: 9
Data Set A: 8, 8, 8, 8
Data Set B: 2, 6, 10, 14
Which has more variability?
Answer: Data Set B
Volume: 1/2 × 2 × 3
Answer: 3
(0,1), (0,5), (4,5), (?)
Answer: (4,1)
Data A: 5, 5, 5
Data B: 3, 5, 7
Which has greater MAD?
Answer: Data B
A student says: “If 4 pencils cost $2, then 10 pencils cost $6.”
Is this correct? Explain.
Answer: No, unit rate is $0.50 → 10 pencils = $5
Explain why:
3(x − 2) = 3x − 6
Answer: Distributive property
Solve and explain:
4x + 2 = 42
X = 10
Explain why the median is useful when data has extreme values.
Answer: It is not affected by outliers
A prism is 6 × 2 × 3. If length doubles, what is new volume?
Answer: 72
Point moves from (2,2) to (7,5). Describe change.
Answer: +5 in x, +3 in y
Box plot shows Q1=2, Median=6, Q3=8
What is IQR and what does it represent?
Answer: IQR = 6; spread of middle 50%