Lines & Points
What is the distance between (1, -2) and (1, 6)?
A. 0 B. 10 C. 4 D. 8
Since the x-coordinates are the same, the distance is simply the difference in y-values:
6 - (-2) = 8
.
In the exponential function:
y = 18.3(0.73)^x, what is the starting value?
A. 27 B. 0.73 C. 18.3 D. 0
C. 18.3
What is the rate of change (slope) for the linear equation y = -2x + 6?
A. 2 B. 0 C. 6 D. −2
D. −2
In the form y=mx+b, m is the rate of change.
What is the length of the hypotenuse of a right triangle with legs of length 3 and 4?
A. 5 B. 25 C. 12 D. 7
A. 5
In Chicago, the 'L' is the famous train system. What does the 'L' actually stand for?
A. Linear B. Loop C. Local D. Elevated
D. Elevated
It is short for 'elevated,' referring to the tracks that run above the city streets.
Using the points (1, -2) and (1, 6), what is the slope of the line passing through them?
A. 1 B. 8 C. 0 D. Undefined
D. Undefined
The slope formula gives 8/0. Division by zero is undefined, which is characteristic of a vertical line.
Given the equation y = 52.1(1.082)^x, what is the rate of growth?
A. 0.082% B. 8.2% C. 52.1% D. 1.082%
B. 8.2%
Since the base is 1.082, the growth rate is 108.2% - 100% = 8.2%.
Is this relationship linear?
x y
0 5
1 10
2 20
No
A linear function has a constant rate of change. Here, the change in y increases from +5 to +10.
A staircase has a vertical height of 14 ft and a horizontal length of 25.4 ft. What is its slope?
A. 1.81 B. 29 C. 0.44 D. 0.55
D. ~0.55 ft
Slope is rise/run.
To graduate from a CPS high school, how many service learning projects must a student complete?
A. 0 B. 40 C. 1 D. 2
D. 2
CPS requires two civic-oriented service learning projects as part of the graduation requirements.
What is the equation of the line passing through the point (-5, 13) that is vertical?
A. x=−5 B. x=13 C. y=−5x+13 D. y=13
A. x=−5
Remember: Vertical Undefined X-axis (VUX).
If an exponential function has a starting value of 100 and a growth rate of 15%, what is the equation?
A. y=100(0.15)^x B. y=100(1.15)^x
C. y=15(100)^x D. y=100(1.5)^x
B. y=100(1.15)^x
A 15% growth means the multiplier is 100% + 15% = 115% --> 1.15.
Find the rate of change for the following table:
x: y:
0 10
2 20
4 30
A. 2 B. 10 C. 2.5 D. 5
D. 5
Rate of change = 10/2 = 5.
If a right triangle has a hypotenuse of 13 and one leg of 5, what is the length of the other leg?
A. 18 B. 12 C. 144 D. 8
B. 12
This famous host of 'Wheel of Fortune' is a proud graduate of Chicago's Farragut Career Academy.
A. Chance the Rapper B. Pat Sajak
C. Alex Trebek D. Steve Harvey
B. Pat Sajak
Pat Sajak grew up in Chicago and graduated from Farragut on the West Side.
What is the equation of the line passing through the point (-5, 13) that is horizontal?
A. y=−5 B. y=13 C. x=13 D. x=−5
B. y=13
Remember: Horizontal 0-slope Y-axis (HOY).
If an exponential equation is y = 200(0.85)^x, what is the percentage of decay?
A. 200% B. 15% C. 85% D. 0.15%
B. 15%
The decay rate is 100% - 85% = 15%.
What is the equation of the line?
X: Y:
-3 12
0 6
5 -4
6 -6
A. y=2x+6 B. y=−2x+12
C. y=6x−2 D. y=−2x+6
y=−2x+6
Find the 'slant length' (hypotenuse) of a ramp that is 14 ft tall and covers a horizontal distance of 29 ft.
A. 25.39 B. 30.50 C. 43.00 D. 32.20
D. ~32.20 ft
If a classmate tells you a wild story and you say 'Merch it!', what are you asking them for?
A. Proof or evidence B. Money
C. To leave the room D. A hoodie or t-shirt
A. Proof or evidence
In Chicago slang, 'merch' means to prove that what you are saying is true.
What is the distance between the points (-2, 3) and (4, 7)? Round your answer to the hundredths.
A. 7.21 B. 5.00 C. 6.32 D. 10.00
A. 7.21
Using the distance formula:
\sqrt{(4 - -2)^{2} + (7 - 3)^{2}} = \sqrt{6^{2} + 4^{2}} = \sqrt{52} \approx 7.21
For the function y = 10(1.2)^x, what is the value of y when x = 2?
A. 144 B. 14.4 C. 24 D. 12
B. 14.4
10(1.2)^2 = 10(1.44) = 14.4.
Find the y-intercept (b) of a line that has a slope of 4 and passes through the point (2, 10).
A. 10 B. 2 C. −2 D. 8
B. 2
y = mx + b
A staircase has a height of 7 feet. If the horizontal distance of the staircase is 26 feet, what is the slope of each step? Round to the nearest hundredth if needed.
A. 7 feet B. ~.27 feet/ step
C. 0.33 feet/ step D. 26 feet
B. ~.27 feet/ step
Which of the following is an accepted 'concrete step' to meet the CPS graduation requirement for a postsecondary plan?
A. A social media post about your plans
B. A college acceptance letter
C. Turning 18
D. Buying a new backpack
B. A college acceptance letter
Receiving and returning a college acceptance letter is one of the primary ways to fulfill the Learn.Plan.Succeed requirement.