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Worksheet: Slope and a Rate of Change
Q1:
Determine which of the given functions has the greatest rate of change.
(a)
| 0 | 1 | 2 | |||
| 2 | 6 | 10 | 14 |
(b) a function where the input is multiplied by 3 and subtracted from 4
(c)
(d)
- Ac
- Bb
- Cd
- Da
- EThey have the same rate of change.
Q2:
Find the rate of change for the following graph.
Q3:
Which of the following best describes the gradient of the line on the diagram?
- Aundefined
- Bpositive
- C0
- Dnegative
Q4:
The graph shows the distance covered in kilometers over a 15-hour hike. What were the fastest and slowest speeds recorded?
- Afastest speed: 3 km/h, slowest speed: km/h
- Bfastest speed: 6 km/h, slowest speed: km/h
- Cfastest speed: 3 km/h, slowest speed: km/h
- D fastest speed: 6 km/h, slowest speed: km/h
- Efastest speed: km/h, slowest speed: km/h
Q5:
Jennifer and Hannah are playing a video game. The given functions represent the number of levels each of them has finished. Who plays better?
| Hannah’s Progress | |
|---|---|
| Time (min) | Number of Levels |
| 4 | 3 |
| 36 | 9 |
| 100 | 15 |
| 144 | 18 |
- AJennifer
- BHannah
Q6:
At an amusement park, a booth was selling soft drinks. By 2:00 pm, 37 soft drinks were sold, and, by 4:00 pm, 69 were sold. Assuming that the booth was selling at a linear rate during this period, determine the slope of the line representing this information.
Q7:
Which of the following functions has a rate of change that is more rapid than the function shown in the graph?
- A
- B
- C
- D
- E
Q8:
Use the graph to find out how many action figures each boy has.
Q9:
Which of the following functions has a lower rate of change?
(a)
| 9 | 3 | |||
| 2 |
(b) A function with an output that is equal to the input divided by 3 and added to 5.
- AThey have the same rate of change.
- B(a)
- C(b)
Q10:
The scores of a class of students in their end-of-year math and physics examinations can be described by the model , where is the score in math and is the score in physics. What is the interpretation of the value of 0.43 in the model?
- AFor every additional point scored in the math examination, students’ scores decrease by, on average, 0.43 points in their physics examination.
- BFor every additional point scored in the physics examination, students’ scores increase by, on average, 0.43 additional points in their math examination.
- CFor every additional point scored in the physics examination, students’ scores decrease by, on average, 0.43 points in their math examination.
- DFor every additional point scored in the math examination, students’ scores increase by, on average, 0.43 additional points in their physics examination.
- EFor every additional point scored in the math examination, students’ scores increase by, on average, 31.8 points in their physics examination.
Q11:
Find the gradients of , , and .
- A The gradient of is 10, the gradient of is 1, and the gradient of is .
- B The gradient of is , the gradient of is 0, and the gradient of is .
- C The gradient of is , the gradient of is 1, and the gradient of is .
- D The gradient of is 10, the gradient of is 0, and the gradient of is .
- E The gradient of is 10, the gradient of is undefined, and the gradient of is .