# Worksheet: Slope and Rate of Change

In this worksheet, we will practice interpreting the slope of a straight line as the rate of change of two quantities.

**Q1: **

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

**Q2: **

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
- BThey have the same rate of change.
- Ca
- Db
- Ed

**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?

Hannahβs Progress | |
---|---|

Time (min) | Number of Levels |

4 | 3 |

12 | 9 |

20 | 15 |

24 | 18 |

- AJennifer
- BHannah

**Q6: **

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(b)
- C(a)

**Q7: **

Find the slopes of , , and .

- AThe slope of is 10, the slope of is 0, and the slope of is .
- BThe slope of is , the slope of is 0, and the slope of is .
- CThe slope of is 10, the slope of is undefined, and the slope of is .
- DThe slope of is 10, the slope of is 1, and the slope of is .
- EThe slope of is , the slope of is 1, and the slope of is .

**Q8: **

Which of the following best describes the slope of the line on the diagram?

- Apositive
- B0
- Cnegative
- Dundefined

**Q9: **

The graph shows the distance covered in kilometers over a 15-hour hike. What were the fastest and slowest speeds recorded?

- Afastest speed: km/h, slowest speed: km/h
- Bfastest speed: 6 km/h, slowest speed: km/h
- Cfastest speed: 3 km/h, slowest speed: km/h
- Dfastest speed: 6 km/h, slowest speed: km/h
- Efastest speed: 3 km/h, slowest speed: km/h

**Q11: **

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, studentsβ scores increase by, on average, 31.8 points in their physics examination.
- BFor every additional point scored in the physics examination, studentsβ scores increase by, on average, 0.43 additional points in their math examination.
- CFor every additional point scored in the physics examination, studentsβ scores decrease by, on average, 0.43 points in their math examination.
- DFor every additional point scored in the math examination, studentsβ scores increase by, on average, 0.43 additional points in their physics examination.
- EFor every additional point scored in the math examination, studentsβ scores decrease by, on average, 0.43 points in their physics examination.

**Q12: **

Let and be the quadratic function given by the following table.

β2 | β1 | 0 | 1 | 2 | 3 | |

0 | 3 | 0 | β9 | β24 | β45 |

Which of the following statements is true?

- AOn the interval , function has the lower average rate of change.
- BOn the interval , function has the higher average rate of change.
- CThe minimum value of is greater than the maximum value of .
- DBoth functions have the same axis of symmetry.
- EThe sums of zeros of the two functions are the same.

**Q21: **

The relation between the cost of wrapping paper and the number of rolls bought is shown in the table. Is the relationship between the two quantities linear? If so, find the constant rate of change.

Number of Rolls | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Total Cost ($) | 3 | 7 | 9 | 12 |

- Ayes, 3
- Byes,
- Cyes,
- Dno
- Eyes, 4

**Q23: **

What is the average speed of a sound wave that travels 895 meters in 2.5 seconds?

**Q24: **

If a worker who can paint a house in 300 hours and another who can paint the same house in 100 hours work together, how many minutes do they need to paint the house?

**Q25: **

Given the exponential function , what is the percentage rate of change? Give your answer to the nearest percent.