Purchase this Material for $15

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
18 Videos

The following table shows the daily number of watches sold at a shop and the amount of money made from the sales.

**a)** Does the data in the table appear to follow a linear relation? Explain.

**b)** What is the average rate of change in revenue from `w = 20`

to `w = 25`

?

**c)** What is the cost of one watch, and how does this cost relate to the graph?

Buy to View

4.41mins

Q1

The graph shows the height above the ground of a person riding a Ferris wheel.

**a)** Calculate the average rate of change in height on the interval `[0, 4]`

.

**b)** Calculate the average rate of change in height on the interval `[4, 8]`

.

Buy to View

1.22mins

Q2

A company is opening a new office. The initial expense to set up the office is `\$10 000`

, and the company will spend another `\$2500`

each month in utilities until the new office opens.

**a)** Write the equation that represents the company’s total expenses in terms of
months until the office opens.

**b)** What is the average rate of change in the company’s expenses from `3 \leq m \leq 6`

?

Buy to View

0.52mins

Q3

In investments value, `V( t)`

, is modelled by the function `V(t) = 2500(1.15)^t`

, where `t`

is the number of years after funds are invested.

Find the instantaneous rate of change in the value of the investment at `t = 4`

.

Buy to View

2.04mins

Q4

The height, in centimetres, of a piston attached to a turning wheel at time t, in seconds, is modelled by the equation `y = 2 \sin (120^ot)`

.

Find the instantaneous rate of change at `t = 12`

s.

Buy to View

2.37mins

Q5

For the graph shown, estimate the slope of the tangent line at `(4, 2)`

.

Buy to View

1.35mins

Q6a

For the graph shown, estimate the slope of the tangent line at `(5, 1)`

.

Buy to View

0.15mins

Q6b

For the graph shown, estimate the slope of the tangent line at `(7, 5)`

.

Buy to View

0.39mins

Q6c

A sculptor makes a vase for flowers. The radius and circumference of the vase increase as the height of the vase increases. The vase is filled with water. Draw a possible graph of the height of the water as time increases.

Buy to View

1.03mins

Q8

A newspaper carrier delivers papers on her bicycle. She bikes to the first neighbourhood at a rate of 10 km/h. She slows down at a constant rate over a period of7 s, to a speed of 5 km/h, so that she can deliver her papers. After travelling at this rate for 3 5, she sees one of her customers and decides to stop. She slows at a constant rate until she stops. It takes her 6 s to stop.

**a)** What is the average rate of change in speed over the first 7 s?

**b)** What is the average rate of change in speed from second 7 to 12 seconds.

**c)** What is the instantaneous rate of change in speed at 12 s?

Buy to View

3.50mins

Q9

The graph shows the height of a roller coaster versus time. Describe how the vertical speed of the roller coaster will vary as it travels along the track from A to G. Sketch a graph to show the vertical speed of the roller coaster.

Buy to View

2.23mins

Q10

A maximum or minimum is given for each of the following functions. Select a strategy, and verify whether the point given is a maximum or a minimum.

`f(x) =x^2 -10x + 7; (5, -18)`

Buy to View

0.21mins

Q11a

A maximum or minimum is given for each of the following functions. Select a strategy, and verify whether the point given is a maximum or a minimum.

`g(x) = -x^2 -6x - 4; (-3, 5)`

Buy to View

0.19mins

Q11b

A maximum or minimum is given for each of the following functions. Select a strategy, and verify whether the point given is a maximum or a minimum.

`h(x) = -2x^2 + 68x + 75; (17, 653)`

Buy to View

0.10mins

Q11c

`j(x) = \sin(-2x); (45^o, -1)`

Buy to View

0.28mins

Q11d

`k(x) = -4\cos(x + 25); (-25^o, -4)`

Buy to View

0.45mins

Q11e

`m(x) = \frac{1}{20}(x^3 + 2x^2 -15x); (-3, \frac{9}{5})`

Buy to View

0.59mins

Q11f

**a)** For `f(x)`

, find the equation for the slope of the secant line between any general point on the function `(a + h, f(a + h))`

and the given x-coordinate of another point.

`f(x) = x^2 -30x; a = 2`

**b)** Use each slope equation you found in part a) to estimate the slope of the tangent line at the point with the given x—coordinate.

Buy to View

2.03mins

Q12i