New Zealand
Level 8 - NCEA Level 3

# Gradient as a measure or rate

## Interactive practice questions

A plane starts at an altitude of $0$0 metres and ascends $160$160 metres each minute until it reaches cruising altitude.

a

Complete the table of values.

 Time after take-off ($x$x minutes) Altitude ($y$y metres) $0$0 $1$1 $2$2 $3$3 $10$10 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

State the equation relating altitude ($y$y) and time after take-off ($x$x).

c

Graph the equation $y=160x$y=160x

d

State the gradient of the straight line.

e

What does the gradient of the straight line represent?

The rate at which the plane is gaining altitude.

A

The altitude of the plane $x$x minutes after take-off.

B

The rate at which the plane is gaining altitude.

A

The altitude of the plane $x$x minutes after take-off.

B
Easy
Approx 3 minutes

After Mae starts running, her heartbeat increases at a constant rate.

A racing car starts the race with $210$210 litres of fuel. From there, it uses fuel at a rate of $3$3 litres per kilometre, so that the amount of fuel remaining after $x$x kilometres is given by $y=-3x+210$y=3x+210. The graph of the line is shown below.

Consider the graph of $y=2x+5$y=2x+5.

The coordinates of point $A$A are $\left(3,11\right)$(3,11), and the coordinates of point $B$B are $\left(6,17\right)$(6,17).

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91578

Apply differentiation methods in solving problems