NZ Level 7 (NZC) Level 2 (NCEA) Applications of maximisation and minimisation

## Interactive practice questions

The height $h$h, in meters, reached by a ball thrown in the air after $t$t seconds is given by the equation $h=12t-t^2$h=12tt2.

a

Fill in the following table of values for $h=12t-t^2$h=12tt2

 $t$t $h$h $1$1 $2$2 $3$3 $4$4 $5$5 $6$6 $7$7 $8$8 $9$9 $10$10 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Graph the relationship $h=12t-t^2$h=12tt2.

c

Determine the height of the ball after $7.5$7.5 seconds have elapsed.

d

What is the maximum height reached by the ball?

Easy
Approx 6 minutes

The sum of two integers is $80$80.

A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40xx2, where $x$x is the length of one side of the rectangle.

The sum of two whole numbers is $24$24. Let one of the numbers be $x$x.

### Outcomes

#### M7-7

Form and use linear, quadratic, and simple trigonometric equations

#### 91261

Apply algebraic methods in solving problems