Hong Kong
Stage 4 - Stage 5

# Applications of Polynomials

## Interactive practice questions

In a study, scientists found that the more someone sleeps, the quicker their reaction time. The attached table shows the findings. Use a positive number to express increase, and a negative number to express decrease.

 Number of hours of sleep ($x$x) Reaction time in seconds ($y$y) $0$0 $1$1 $2$2 $3$3 $4$4 $5$5 $6$6 $5.8$5.8 $5.6$5.6 $5.4$5.4 $5.2$5.2 $5$5
a

How much does the reaction time change for each extra hour of sleep? Express your answer correct to one decimal place.

b

Which one of the following algebraic equations relates the number of hours of sleep ($x$x) and the reaction time ($y$y)?

$y=6x-0.2$y=6x0.2

A

$y=-0.2x-6$y=0.2x6

B

$y=-0.2x+6$y=0.2x+6

C
c

What would be the reaction time for someone who has slept $4.5$4.5 hours?

Express your answer correct to two decimal places.

d

By rearranging the equation found in part (b), calculate the number of hours, correct to one decimal place, someone sleeps if they have a reaction time of $5.5$5.5 seconds.

Enter each line of working as an equation.

Easy
4min

The recommended level of good cholesterol in women, in mg/dL, can be modeled by the function $f\left(x\right)=0.13x+51.25$f(x)=0.13x+51.25, where $x$x is measured in years.

Easy
2min

A ball is rolled down a slope. The table attached shows the velocity of the ball after a given number of seconds.

Easy
4min

Consider the figure shown below.

Easy
2min