DP Mathematics: Applications and Interpretation Questionbank

By dividing the area between the curve and the $x$‐axis into two trapezoids of unequal width show that $A>14.5$, justifying the direction of the inequality.

Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel.

Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel.

Use the trapezoidal rule with an interval width of $0.4$ to estimate the total amount of carbon dioxide emitted during these two hours.

The real amount of carbon dioxide emitted during these two hours was $72$ tonnes.

Find the percentage error of the estimate found in part (a).

Use the trapezoidal rule, with the values given in the following table, to approximate the area of the shaded region.

The shape of a vase is formed by rotating a curve about the $y$-axis.

The vase is $10 \text{cm}$ high. The internal radius of the vase is measured at $2 \text{cm}$ intervals along the height:

Use the trapezoidal rule to estimate the volume of water that the vase can hold.

Use all the coordinates in the table to find the equation of the least squares cubic regression curve.

Find the value of this area.

Use the trapezoidal rule to find an estimate for the area.

Write down the coefficient of determination.

Write down an expression for the area enclosed by the cubic regression curve, the $x$-axis, the $y$-axis and the line $x=10$.

Use the trapezoidal rule to find an estimate for the area.

Find the value of this area.

Write down the coefficient of determination.

With reference to the shape of the graph, explain whether your answer to part (a)(i) will be an over-estimate or an underestimate of the area.

Show that $\text{ln}y=qx+\text{ln}p$.

Hence find the area enclosed by the exponential function, the $x$-axis, the $y$-axis and the line $x=4.4$.

Use all the coordinates in the table to find the equation of the least squares cubic regression curve.

By finding the equation of a suitable regression line, show that $p=1.83$ and $q=0.986$.

Write down an expression for the area enclosed by the cubic function, the $x$-axis, the $y$-axis and the line $x=4.4$.

Hence explain how a straight line graph could be drawn using the coordinates in the table.