Higher June 2018 Paper 3 Q9
9 \(T = \sqrt{\dfrac{w}{d^3}}\)
\(w = 5.6 \times 10^{-5}\)
\(d = 1.4 \times 10^{-4}\)
(a) Work out the value of \(T\).
Give your answer in standard form correct to 3 significant figures. (2)
Give your answer in standard form correct to 3 significant figures. (2)
\(w\) is increased by 10%
\(d\) is increased by 5%
Lottie says,
“The value of \(T\) will increase because both \(w\) and \(d\) are increased.”
(b) Lottie is wrong.
Explain why. (2)
Explain why. (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(4.52 \times 10^3\) | M1 | for \(2.04.... \times 10^7\) oe eg \(2.04.... \times 10^{-5} \div 10^{-12}\) or \(20.4... \times 10^6\) or 204(08163.27) or for correct value of \(T\), 4517.(53....), not written in standard form, eg 4520 |
| A1 | for answer in the range \(4.51 \times 10^3\) to \(4.52 \times 10^3\) (SC B1 for \(6.32... \times 10^{-1}\)) |
Additional guidance
May be given correct to 3 sig figs or more
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | M1 | for method to find the scale factor or decreased value in \(T\), eg \(\sqrt{\dfrac{1.1}{1.05^3}}\) (= 0.97......) oe or \(\sqrt{\dfrac{5.6 \times 10^{-5} \times 1.1}{(1.4 \times 10^{-4} \times 1.05)^3}}\) (\(= 4.40.... \times 10^3\)) oe |
| C1 | (dep M1) for explanation eg value of scale factor less than 1, so a decrease in \(T\) OR compares \(4.40... \times 10^3\) with their value of \(T\) from (a) provided answer to (a) is greater |
Additional guidance
Award mark for a correct method to calculate the scale factor or the percentage increases in \(w\) and \(d^3\) or the decreased value of \(T\)
This mark may only be awarded if supported by numerical evidence