4MA0 Higher June 2014 Paper 4R Q14
14 Rob is making a scale model of the Solar System on the school field.
He wants the distance from the Sun to Jupiter to be 8 metres on his scale model.
The real distance from the Sun to Jupiter is \(7.8 \times 10^8\) kilometres.
(a) Find the scale of the model.
Give your answer in the form \(1 : n\), where \(n\) is written in standard form. (3)
Give your answer in the form \(1 : n\), where \(n\) is written in standard form. (3)
Rob wants to put the position of a space probe on the scale model.
The real distance of the space probe from the Sun is \(1.9 \times 10^{10}\) kilometres, correct to 2 significant figures.
(b) Work out the maximum distance of the space probe from the Sun on the scale model.
Give your answer in metres. (3)
Give your answer in metres. (3)
| Scheme | Marks |
|---|---|
| \(7.8 \times 10^8 \times 1000\) or \(7.8 \times 10^{11}\) oe or 8 ÷ 1000 or 0.008 | M1 |
| \(7.8 \times 10^8 \times 1000 \div 8\) or \(7.8 \times 10^8 \div 0.008\) | M1 |
| \(9.75 \times 10^{10}\) | A1 |
| (3) |
Notes
M1: for correct conversion from m to km or from km to m
M1: (indep) award for digits 975
(eg. an answer of \(9.75 \times 10^7\) gets M0 M1 A0)
A1: cao
| Scheme | Marks |
|---|---|
| \(1.95 \times 10^{10}\) km | B1 |
\(\dfrac{1.95 \times 10^{10}}{\text{“}9.75 \times 10^{10}\text{”}}\) (=0.2(km)) or \(\dfrac{1.95 \times 10^{13}}{\text{“}9.75 \times 10^{10}\text{”}}\) (=200(m)) or \(\dfrac{1.95 \times 10^{10}}{7.8 \times 10^8} \times 8\) (=200(m)) or \(\dfrac{1.95 \times 10^{13}}{7.8 \times 10^{11}} \times 8\) (=200(m)) NB: 1.95 may be the candidate’s upper bound | M1 |
| 200 | A1 |
| (3) | |
| (6 marks) |
Notes
B1: cao
M1: ft from (a) also award for
\(\dfrac{1.9 \times 10^{10}}{\text{“}9.75 \times 10^{10}\text{”}}\) or \(\dfrac{1.9 \times 10^{13}}{\text{“}9.75 \times 10^{10}\text{”}}\)
or \(\dfrac{1.9 \times 10^{10}}{7.8 \times 10^8} \times 8\) or \(\dfrac{1.9 \times 10^{13}}{7.8 \times 10^{11}} \times 8\)
A1: cao must be from correct figures used in a correct calculation
The mark scheme states that for this question the correct answer alone does not imply a correct method.