1MA0 Higher June 2016 Paper 2 Q14
14 The diagram shows a metal bar in the shape of a prism.
Diagram NOT accurately drawn
The length of the metal bar is 120 cm.
The cross section of the metal bar is shown below.
Diagram NOT accurately drawn
All corners are right angles.
The metal bar is made from steel with density 8 g/cm\(^3\).
Sean has a trolley.
The trolley can carry a maximum mass of 250 kg.
How many metal bars can the trolley carry at the same time?
You must show your working. (5)
| Answer | Mark | Notes |
|---|---|---|
| 3 | 5 | M1 for a complete method to find the area of the cross section, eg. \(15 \times 2 + \text{``}(12 - 4)\text{''} \times 2 + 15 \times 2\) (= 76) or for finding the volume of a relevant prism, eg. \(15 \times 2 \times 120\) (= 3600) NB: "(12 − 4)" maybe just seen on the diagram M1 for a method to find the volume of the bar, eg. \(\text{``}76\text{''} \times 120\) (= 9120) or ft "area of cross section" \(\times\) 120 provided "area of cross section" includes a method to find the area of at least two relevant rectangles M1 for "volume" \(\times\) 8, eg. \(\text{``}9120\text{''} \times 8\) (= 72960) or \(250 \times 1000 \div 8\) (= 31250) NB "volume" must be dimensionally correct M1 (dep on previous M1) for \(250 \div (\text{``}\text{volume}\text{''} \times 8 \div 1000)\), eg. \(250 \div \text{``}72960 \div 1000\text{''}\) (= 3.4265….) or \(\text{``}31250\text{''} \div \text{``}9120\text{''}\) A1 for an answer of 3 with correct working |