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18 A cube has a volume of 512 cm3
Work out the surface area of the cube. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 384 | P1 | for \(\sqrt[3]{512}\ (= 8)\) or \(512 \div 8\ (= 64)\) |
| P1 | for \(\text{``}8\text{''}^2 \times 6\) \(\text{``}\sqrt[3]{512}\text{''} \times \text{``}\sqrt[3]{512}\text{''} \times 6\) | |
| A1 | cao |
A correct answer coming from an incorrect method, eg \(512 \div 4 = 128\) and \(128 \times 3 = 384\) will score no marks
14 Here is a cuboid of length 10 cm and width 4 cm.
The cuboid has a volume of 200 cm3
Here is a different cuboid.
| Answer | Mark | Mark scheme |
|---|---|---|
| 5 | P1 | for a start of a method to find the height, eg \(10 \times 4\ (= 40)\) or \(200 \div 10\ (= 20)\) or \(200 \div 4\ (= 50)\) or for forming a correct equation \(10 \times 4 \times h = 200\) |
| A1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| 126 | M1 | for a start to find the area of at least one face, eg \(6 \times 3\ (= 18)\) or \(5 \times 3\ (= 15)\) or \(6 \times 5\ (= 30)\) |
| M1 | for combining the area of at least three of the correct faces eg \(\text{``}18\text{''} + \text{``}15\text{''} + \text{``}30\text{''}\ (= 63)\) or \(2 \times \text{``}18\text{''} + \text{``}15\text{''}\) | |
| A1 | cao |
Do not award first M if multiplied by a third length (ie volume calculation)
May be part of a larger addition including incorrect areas.
Do not award if more than 6 areas added.
13 The diagram shows a crate and a box.
The crate is 3 m by 1 m by 1.5 m.
The crate is completely filled with boxes.
Each box is 20 cm by 10 cm by 75 cm.
Work out the number of boxes in the crate. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 300 | B1 | (indep) for process to convert to common units, eg \(3 \times 100\ (= 300)\) or \(1 \times 100\ (= 100)\) or \(1.5 \times 100\ (= 150)\) or \(20 \div 100\ (= 0.2)\) or \(10 \div 100\ (= 0.1)\) or \(75 \div 100\ (= 0.75)\) or \(\text{``}4.5\text{''} \times 100^3\ (= 4\,500\,000)\) or \(\text{``}15\,000\text{''} \div 100^3\ (= 0.015)\) |
| P1 | for finding the volume of either shape, eg \(3 \times 1 \times 1.5\ (= 4.5)\) or \([300] \times [100] \times [150]\ (= 4\,500\,000)\) or \(20 \times 10 \times 75\ (= 15\,000)\) or \([0.2] \times [0.1] \times [0.75]\ (= 0.015)\) OR for start of the process to find the number of boxes using one dimension, eg \([300] \div 20\ (= 15)\) or \([100] \div 10\ (= 10)\) or \([150] \div 75\ (= 2)\) or \(3 \div [0.2]\ (= 15)\) or \(1 \div [0.1]\ (= 10)\) or \(1.5 \div [0.75]\ (= 2)\) | |
| P1 | (dep on P1) for a complete process with or without unit conversion eg \(\text{``}4\,500\,000\text{''} \div \text{``}15\,000\text{''}\) or \(\text{``}4.5\text{''} \div \text{``}0.015\text{''}\) or \(\text{``}15\text{''} \times \text{``}10\text{''} \times \text{``}2\text{''}\) | |
| A1 | cao |
This mark can be awarded at any stage
One correct conversion for their process is enough for the award of this mark
Working may be seen on the diagram
[300] = 3 or 30 or “300” or 3000
[100] = 1 or 10 or “100” or 1000
[150] = 1.5 or 15 or “150” or 1500
[0.2] = 20 or 2 or “0.2” or 0.02
[0.1] = 10 or 1 or “0.1” or 0.01
[0.75] = 75 or 7.5 “0.75” or 0.075
May be implied by correctly dividing the areas of the corresponding faces
eg \(\dfrac{[300] \times [100]}{20 \times 10}\)
Condone an incorrect attempt to convert volume before division
23 Here is a solid prism.
volume = 3500 cm\(^3\)
and
length = 20 cm
Work out the area of the cross-section of the prism. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| 8 | B1 |
| Answer | Mark | Comments |
|---|---|---|
| \(3500 \div 20\) or \(\dfrac{3500}{20}\) | M1 | oe eg \(350 \div 2\) |
| 175 | A1 | SC1 digits 175 |
Ignore units
6 Here are three solids.
| Answer | Mark | Comments |
|---|---|---|
| 6 | B1 |
| Answer | Mark | Comments |
|---|---|---|
| 8 | B1 |
| Answer | Mark | Comments |
|---|---|---|
| 1 | B1 |
26 Here is a prism drawn on an isometric grid.
Work out the volume of the prism. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Correct method or evaluation of the area of any face or correct method or evaluation of the volume of any relevant cuboid of length 6 cm | M1 | eg \(5 \times 6\) or 30 or \(2 \times 6\) or 12 or \(3 \times 6\) or 18 or \(4 \times 6\) or 24 or \(2 \times 5 + 2 \times 2\) or \(10 + 4\) or 14 or \(2 \times 5 \times 6\) or 60 or \(2 \times 2 \times 6\) or 24 or \(2 \times 3 \times 6\) or 36 or \(4 \times 2 \times 6\) or 48 or \(5 \times 4 \times 6\) or 120 |
| Correct method for volume of prism | M1dep | eg \(2 \times 5 \times 6 + 2 \times 2 \times 6\) or \(60 + 24\) or \(14 \times 6\) |
| 84 | A1 |
The first M1 may be awarded even if this is seen amongst multiple attempts
22 How many edges does a triangular prism have? [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| 9 | B1 |
21 Eva thinks she can save water by having a shower instead of a bath.
Eva’s shower
uses 10.8 litres per minute
lasts for 8 minutes.
Eva assumes that the water in her bath is in the shape of this cuboid.
1000 cm\(^3\) = 1 litre
\(B\) shows the cuboid in the empty bath.
Not drawn accurately
What does this tell you about the amount of water saved? [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(10.8 \times 8\) or 86.4 | M1 | |
| \(50 \times 110 \times 35\) or 192 500 | M1 | Must use correct volume formula |
| their 192 500 \(\div\) 1000 or 192.5 | M1dep | dep on 2nd M1 |
| their 192.5 \(-\) their 86.4 | M1dep | dep on M1M1M1 |
| 106.1 or 106 | A1 | |
| Alternative method 2 | ||
| \(10.8 \times 8 \times 1000\) or 86 400 | M1 | oe |
| \(50 \times 110 \times 35\) or 192 500 | M1 | Must use correct volume formula |
| their 192 500 \(-\) their 86 400 or 106 100 | M1dep | dep on M1M1 |
| their 106 100 \(\div\) 1000 | M1dep | dep on M1M1M1 |
| 106.1 or 106 | A1 | |
| 192.5 | 2ndM1M1dep |
| 106 100 | M1M1M1dep |
| \(50 \times 110 \times 35 = 192\,500 \div 2\) | 2ndM0 |
| Answer | Mark | Comments |
|---|---|---|
| A comment that the answer to part (a) was too low or that the amount saved would be greater | B1 |
| It was more | B1 |
| More water saved | B1 |
| She underestimated it | B1 |
| She underestimated the water saved | B1 |
| She’s saving more water because she’s using more water than the cuboid | B1 |
| Greater than 106.1 litres (may need to check value in part (a) if they quote a different value) | B1 |
| More than Eva’s assumption | B1 |
| Eva’s assumption was not accurate therefore the prediction was wrong | B0 |
| She underestimated the water | B0 |
| Less water used | B0 |
| It was inaccurate | B0 |
| A uses more water than B (only talking about the diagram) | B0 |
| B saves more than A (only talking about the diagram) | B0 |
| Saves a lot of water | B0 |
| More water used | B0 |
| Cuboid smaller than bath | B0 |
| Used more water in the bath than she thought | B0 |
No questions match these filters.