Foundation November 2022 Paper 2 Q21
21
(a) \(k\) is a whole number between 40 and 50
The cube root of \(k\) is 3, to the nearest whole number.
Work out the largest possible value of \(k\). [2 marks]
(b) Fay tries to solve \(\quad x^2 = 100\)
She says,
“The only possible value of \(x\) is 10”
Give a reason why she is not correct. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Correct evaluation of the cube root of an integer \([40, 50]\) or correct evaluation of the cube of a decimal or fraction \((3, 3.5]\) | M1 | eg \(\sqrt[3]{40} = 3.4\) or \(40 \to 3.4\) eg \(3.5^3 = 42.8\) or \(3.5 \to 42.8\) |
| 42 | A1 | SC1 answer given as \(\sqrt[3]{42}\) |
Additional guidance
| Up to M1 may be awarded for correct work with no answer, or incorrect answer, even if this is seen amongst multiple attempts | |||||||||||||||||||||||
| Condone eg \(40 = 3.4\) or \(\sqrt{40} = 3.4\) to mean \(\sqrt[3]{40} = 3.4\) | |||||||||||||||||||||||
| Answer only 42 | M1A1 | ||||||||||||||||||||||
| Must select 42 as final answer for M1A1 ie 42 as the last in a list with a blank answer line is not enough for A1 unless 42 selected | |||||||||||||||||||||||
| If \(\sqrt[3]{42}\) or \(3.5^3\) is evaluated then it must be correct to award the A1 for 42 | |||||||||||||||||||||||
| NB 42 only from incorrect method eg listing multiples of 3 or \(42 \div 3\) seen or 42 is divisible by 3 as the working | M0A0 | ||||||||||||||||||||||
Acceptable values for cube roots of integers in range
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Examples of cubes of numbers in range with their acceptable values
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| Answer | Mark | Comments |
|---|---|---|
| Valid response that indicates there is one (negative) answer missing | B1 | eg −10 (is also an answer) or there is a negative value as well or square roots have two answers or answer is 10 and −10 |
Additional guidance
| \(-10 \times -10\;(= 100)\) | B1 |
| Another number can square to make 100 (implies exactly two) | B1 |
| She has forgotten the other value (implies exactly two) | B1 |
| There is another value it could be (implies exactly two) | B1 |
| It could be a different number (implies exactly two) | B1 |
| It could be negative (bod means 10 could be −10) | B1 |
| \(-10^2\;(= 100)\) (condone missing brackets around −10) | B1 |
| \(\pm\sqrt{100}\) | B1 |
| Indication that there might be more than two possible values for \(x\) eg There are other possible numbers eg There could be other values eg Other numbers square to make 100 eg She hasn’t included negatives | B0 B0 B0 B0 |
| Repeating the question eg There is more than 1 possible value eg 10 is not the only possible value eg More than 1 number works | B0 B0 B0 |
| A partially correct statement eg \(x\) could be negative or decimal eg \(-10 \times -10 = -100\) eg \(x^2 = -10\) | B0 B0 B0 |