Intermediate November 2021 Unit 2 Q15
15.
(a)
(i) Expand \(x(x^2 + 7)\). [2]
(ii) Expand and simplify \((x - 5)(3x - 4)\). [2]
(b) Sarah buys and sells antique clocks.
On Monday, Sarah had \(n\) clocks.
At the end of the day on Tuesday, she had 5 times as many clocks as she had on Monday.
On Wednesday, she sold 27 clocks.
On Monday, Sarah had \(n\) clocks.
At the end of the day on Tuesday, she had 5 times as many clocks as she had on Monday.
On Wednesday, she sold 27 clocks.
(i) At the end of the day on Wednesday, Sarah had fewer clocks than she had on Monday.
Write an inequality, in terms of \(n\), that shows this information. [2]
Write an inequality, in terms of \(n\), that shows this information. [2]
(ii) Solve your inequality to find the greatest number of clocks that Sarah could have had on the Monday. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(x^3 + 7x\) | B2 | B1 for sight of \(x^3\) + ……. OR ……+ 7x. Do not accept x×x×x + x×7 etc. Mark final answer. |
| (ii) \(3x^2 - 4x - 15x + 20\) | B1 | Must be an expression. |
| \(3x^2 - 19x + 20\) | B1 | FT from an error in only one term (out of 4) only if of the form ax2 ± bx ± cx ± d. |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 5n – 27 < n OR n > 5n − 27 | B2 | Allow B2 for an equivalent correct inequality. e.g. 4n – 27 < 0. B1 if ≤ or ≥ used in a ‘correct’ inequality. OR B1 for 5n – 27 > n OR n < 5n − 27 |
| (ii) 4n < 27 | B1 | FT ‘their inequality’ if of equivalent difficulty. |
| n < \(\dfrac{27}{4}\) | B1 | FT only from an < b OR an ≤ b OR an > b OR an ≥ b. |
| (Greatest number of clocks =) 6 | B1 | FT only from n < c where c is positive OR n ≤ d where d is positive and not an integer An answer of 6 gains all 3 marks. |