Higher June 2017 Unit 1 Q11
11.
(a) Evaluate \(49^{-\frac{1}{2}}\). [1]
(b) Express \(0{\cdot}3\dot{7}\dot{2}\) as a fraction. [2]
(c) Find the value of \(\left(\sqrt{63} - \sqrt{7}\right)^2\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| 1/7 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| x = 0·37272… AND 100x = 37·2727… with an attempt to subtract. | M1 | Or 10x AND 1000x or equivalent with an attempt to subtract. |
| \(\dfrac{369}{990}\) ISW (= 41/110) | A1 | An answer of 36·9 / 99 gains M1 only. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| 0·3 + 0·0727272..= 3/10 + 72/990 or equivalent | M1 | |
| 369/990 (= 41/110) ISW | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (√63)2 − √63√7 − √63√7 + (√7)2 | B1 | |
| = 63 − √441 − √441 + 7 | B1 | Accept equivalent methods of processing √63√7 e.g. √9√7√7 or 3(√7)2. F.T. only from ‘– (√7)2’ in first line. |
| = 28 | B1 | Accept ’14’ only if as a result of F.T. ‘– (√7)2’ in first line. If no marks awarded, SC1 for 3 out of 4 terms correct in initial expansion. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| Sight of √63 = 3√7 | B1 | |
| (2√7)2 | B1 | |
| = 28 C.A.O. | B1 |