C2 June 2010 Q1
1.
\[y = 3^x + 2x\]| \(x\) | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
|---|---|---|---|---|---|---|
| \(y\) | 1 | 1.65 | 5 |
| Scheme | Marks |
|---|---|
| (a) 2.35, 3.13, 4.01 (One or two correct B1 B0, all correct B1 B1) Important: If part (a) is blank, or if answers have been crossed out and no replacement answers are visible, please send to Review as ‘out of clip’. | B1 B1 |
| (2) |
Notes
(a) Answers must be given to 2 decimal places.
No marks for answers given to only 1 decimal place.
| Scheme | Marks |
|---|---|
| (b) \(\dfrac{1}{2} \times 0.2\ \ldots\ldots\) (or equivalent numerical value) | B1 |
| \(k\left\{(1 + 5) + 2(1.65 + p + q + r)\right\}\), \(k\) constant, \(k \neq 0\) (See notes below) | M1 A1 |
| \(= 2.828\) (awrt 2.83, allowed even after minor slips in values) The fractional answer \(\dfrac{707}{250}\) (or other fraction wrt 2.83) is also acceptable. Answers with no working score no marks. | A1 |
| (4) | |
| 6 |
Notes
(b) The \(p\), \(q\) and \(r\) below are positive numbers, none of which is equal to any of: 1, 5, 1.65, 0.2, 0.4, 0.6 or 0.8
M1 A1: \(k\left\{(1 + 5) + 2(1.65 + p + q + r)\right\}\)
M1 A0: \(k\left\{(1 + 5) + 2(1.65 + p + q)\right\}\) or \(k\left\{(1 + 5) + 2(p + q + r)\right\}\)
M0 A0: \(k\left\{(1 + 5) + 2(1.65 + p + q + r + \textit{other value}(s))\right\}\)
Note that if the only mistake is to omit a value from the second bracket, this is considered as a slip and the M mark is allowed.
Bracketing mistake: i.e. \(\dfrac{1}{2} \times 0.2(1 + 5) + 2(1.65 + 2.35 + 3.13 + 4.01)\)
instead of \(\dfrac{1}{2} \times 0.2\left\{(1 + 5) + 2(1.65 + 2.35 + 3.13 + 4.01)\right\}\), so that only the (1 + 5) is multiplied by 0.1 scores B1 M1 A0 A0 unless the final answer implies that the calculation has been done correctly (then full marks can be given).
Alternative:
Separate trapezia may be used, and this can be marked equivalently.