C2 January 2009 Q3

Notes

B1 for one answer correct    Second B1 for all three correct

Accept awrt ones given or exact answers so \(\sqrt{21}\), \(\sqrt{\left(\dfrac{369}{25}\right)}\) or \(\dfrac{3\sqrt{41}}{5}\), and \(\sqrt{\left(\dfrac{429}{25}\right)}\) or \(\dfrac{\sqrt{429}}{5}\), score the marks.

Notes

B1 is for using 0.2 or \(\tfrac{0.4}{2}\) as \(\tfrac{1}{2}h\).

M1 requires first bracket to contain first plus last values and second bracket to include no additional values from those in the table.
If the only mistake is to omit one value from 2^nd bracket this may be regarded as a slip and can be allowed ( An extra repeated term forfeits the M mark however)
\(x\) values: M0 if values used in brackets are \(x\) values instead of \(y\) values.
Separate trapezia may be used : B1 for 0.2, M1 for \(\tfrac{1}{2}h(a + b)\) used 4 or 5 times ( and A1ft all correct)
e.g.. \(0.2(3 + 3.47) + 0.2(3.47 + 3.84) + 0.2(3.84 + 4.14) + 0.2(4.14 + 4.58)\) is M1 A0 equivalent to missing one term in { } in main scheme
A1ft follows their answers to part (a) and is for {correct expression}

Final A1 must be correct. (No follow through)

Special cases

Bracketing mistake: i.e. \(\dfrac{1}{2} \times 0.4(3 + 4.58) + 2(3.47 + 3.84 + 4.14 + 4.39)\) scores B1 M1 A0 A0 unless the final answer implies that the calculation has been done correctly (then full marks can be given).

Need to see trapezium rule – answer only (with no working) is 0/4.