Moderate -0.8 This is a straightforward definite integration question requiring only basic power rule application (rewriting as x^(1/2) and x^(-1/2)), integration to get (2/3)x^(3/2) + 4x^(1/2), and substitution of limits. It's routine practice with no problem-solving element, making it easier than average but not trivial since it requires careful handling of fractional powers and arithmetic with surds.
B1 for each term correct – allow unsimplified. C not
required.
4
3 1
x2 x2 40 14
+ 2 → −
3 1 3 3
2 2
Answer
Marks
Guidance
1
M1
Evidence of 4 and 1 used correctly in their integrand ie at
least one power increased by 1.
26
= oe
Answer
Marks
Guidance
3
A1
Allow 8.67 awrt. No integrand implies use of integration
function on calculator 0/4. Beware a correct answer from
wrong working.
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | 3 1
x2 x2
Integrate → + 2 (+C)
3 1
2 2 | B1 B1 | B1 for each term correct – allow unsimplified. C not
required.
4
3 1
x2 x2 40 14
+ 2 → −
3 1 3 3
2 2
1 | M1 | Evidence of 4 and 1 used correctly in their integrand ie at
least one power increased by 1.
26
= oe
3 | A1 | Allow 8.67 awrt. No integrand implies use of integration
function on calculator 0/4. Beware a correct answer from
wrong working.
4
Question | Answer | Marks | Guidance