Pre-U Pre-U 9794/2 2010 June — Question 1 3 marks

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
Year2010
SessionJune
Marks3
TopicIndefinite & Definite Integrals
TypePure definite integration
DifficultyEasy -1.8 This is a straightforward integration question requiring only basic power rule application and evaluation at limits. The arithmetic is simple (integrating 7x² to get 7x³/3), and with only 3 marks, it's a routine warm-up question testing fundamental calculus mechanics with no problem-solving element.
Spec1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits
Find the exact value of $$\int_1^4 \left(10x^2 - 3x^2\right) dx.$$ [3]
AnswerMarks Guidance
Obtain the indefinite integral \(4x^{\frac{5}{3}} - 2x^{\frac{3}{2}}\)B1
Correctly substitute the limits in \(Ax^a + Bx^b\)M1
Obtain 110A1 [3] 
Obtain the indefinite integral $4x^{\frac{5}{3}} - 2x^{\frac{3}{2}}$ | B1 | 
Correctly substitute the limits in $Ax^a + Bx^b$ | M1 |
Obtain 110 | A1 | [3]
Find the exact value of
$$\int_1^4 \left(10x^2 - 3x^2\right) dx.$$ [3]

\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2010 Q1 [3]}}
This paper (13 questions)
View full paper
Q1 3 Q2 5 Q3 6 Q4 6 Q5 9 Q6 10 Q7 12 Q8 14 Q9 15 Q10 9 Q11 10 Q12 13 Q13 8