QCAA Maths Methods Paper 1 Integral Calculus Mini Test 3
External Assessment Paper 1 — Technology-free
Number of marks: 10
Perusal time: 1 minute
Writing time: 15 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
The approximate area under the curve \(f(x) = \sqrt{2x+1}\) between \(x=0\) and \(x=4\) using the trapezoidal rule with four strips is
- (A) \(2+\sqrt{3}+\sqrt{5}+\sqrt{7}\)
- (B) \(2+2(\sqrt{3}+\sqrt{5}+\sqrt{7})\)
- (C) \(4+2(\sqrt{3}+\sqrt{5}+\sqrt{7})\)
- (D) \(4+\sqrt{3}+\sqrt{5}+\sqrt{7}\)
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
Determine the value of \(b\) given \(\int_a^b 3x^2 \,dx = 117\) and \(\int_a^{b-1} 3x^2 \,dx = 56\) for \(b > 1\).
Consider the functions \(f(x) = x^2\) and \(g(x) = 4x\).
a) Determine the \(x\)-coordinates of the points of intersection of the graphs of the two functions. [2 marks]
b) Use the results from Question 13a) to calculate the area enclosed by the graphs of \(f(x)\) and \(g(x)\). [3 marks]
END OF PAPER
