ACSEE (Form 6) Numerical Methods — practice questions

Explore 3 free Numerical Methods questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Numerical Methods questions and exercises with answers

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The area enclosed by $x^2+y^2=100$ with $x\ge0$ and $y\ge0$ is split into ten equal intervals. The correct limits and strip width are:Read the answer and worked solution →Which error is bigger?Read the answer and worked solution →Spot the false claimRead the answer and worked solution →

Worked practice questions

The area enclosed by $x^2+y^2=100$ with $x\ge0$ and $y\ge0$ is split into ten equal intervals. The correct limits and strip width are:

$-10$ to $10$, $h=2$
$0$ to $10$, $h=1$
$0$ to $100$, $h=10$
$-10$ to $10$, $h=1$

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Correct answer: B. $0$ to $10$, $h=1$

1. The conditions $x\ge0$ and $y\ge0$ restrict the region to the first quadrant. 2. There the circle of radius $10$ runs from $x=0$ to $x=10$, so those are the limits. 3. Ten equal intervals over that range give $h=\dfrac{10-0}{10}=1$. 4. Taking $-10$ to $10$ ignores $x\ge0$ and doubles the region, which forces $h=2$ and a wrong area. 5. Limits of $0$ to $100$ confuse the radius squared with the radius. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 7: Numerical Methods_

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Which error is bigger?

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Questions

A
Trapezoidal error 0.04
B
Simpson error 0.01
Higher value
Trapezoidal error 0.04
A
Trapezoidal π = 3.10
B
Simpson π = 3.13
Higher value
Simpson π = 3.13
A
Simpson area 78.17563
B
Trapezoidal area 77.6131
Higher value
Simpson area 78.17563
A
Strip width h = 1
B
Strip width h = 2
Higher value
Strip width h = 2

Instructions

Tap the one with the larger value.

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Spot the false claim

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Questions

False statement
Simpson's rule always gives a larger area than the trapezoidal rule
Statements
1. Simpson's rule needs an even number of strips
2. The trapezoidal rule joins points with straight lines
3. Simpson's rule always gives a larger area than the trapezoidal rule
False statement
The quarter circle of radius 10 has area 100π
Statements
1. x ≥ 0 and y ≥ 0 restrict the region to one quadrant
2. Ten equal strips over 0 to 10 give h = 1
3. The quarter circle of radius 10 has area 100π

Instructions

Two statements are true and one is false. Tap the false one.

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