9.4.1 Numerical integration Quiz: Pearson Edexcel Maths, Unit 9

The 20 questions

1. What is the primary purpose of numerical integration in A-level maths?

   • Finding derivatives
   • Approximating definite integrals
   • Solving differential equations
   • Calculating gradients

2. Which rule uses linear interpolation between points to estimate definite integrals?

   • Rectangle rule
   • Midpoint rule
   • Trapezium rule
   • Simpson's rule

3. What is the formula for the strip width h given limits a and b with n strips?

   • n / (b - a)
   • (a - b) / n
   • (b + a) / n
   • (b - a) / n

4. How many y-values are needed to use the trapezium rule with 4 strips?

   • 5
   • 8
   • 4
   • 6

5. What shape are the approximating segments assumed to be in the trapezium rule?

   • Rectangles
   • Triangles
   • Trapezia
   • Parabolas

6. When does the trapezium rule give an overestimate for a convex curve?

   • Always
   • Never
   • At turning points
   • Only sometimes

7. When does the trapezium rule give an underestimate for a concave curve?

   • At inflection points
   • Always
   • Never
   • Only sometimes

8. What is the general bracket multiplier for intermediate y-values in the trapezium rule?

   • 1
   • 4
   • 2
   • 3

9. Calculate h for interval [0, 2] divided into 4 strips.

   • 2
   • 1
   • 0.25
   • 0.5

10. Find the strip width h for the interval [1, 4] with 6 strips.

    • 0.5
    • 3/4
    • 0.3
    • 1

11. What multiplier is applied to the first and last y-values in the trapezium rule formula?

    • 1
    • 2
    • 0.5
    • 4

12. Find the second x-ordinate when integrating from 0 to 1 with 4 strips.

    • 0.5
    • 0.2
    • 0.25
    • 0.1

13. Estimate int(x^2) dx from 0 to 2 using 2 strips.

    • 2
    • 4
    • 2.67
    • 3

14. What happens to the approximation error as the number of strips increases towards infinity?

    • Oscillates infinitely
    • Remains constant
    • Decreases to zero
    • Increases

15. How can you determine if a trapezium rule estimate is an overestimate without graphing?

    • Integral is negative
    • Second derivative positive
    • First derivative positive
    • Second derivative negative

16. Which algebraic curve shape causes the trapezium rule to yield the exact analytical integral?

    • Quadratic
    • Exponential
    • Linear
    • Cubic

17. Find the third x-ordinate when evaluating from 2 to 5 with 3 strips.

    • 4
    • 3.5
    • 4.5
    • 3

18. What is the outer factor in the standard trapezium rule formula outside the brackets?

    • h / 3
    • h / 2
    • 2 / h
    • h

19. Estimate int(2^x) dx from 0 to 2 using 2 strips.

    • 3.5
    • 4.33
    • 4
    • 4.25

20. Why might a student get a math error when evaluating a trapezium rule table?

    • Wrong variable
    • Negative limit
    • Too many strips
    • Undefined ordinate

Related quizzes

• Locating roots by change of sign Quiz · 9.1.1 · 20 questions
• Solving equations by simple iteration Quiz · 9.2.1 · 20 questions
• Newton-Raphson method Quiz · 9.3.1 · 20 questions
• Numerical methods in context Quiz · 9.5.1 · 20 questions
• Structure of mathematical proof and methods of proof Quiz · 1.1.1 · 20 questions
• Vectors in two and three dimensions Quiz · 10.1.1 · 20 questions
• Laws of indices for all rational exponents Quiz · 2.1.1 · 20 questions
• Straight lines and their equations Quiz · 3.1.1 · 20 questions
• Binomial expansion Quiz · 4.1.1 · 20 questions
• Sine, cosine and tangent for all angles Quiz · 5.1.1 · 20 questions