Take your time to read instructions before taking this test.

There are 30 questions which you are to answer in 10 minutes that gives you roughly 30 seconds per question.

If you can get at least 60%, you can be rest assured that you’ll ace MTH 201 exam

In a normal exam you will be asked between 40 – 60 questions but I only arranged 40 questions

Note

Do not be in a hurry to answer the questions

Do not waste time on a question you don’t know

Move as fast as possible and starting with questions that don’t have calculation first to save time

Always crosscheck

Don’t be in a hurry to submit, you are not in a competition

Don’t be scared. Getting an A is easy

Don’t be over confident, you can end up a D, E or F. Calm your blood, no be only you sabi book

Please do well to use our comment box incase there’s a message you want to pass to us

70 – 100 A

60 – 69 B

50 – 59 C

45 – 49 D

40 – 44 E

0 – 39 F

I wish you success

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MTH 201

1 / 30

1. The main limitation of the Trapezoidal Rule is:

A. It is always less accurate than Simpson's 1/3 rule

B. It assumes linear behavior over small intervals

C. It is time-consuming for smooth functions

D. It can only approximate discontinuous functions

2 / 30

2. Simpson’s rules are based on:

A. Summing areas under exponential functions

B. Polynomial approximations of data points

C. Integrating non-continuous data

D. Linear interpolations

3 / 30

3. A transcendental function is one that

A. Is always continuous and differentiable

B. Involves trigonometric, exponential, or logarithmic expressions

C. Can be solved algebraically

D. Represents only polynomial equations

4 / 30

4. In the Trapezoidal Rule, the formula includes:

A. The difference between the limits of integration

B. Function values at all midpoints

C. The average of the first and last function values

D. All derivatives of the function

5 / 30

A. Always equals zero

B. Represents the indefinite integral of the function

C. Gives an exact number representing the area under the curve between 𝑎 a and 𝑏 b

D. Cannot be solved without differentiating first

6 / 30

6. The integral of a function is commonly used to determine:

A. Instantaneous velocity of a particle

B. The area under a curve

C. Points of inflection

D. The slope of a tangent line

7 / 30

7. Quadrature methods for numerical integration require:

A. Transforming all values into logarithmic form

B. Discrete data values for functions

C. Solving differential equations explicitly

D. Finding the roots of integrands

8 / 30

8. The Simpson's 3/8 Rule differs from the 1/3 Rule by:

A. Using intervals divisible by 3

B. Approximating functions with degree 1

C. Requiring only one interval

D. Avoiding higher-order derivatives

9 / 30

9. The derivative of a constant function is:

A. The function itself

B. Undefined

C. Zero

D. A non-zero constant

10 / 30

10. Differential calculus focuses on:

A. The rate of change of quantities and slope of curves

B. Simplifying arithmetic operations

C. The study of integrals and their properties

D. Solving quadratic equations analytically

11 / 30

11. Numerical integration is used to:

A. Solve algebraic equations

B. Eliminate transcendental functions from models

C. Find derivative values at certain points

D. Approximate definite integrals that cannot be solved analytically

12 / 30

12. Newton-Cotes quadrature methods are used to approximate:

A. Solutions of differential equations

B. Definite integrals of functions

C. Zeros of transcendental functions

D. Infinite sums

13 / 30

13. The Trapezoidal Rule approximates the area under a curve by:

A. Splitting the interval into trapezoids

B. Drawing straight lines through function values

C. Fitting cubic functions across each segment

D. Connecting endpoints with parabolas

14 / 30

14. An integral is best interpreted as:

A. The relationship between velocity and mass

B. The measurement of angles between two lines

C. The difference between two functions

D. The accumulation of quantities or areas under a curve

15 / 30

15. The primary objective of calculus is to:

A. Simplify algebraic expressions

B. Analyze changes and accumulation in mathematical models

C. Study arithmetic operations exclusively

D. Solve matrix-based problems

16 / 30

16. Newton’s Method starts with

A. Using random values for calculation

B. Solving equations for definite integrals

C. Eliminating derivatives from a function

D. Approximating a root using the tangent line of 𝑓 ( 𝑥 )

17 / 30

17. The Bisection method requires that the function:

A. Have opposite signs at the endpoints of the interval

B. Be linear in form

C. Be differentiable at all points

D. Be integrable

18 / 30

18. The second derivative of a function determines:

A. The intercept of a function

B. The tangent line's slope

C. The rate of change of the slope of the function

D. Points where the function is undefined

19 / 30

19. Newton’s method is generally used when:

A. Solving differential equations only

B. The root of f(x)=0 is not easily accessible

C. Function 𝑓 ( 𝑥 ) has no derivative

D. Calculating integrals over infinite intervals

20 / 30

20. The advantage of Newton’s method over the Bisection method is:

A. Guaranteed success for any function

B. Independence from derivatives

C. Faster convergence

D. Lower computation cost

21 / 30

21. Differentiability implies:

A. A function has a defined slope at a specific point

B. There are discontinuities in the function

C. A function is not defined at that point

D. A function is always continuous everywhere

22 / 30

22. A function is said to be continuous if:

A. Its derivative exists at every point

B. It has a second derivative everywhere

C. It has breaks or holes in its graph

D. It can be drawn without lifting the pencil off the paper

23 / 30

23. Simpson’s 1/3 rule is applicable when:

A. Subintervals are odd

B. Subintervals are divisible by 3

C. Subintervals are even

D. Only two data points exist

24 / 30

24. A definite integral represents:

A. The area under a curve between two bounds

B. The slope of the tangent line

C. The value of a function at one endpoint

D. The derivative at a point

25 / 30

25. A first-order differential equation is characterized by:

A. Only one derivative of the unknown function

B. No derivatives at all

C. A partial derivative

D. A derivative of the second order

26 / 30

26. A function has a maximum when:

A. 𝑓 ′ ( 𝑥 ) 0

B. f(x)=0 and f ′′ (x)=0

C. 𝑓 ′ ( 𝑥 ) > 0 and f ′′ (x)>0

D. f ′ (x)=0 and 𝑓 ′ ′ ( 𝑥 ) < 0 f ′′ (x)<0

27 / 30

27. For $\ln(x)$ , the derivative $f^{'} (x)$ is:

A. ln ⁡ ( 𝑥^2 )

B. x^2

C. ln(x)/x

D. 1/x

28 / 30

28. An inflection point of a curve occurs when:

A. The curve is discontinuous

B. The concavity of the curve changes

C. The curve reaches a maximum value

D. The first derivative equals zero

29 / 30

29. Newton’s method may fail if:

A. f ′ (x)=0 at some iteration

B. The function f(x) is continuous

C. The initial guess is too close to the root

D. 𝑓 ( 𝑥 ) is undefined in the interval

30 / 30

30. Partial differentiation deals with functions:

A. Having a single variable

B. That depend on multiple variables

C. Containing only constant terms

D. Defined implicitly

Your score is

The average score is 28%

MTH 201 CBT PRACTICE

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