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CBT TEST

MTH 201 CBT PRACTICE

Phil

January 17, 2025

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. Newton-Cotes quadrature methods are used to approximate:

A. Solutions of differential equations

B. Zeros of transcendental functions

C. Infinite sums

D. Definite integrals of functions

2 / 30

2. 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

3 / 30

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

A. Subintervals are even

B. Subintervals are divisible by 3

C. Only two data points exist

D. Subintervals are odd

4 / 30

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

A. Independence from derivatives

B. Faster convergence

C. Lower computation cost

D. Guaranteed success for any function

5 / 30

5. The derivative of a constant function is:

A. The function itself

B. Zero

C. A non-zero constant

D. Undefined

6 / 30

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

A. Connecting endpoints with parabolas

B. Drawing straight lines through function values

C. Fitting cubic functions across each segment

D. Splitting the interval into trapezoids

7 / 30

7. A function is said to be continuous if:

A. It has breaks or holes in its graph

B. Its derivative exists at every point

C. It has a second derivative everywhere

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

8 / 30

8. A transcendental function is one that

A. Can be solved algebraically

B. Involves trigonometric, exponential, or logarithmic expressions

C. Represents only polynomial equations

D. Is always continuous and differentiable

9 / 30

9. Newton’s Method starts with

A. Eliminating derivatives from a function

B. Using random values for calculation

C. Solving equations for definite integrals

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

10 / 30

10. Partial differentiation deals with functions:

A. Containing only constant terms

B. That depend on multiple variables

C. Having a single variable

D. Defined implicitly

11 / 30

11. In the Trapezoidal Rule, the formula includes:

A. The difference between the limits of integration

B. All derivatives of the function

C. The average of the first and last function values

D. Function values at all midpoints

12 / 30

12. A definite integral represents:

A. The derivative at a point

B. The slope of the tangent line

C. The value of a function at one endpoint

D. The area under a curve between two bounds

13 / 30

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

A. Only one derivative of the unknown function

B. A derivative of the second order

C. A partial derivative

D. No derivatives at all

14 / 30

14. An inflection point of a curve occurs when:

A. The concavity of the curve changes

B. The curve reaches a maximum value

C. The curve is discontinuous

D. The first derivative equals zero

15 / 30

15. Newton’s method may fail if:

A. 𝑓 ( 𝑥 ) is undefined in the interval

B. The initial guess is too close to the root

C. f ′ (x)=0 at some iteration

D. The function f(x) is continuous

16 / 30

16. Differentiability implies:

A. A function is always continuous everywhere

B. A function is not defined at that point

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

D. There are discontinuities in the function

17 / 30

17. The second derivative of a function determines:

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

B. Points where the function is undefined

C. The intercept of a function

D. The tangent line's slope

18 / 30

18. The primary objective of calculus is to:

A. Solve matrix-based problems

B. Analyze changes and accumulation in mathematical models

C. Simplify algebraic expressions

D. Study arithmetic operations exclusively

19 / 30

19. The Bisection method requires that the function:

A. Be integrable

B. Have opposite signs at the endpoints of the interval

C. Be linear in form

D. Be differentiable at all points

20 / 30

20. The main limitation of the Trapezoidal Rule is:

A. It assumes linear behavior over small intervals

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

C. It can only approximate discontinuous functions

D. It is time-consuming for smooth functions

21 / 30

21.

A. Cannot be solved without differentiating first

B. Always equals zero

C. Represents the indefinite integral of the function

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

22 / 30

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

A. 1/x

B. ln(x)/x

C. x^2

D. ln ⁡ ( 𝑥^2 )

23 / 30

23. Newton’s method is generally used when:

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

B. Calculating integrals over infinite intervals

C. Solving differential equations only

D. Function 𝑓 ( 𝑥 ) has no derivative

24 / 30

24. An integral is best interpreted as:

A. The accumulation of quantities or areas under a curve

B. The difference between two functions

C. The measurement of angles between two lines

D. The relationship between velocity and mass

25 / 30

25. Simpson’s rules are based on:

A. Linear interpolations

B. Integrating non-continuous data

C. Summing areas under exponential functions

D. Polynomial approximations of data points

26 / 30

26. A function is continuous at a point if:

A. Its integral converges

B. It is differentiable at every point of the domain

C. The left-hand limit, right-hand limit, and function value are equal

D. It is differentiable at every point of the domain

27 / 30

27. Quadrature methods for numerical integration require:

A. Finding the roots of integrands

B. Discrete data values for functions

C. Solving differential equations explicitly

D. Transforming all values into logarithmic form

28 / 30

28. A function has a maximum when:

A. f(x)=0 and f ′′ (x)=0

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

C. 𝑓 ′ ( 𝑥 ) > 0 and f ′′ (x)>0

D. 𝑓 ′ ( 𝑥 ) 0

29 / 30

29. The main disadvantage of the Bisection method is:

A. It is slower compared to other methods

B. Its inability to converge

C. It requires the function to be discontinuous

D. It needs a large initial interval

30 / 30

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

A. Approximating functions with degree 1

B. Using intervals divisible by 3

C. Avoiding higher-order derivatives

D. Requiring only one interval

Your score is

The average score is 28%

MTH 201 CBT PRACTICE

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