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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. Differentiability implies:

A. A function is not defined at that point

B. A function is always continuous everywhere

C. There are discontinuities in the function

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

2 / 30

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

A. Definite integrals of functions

B. Zeros of transcendental functions

C. Infinite sums

D. Solutions of differential equations

3 / 30

3. An integral is best interpreted as:

A. The relationship between velocity and mass

B. The difference between two functions

C. The measurement of angles between two lines

D. The accumulation of quantities or areas under a curve

4 / 30

4. A function is continuous at a point if:

A. It is differentiable at every point of the domain

B. Its integral converges

C. It is differentiable at every point of the domain

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

5 / 30

5. 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 is time-consuming for smooth functions

D. It can only approximate discontinuous functions

6 / 30

6. A function has a maximum when:

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

B. f(x)=0 and f ′′ (x)=0

C. 𝑓 ′ ( 𝑥 ) 0

D. 𝑓 ′ ( 𝑥 ) > 0 and f ′′ (x)>0

7 / 30

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

A. The area under a curve

B. Instantaneous velocity of a particle

C. The slope of a tangent line

D. Points of inflection

8 / 30

8. A definite integral represents:

A. The slope of the tangent line

B. The derivative at a point

C. The area under a curve between two bounds

D. The value of a function at one endpoint

9 / 30

9. Numerical integration is used to:

A. Eliminate transcendental functions from models

B. Solve algebraic equations

C. Find derivative values at certain points

D. Approximate definite integrals that cannot be solved analytically

10 / 30

10. A function is said to be continuous if:

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

B. It has a second derivative everywhere

C. Its derivative exists at every point

D. It has breaks or holes in its graph

11 / 30

11. Newton’s method may fail if:

A. The function f(x) is continuous

B. 𝑓 ( 𝑥 ) is undefined in the interval

C. The initial guess is too close to the root

D. f ′ (x)=0 at some iteration

12 / 30

12. The main disadvantage of the Bisection method is:

A. It needs a large initial interval

B. Its inability to converge

C. It requires the function to be discontinuous

D. It is slower compared to other methods

13 / 30

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

A. Only one derivative of the unknown function

B. A partial derivative

C. No derivatives at all

D. A derivative of the second order

14 / 30

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

A. Subintervals are divisible by 3

B. Subintervals are even

C. Only two data points exist

D. Subintervals are odd

15 / 30

15. In the Trapezoidal Rule, the formula includes:

A. The average of the first and last function values

B. All derivatives of the function

C. The difference between the limits of integration

D. Function values at all midpoints

16 / 30

16. A transcendental function is one that

A. Involves trigonometric, exponential, or logarithmic expressions

B. Represents only polynomial equations

C. Can be solved algebraically

D. Is always continuous and differentiable

17 / 30

17. The primary objective of calculus is to:

A. Analyze changes and accumulation in mathematical models

B. Solve matrix-based problems

C. Simplify algebraic expressions

D. Study arithmetic operations exclusively

18 / 30

18. 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

19 / 30

19. Newton’s Method starts with

A. Using random values for calculation

B. Eliminating derivatives from a function

C. Solving equations for definite integrals

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

20 / 30

20. Quadrature methods for numerical integration require:

A. Transforming all values into logarithmic form

B. Finding the roots of integrands

C. Discrete data values for functions

D. Solving differential equations explicitly

21 / 30

21. The Bisection method requires that the function:

A. Be linear in form

B. Be differentiable at all points

C. Be integrable

D. Have opposite signs at the endpoints of the interval

22 / 30

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

A. Lower computation cost

B. Guaranteed success for any function

C. Independence from derivatives

D. Faster convergence

23 / 30

23.

A. Represents the indefinite integral of the function

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

C. Always equals zero

D. Cannot be solved without differentiating first

24 / 30

24. The second derivative of a function determines:

A. Points where the function is undefined

B. The intercept of a function

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

D. The tangent line's slope

25 / 30

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

A. ln(x)/x

B. x^2

C. ln ⁡ ( 𝑥^2 )

D. 1/x

26 / 30

26. Differential calculus focuses on:

A. Simplifying arithmetic operations

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

C. The study of integrals and their properties

D. Solving quadratic equations analytically

27 / 30

27. 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

28 / 30

28. Partial differentiation deals with functions:

A. Defined implicitly

B. That depend on multiple variables

C. Having a single variable

D. Containing only constant terms

29 / 30

29. The derivative of a constant function is:

A. The function itself

B. Undefined

C. A non-zero constant

D. Zero

30 / 30

30. Newton’s method is generally used when:

A. Calculating integrals over infinite intervals

B. Function 𝑓 ( 𝑥 ) has no derivative

C. Solving differential equations only

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

Your score is

The average score is 28%

MTH 201 CBT PRACTICE

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