1st year Calculus 1 Prelim 1 Exam Hint PDF

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Started on State Completed on Time taken Marks Grade

Saturday, 2 October 2021, 10:11 AM Finished Saturday, 2 October 2021, 10:26 AM 15 mins 2 secs 30.00/30.00 100.00 out of 100.00

Question 1 Complete Mark 2.00 out of 2.00

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Question text Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fractional answer) 11

Answer: length = Answer and midpoint x = Answer

3.5

Question 2 Complete Mark 1.00 out of 1.00

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Question text The following problems could be solved by differential calculus: Select one or more: a. rate or speed b. largest or smallest volume of a solid c. summation of small areas d. area between the graph of a function and the x-axis

Question 3 Complete Mark 1.00 out of 1.00

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Question text The slope of the tangent line is called the Answer point P.

Derivative

of the function f(x) at

Question 4 Complete Mark 1.00 out of 1.00

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Question text Calculus was developed by Leibniz and Answer name)

Newton

. (Indicate only the last

Question 5 Complete Mark 1.00 out of 1.00

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Question text Sketch the lines x=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew.

Select one or more: a. The slope of the tangent lines at x=1 is 1 and at x=3 is -1. b. The slope of the tangent lines at x=1 and x=3 is 0. c. The slope of the tangent line at x=2 is 1. d. The slope of the tangent lines at x=1, x=2 and x=3 is 1. e. The slope of the tangent line at x=2 is 0. Question 6 Complete Mark 1.00 out of 1.00

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Question text The slope of a horizontal line is Answer Question 7 Complete Mark 1.00 out of 1.00

0

. (Answer should be numeric)

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Question text The slope of a vertical line is Answer

undefined

.

Question 8 Complete Mark 3.00 out of 3.00

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Question text Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2. (write the numerical coefficient of each term to complete the required equation) Answer: 3

Answer: Answer x + Answer y + Answer =0

7 29

Question 9 Complete Mark 3.00 out of 3.00

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Question text Find the slope and midpoint of the line segment from P(2,-3) to Q(2+n,-3+5n). 5

Answer: slope = Answer , midpoint(0.5n+Answer , Answer

2.5

2

n-3) Question 10 Complete Mark 2.00 out of 2.00

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Question text Find the equation of the line which goes through the point (3,10) and is parallel to the line 7x-y=1. 7

Answer: Answer x - y - Answer =0

11

Question 11 Complete Mark 6.00 out of 6.00

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Question text Find the equation of a circle with radius=6 and center C(2,-5). (write the required exponent after the ^ symbol; write the numerical coefficient of each term to complete the required equation) 2

Answer: x^Answer + y^Answer - Answer

4

x + Answer y - Answer =0

2

10 7

Question 12 Complete Mark 1.00 out of 1.00

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Question text The process of taking the limit of a sum of little quantities is called Answer Integration

.

Question 13 Complete Mark 2.00 out of 2.00

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Question text Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8,13). Answer: slope of the tangent line = -5/Answer

12

Question 14 Complete Mark 1.00 out of 1.00

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Question text Sketch the lines X=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew.

Select one or more: a. The slope of the tangent line x=2 is 0. b. The slope of the tangent lines x=1 and x=3 is 0. c. The slope of the tangent line x=2 is 1. d. The slope of the tangent lines x=1, x=2 and x=3 is 1. e. The slope of the tangent lines at x=1 is 1 and at x=3 is -1. Question 15 Complete Mark 1.00 out of 1.00

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Question text If a tangent line is inclined 45 degrees, then what is the slope the tangent line? Select one: a. 0

b. 1 c. 2/3 d. 3/2 Question 16 Complete Mark 1.00 out of 1.00

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Question text The 2 divisions of Calculus are: Select one or more: a. Differential b. Integral c. Trigonometry d. Algebra Question 17 Complete Mark 2.00 out of 2.00

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Question text Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value for your final answer. Answer: Answer

-1.44...