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Mcv4u Test

This document contains a multiple choice test with 7 questions in Section 1 and 6 questions in Section 2 involving calculus concepts such as: 1) Determining the slope of tangent lines to curves at given points. 2) Finding the conditions under which a tangent line is horizontal. 3) Relating the instantaneous rate of change (dy/dx) to the slope of a tangent line. 4) Finding values of x where a function has a horizontal tangent. 5) Ensuring the continuity of a piecewise defined function by determining the appropriate value of k.

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530 views2 pages

Mcv4u Test

This document contains a multiple choice test with 7 questions in Section 1 and 6 questions in Section 2 involving calculus concepts such as: 1) Determining the slope of tangent lines to curves at given points. 2) Finding the conditions under which a tangent line is horizontal. 3) Relating the instantaneous rate of change (dy/dx) to the slope of a tangent line. 4) Finding values of x where a function has a horizontal tangent. 5) Ensuring the continuity of a piecewise defined function by determining the appropriate value of k.

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api-483845268
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© © All Rights Reserved
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K/U T A C

7 4 5 4

MCV4U Test Name:

Section 1- Multiple Choice


Identify the choice that best completes the statement or answers the question ( 1K each )

( )​ 1. Under what condition is the tangent to f (x) at ( a, f(a) ) horizontal?

a) f’(a) > 0 b) f’(a) < 0 c) f’(a) = 0 d) f’(a) is undefined

x+k
( ) 2. Determine the value of K for which f’(5)= 8, if f (x) = x−1

a) -129 b) -9 c) 129 d) 9

2
( ) 3. What is the slope of the tangent to the curve y= x 3x+2 when x = 3

9
a) 5
b) 23 c) 21
81
121
d) 169

( ) 4. What is the slope of the tangent to y= x4 - x3 - x2 +13 where x = -8

a) -1344 b) -1684 c) -2060 d) -1987

( ) 5. Determine the slope of the tangent to the rational function f(x)= 3x+6
x
a​ t point (2, 6 )

a) -1.5 b) 3 c) 1.5 d) -3

( ) 6. Find the slope of the tangent to f (x) = √3x at x = 9


−1
a) 4√x
b) √1 c) √1x d) 4−1
√x
6 3
( ) 7. Determine the slope of the tangent to y= 4+x
x−2
, (8,2 )

1
a) 7 b) −1
6 c) 15 d) −1
7

Section 2

1. Explain how I.R.O.C can be obtained from A.R.O.C. You may make use of diagrams,
formulas or paragraphs. ( 4C )

dy
2. If y= 5 x2 -8x+4. Determine dx
from the first principal ( 2A )

3. At what point on the graph of f (x) = 7 x2 +2X is the tangent parallel to the line with the
equation y = 5x +3? ( 2T )

dy
4. Determine the value of dx
at x= 1 if y= ( x2 -3x +1 ) ( x4 + 1 ) ( 1A )

5. Find all the value(s) of x where function f(x) has a horizontal tangent? (3A)

f(x) = x+2
√x

6. Determine K so that m(x) is continuous. (2T)

m(x)= 9x-14, if x =/ 4
5x+ k, if x=4

Good Luck !!! & Have Fun ​☺

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