MCV4U0
PROBLEM SET V: Derivatives II
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) The figure to the right shows the graphs of f ( x ) , f ( x ) and f ( x ) . Match the three function
MCV4U0
PROBLEM SET V: Derivatives II
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) Let y = arcsin x + arctan
a)
Show that
1 x 2
x
, x ( 0,1] .
dy
= 0 for all x ( 0,1) .
dx
SOLUTION:
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
MULTIPLE CHOICE: Choose the ONE BEST
answer to each question. Place all your choices on
the LEGAL SIZE paper provided.
1) (1K) The value of in the diagram below is
4) (1K) If g( x ) is the inverse function
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AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
FULL SOLUTION: Answer each question on the LEGAL SIZE paper provided with COMPLETE STATEMENTS
when required.
1) Evaluate the following limits. Show all your work for full marks.
a) (2K) lim
x 32
x
x
2
4
5
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
FULL SOLUTION: Answer each question on the LEGAL SIZE paper provided with COMPLETE STATEMENTS
when required.
1) Evaluate the following limits. Show all your work for full marks.
a)
(2K) lim
x 0
b) (3K) lim
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
FULL SOLUTION: Place all your choices on the LEGAL SIZE paper provided.
1) Find the value of the following limits:
a)
(2K) lim
x 0
x + tan x
sin x
b) (2K) lim
x 0
arccos x
x
2) (3K, 1C) Let f ( x ) be a co
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
FULL SOLUTION: Place all your choices on the LEGAL SIZE paper provided.
1) Find the value of the following limits (show your work for full credit):
a)
(1 + x) 6 64
x 1 (1 + x ) 2 4
(2K) lim
x 2 + arcsin 2
MCV4U0
PROBLEM SET V: Derivatives II
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) The figure to the right shows the graphs of f ( x ) , f ( x ) and
f ( x ) . Match the three function
MCV4U0
PROBLEM SET V: Derivatives II
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) Let y = arcsin x + arctan
1 x 2
x
, x ( 0,1] .
dy
= 0 for all x ( 0,1) .
dx
a)
Show that
b)
What do
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS II TEST A
FULL SOLUTION: Answer each question on the LEGAL SIZE paper provided with COMPLETE STATEMENTS
when required.
1) (4A, 1C) Let x( t ) = t 2 + 8 ln( t + 1) represent the position of a particle in meters on th
MCV4U0
PROBLEM SET I: Precalculus Solutions
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) What is the equation of the line passing through the point of intersection of the lines x + 5
NAME_
AP CALCULUS
POLYNOMIAL TEST A
MULTIPLE CHOICE: Choose the ONE BEST
answer to each question. Place all your choices on the
LEGAL SIZE paper provided.
1) (1A) A certain laboratory animal weighed
150 grams at age 5 days and 380 grams at age
30 days. As
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AP CALCULUS
POLYNOMIAL TEST A
MULTIPLE CHOICE: Choose the ONE BEST
answer to each question. Place all your choices on the
LEGAL SIZE paper provided.
1) (1K) Which of the following statements is
CORRECT regarding the polynomial
f ( x ) = 5x 3 + 6 x 2
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AP CALCULUS
QUIZ A: PRECALCULUS
FULL SOLUTION: Answer all questions on the LEGAL SIZE paper provided with COMPLETE
STATEMENTS when applicable.
1) (3K, 1C) Solve for x and y:
117 x 39 y = 507
39 x 117 y = 351
(
)
(
2) (2K, 1C) Find the coefficient of
MCV4U0
PROBLEM SET I: Precalculus
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) What is the equation of the line passing through the point of intersection of the lines x + 5 y + 7 = 0
MCV4U0
PROBLEM SET I: Precalculus
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) Consider a circle with diameter AB. Point C lies on the extended line segment AB and point H lies on th
NAME_
AP CALCULUS
QUIZ A: PRECALCULUS
FULL SOLUTION: Answer all questions on the LEGAL SIZE paper provided with COMPLETE STATEMENTS
when applicable.
1) Consider the graphs to the right of the line l , the parabola
y = x 2 + Bx 11 and the various labelled
NAME_
AP CALCULUS
QUIZ A: PRECALCULUS
FULL SOLUTION: Answer all questions on the LEGAL SIZE paper provided with COMPLETE STATEMENTS
when applicable.
1)
4 x + 3y = 7
. Find the coordinates of P.
a)
(3K, 1C) Let point P be the point of intersection of the l
NAME_
AP CALCULUS
QUIZ A: PRECALCULUS
FULL SOLUTION: Answer all questions on the LEGAL SIZE paper provided with COMPLETE
STATEMENTS when applicable.
1) (3K, 1C) In the figure to the right, the line has a slope of 2. What is the
yintercept of the line?
2)
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AP CALCULUS
PRECALCULUS QUIZ A
FULL SOLUTION: Answer with COMPLETE STATEMENTS on the LEGAL SIZE paper
The points A( 3,4) , B( 4,3) and C lie on the circle x 2 + y 2 = 25 with center O. The point P( 5,10) is a point outside the
circle as shown in the
MCV4U0
PROBLEM SET I: Precalculus
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) In the diagram to the right, square EPCD has an area of 196 cm2 . If the area of
BPC is 35 cm2 and the
MCV4U0
PROBLEM SET I: Precalculus
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) Consider a circle with diameter AB. Point C lies on the extended line segment AB and point H lies on th
MCV4U0
PROBLEM SET II: Polynomials
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) The function f ( x ) = Ax 3 + 3x 2 Bx 30 is divisible by ( x + 2) and leaves a remainder of 21 when di
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS TEST A
MULTIPLE CHOICE: Choose the ONE BEST answer
to each question. Place all your choices on the LEGAL
SIZE paper provided.
1) (1K) The function shown below has which of the
following properties?
5)
(1K) The graph
NAME_
AP CALCULUS
POLYNOMIAL TEST A
MULTIPLE CHOICE: Choose the ONE BEST answer to each question. Place all your choices on the LEGAL SIZE paper
provided.
1) (1K) Let f ( x ) be a polynomial with real coefficients and of degree four. Which of the followin
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS TEST A
MULTIPLE CHOICE: Choose the ONE BEST answer to each question. Place all your choices on the LEGAL SIZE paper
provided.
Questions 13 refer to the passage below.
One of the many achievements in mathematics that
MCV4U0
PROBLEM SET IV: Derivatives
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) On the curve f ( x ) = x 2 , there exists a point P(a , f ( a ) ) in which the tangent at this point i
NAME_
AP CALCULUS
DIFFERENTIAL CALCULUS TEST A
MULTIPLE CHOICE: Choose the ONE BEST answer
to each question. Place all your choices on the LEGAL
SIZE paper provided.
1) (1K) Which of the following statements regarding the
graph of the function y = f ( x )
MCV4U0
PROBLEM SET II: Polynomials
In order to receive FULL MARKS for this problem set (as well as future problem sets), you must show ALL your work.
1) Consider the quartic function f ( x ) = x 4 6 x 2 + 8 x 3 .
a)
Find all real roots of f ( x ) . State
NAME_
AP CALCULUS
POLYNOMIAL TEST A
MULTIPLE CHOICE: Choose the ONE BEST
answer to each question. Place all your choices on the
LEGAL SIZE paper provided.
3) (1K) The graphs of the functions f and g in the
interval x [ 2,2] are shown below.
1) (1A) A stud