This document contains an activity sheet for a Calculus with Analytic Geometry course. It includes multiple problems involving graphing points and lines, finding distances, slopes, equations of circles, parabolas, and hyperbolas, as well as limits, functions, continuity, and differentiation. The activity sheet provides spaces for students to show their work and solutions.

1. ACTIVITY SHEET 1
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Solve the following given statements
1. Pot the points (9,4), (5,4) on a graph, find the distance between two points by counting
the squares. Show your graph and solution at the back
2. Determine the distance between two points (9,4), (5,4) using the distance formula. Show
your work.
B. Answer the following question:
1.Write an ordered pair that can be found in any of the quadrants in a Coordinate Plane, plot
the point on a graph
2.Identify the quadrant where the point is located: ________________
3.Identify the x-coordinate or the abscissa: ___________
4.Identify the y-coordinate or the ordinate: _________
5.Determine the distance of the point from the x-axis: _____________
6. Determine the distance of the point from the y-axis: ______________
C. Determine the distance of the following points:
Use the space at the back for the computation
D. PROBLEM SOLVING
1. While training for a marathon, you decided to run from your home at E
through the park C. Get the distance from your home going to the park using
the Distance formula
Item Answer:
A. Distance between (4, 5) , (5, 3)
B. Distance between (5, 0) (5, 6)
C. Distance between (-4, 1) (3, -4)
D. Distance between (2, -5) (7,4)
E. Distance between (-4, 3) (10, 3)
F. Distance between (-9, -2) (-7, -4)
G. Distance between (7, 0) (4, 0)
C

2. ACTIVITY SHEET 2
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Find the slope of the following points. Use the space on the back for
your solutions
Item Answer
A (0, -5) (3, 2)
B (1, 5) (12, 4)
C (-7, -4) (2, 9)
B. Find the slope and intercept of the following equations of a line
1. y= -5x+15 4.
2
3
𝑥 + 5𝑦 = 10
2. y= 3x+9 5. −
2
5
𝑥 −
1
2
𝑦 = 12
3. 2x+5y=10
C. Find the equation of the line of the following items
1.Find the equation of a line that is parallel to y=−3x+5 and passing through the
point (2,−7).
2.Find the equation of a line that is perpendicular to y =
1
2
𝑥 + 2 and passes through the
point (−10,−5).
3.Find the lines that are parallel and perpendicular to y =
2
5
𝑥 + 7and passing through the
point(1,−2).
D. Find the slope of each line below
A. Find the slope of each line below
A
B
C
E. Solve the following problem
1. Find an equation of a line parallel to the line y=3x+1 that contains the point (4,
2).
2. Find the equation of a line that is parallel to y =
5
2
𝑥 − 4and passes through the
point (2,1).
3. Find the lines that are parallel and perpendicular to y =−
3
2
𝑥 − 15and (0,2)

3. ACTIVITY SHEET 3
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Use the information provided to write the
standard form equation of each circle
1.Center (6 -8), radius = 4
2.Center (2,3), radius = 7
B.Give the center and radius of the following circles and sketch the graph.
1.(𝑥 + 1)2
+ (𝑦 − 3)2
= 5
2. (𝑥 − 3)2 + (𝑦 + 4)2 = 2
3. (𝑥 + 5)2 + (𝑦 − 4)2 = 36
4. (𝑥 + 7)2
+ (𝑦 − 6)2
= 121
C. Identify the vertices, foci and endpoints of each and sketch the graph
1.16𝑦2
− 9𝑥2
− 144 = 0
2. 4𝑥2
− 9𝑦2
= 36
3. 144𝑥2 − 225𝑦2 = 400
4. 36𝑥2 + 72𝑦2 = 972

4. ACTIVITY SHEET 4
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Find the equation of the parabola with:
1. vertex at (-2, 3) and focus (-4, 3)
2.vertex at (3, -4), and focus (3,0)
3.vertex (0, 3), focus (4, 3)
4.vertex (2, 3) and focus (6,3)
5.vertex (2, 0), and focus (2, 2)
B.Locate the center, vertices, foci, enpoints, draw the asymptotes and
sketch the graph.
1.2y2 – 4x2 = 18
2. 5x2 -4y2 = 20
3.x2-3y2=27
C. Solve the following problem
1. Write the equation 9y2-4x2=36 in standard form and sketch the graph of the
hyperbola.
2. Find the vertex, focus and directrix of the parabola, x2=6y and sketch the graph of
a parabola

5. ACTIVITY SHEET 5-6
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Determine whether the given relation is a function or not
A.{
(1,2 ), (2, −5),
(3, −2), (1,5)
}
Domain:
_________________
Range:
_________________
Function or not:
_________________
B.
Domain:
_________________
Range:
_________________
Function or not:
_________________
C.{
(6, −5), (5, −5),
(3, −8), (7,2)
}
Domain:
_________________
Range:
_________________
Function or not:
_________________
B.Indicate whether each set of ordered pairs define a function.
1.{(2,4), (3,6), (4,8), (5,10)}
2. {(−1,4), (0,3), (1,2), (2,1}
3. . {(10, −10), (5, −5), (1, 2), (2, 1}
4. {(0,1), (1,1), (2,1), (3,2), (4,2), (5, −2)}
5. {
(𝑂ℎ𝑖𝑜, 𝑂𝑏𝑎𝑚𝑎), (𝐴𝑙𝑎𝑏𝑎𝑚𝑎, 𝑀𝑐𝐶𝑎𝑖𝑛),
(𝑊𝑒𝑠𝑡 𝑉𝑖𝑟𝑔𝑖𝑛𝑖𝑎, 𝑀𝑐𝐶𝑎𝑖𝑛), (𝐶𝑎𝑙𝑖𝑓𝑜𝑟𝑛𝑖𝑎, 𝑂𝑏𝑎𝑚𝑎)
}
D.Perform the following operation given the function below.
1. If 𝒇(𝒙) = 𝒙𝟐
− 𝟒𝒙 + 𝟐 and 𝒈(𝒙) = 𝟑𝒙 − 𝟕
a. Find f+g(x)
b. Find f-g(x)
c. Find f*g(x)
d. Find
𝑓
𝑔
(𝑥)
e. Find (𝑓°𝑔)𝑥
Is it an Even function, Odd function or neither?
_________________________________
E.Each of the following defines a function; tell whether the function is
even, odd or neither
1.f(x)= 3x
2.f(x)= x5-2x3+4
3.f(x)= 12x3-5x2
E.Compute (𝒇°𝒈)𝒙 for each of the given pair of functions
1. (x)=5x+2, g(x)=x2−14x
2.f (x)=x2−2x+1, g(x)=8−3x2
F.Problem Solving
1.An electrician charges a base fee of $70 plus $50 for each hour of work. Create a table that
shows the amount the electrician charges for 1,2,3, and 4 hours of work. Let x represent the
number of hours and y represent the amount charged for x hours. Is this relation a function?

6. ACTIVITY SHEET 7
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Fill in the table provided to find the requested limit
1.lim
𝑥→5
( 3𝑥 − 8) =?
x 4 4.1 4.9 4.99 5 5.01 5.1 5.5 6
3x-8
2. lim
𝑥→3
( 5𝑥 + 2) =?
x 2 2.5 2.9 2.99 3 3.01 3.1 3.5 4
5x+2
3. lim
𝑥→1
( 2𝑥 − 4) =?
x 0.5 0.8 0.9 0.99 0.999 1.001 1.1 1.2 1.5
2x-4
C. Verify the limits given
1. lim
𝑥→3
𝑥2
− 5𝑥 + 6
2. lim
𝑥→−1
=
3𝑥−4
8𝑥2+2𝑥−2
3. lim
𝑡→0
4𝑡2+3𝑡+2
𝑡3+2𝑡−6
C.Prove the statements by means of the theorem used by giving numbers
1. lim
𝑥→3
( 7𝑥 − 4) = 17
2. lim
𝑥→−1
( 2𝑥3
− 5𝑥) = 3
3. lim
𝑥→2
( 𝑥2 + 1)(3𝑥 − 11) = −25
4. lim
𝑥→4
( 3𝑥2
− 2𝑥) = 40
5. lim
𝑥→2
( 5𝑥5
− 13𝑥2
− 10) = 118

7. ACTIVITY SHEET 8
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.State whether the indicated function is continuous at 2;or not
1.𝑓(𝑥) = 4𝑥5
− 2𝑥2
+ 12
2. 𝑓(𝑥) =
8
𝑥−2
3. 𝑓(𝑥) =
3𝑥2
𝑥−1
4. 𝑓(𝑥) =
𝑥2−9
𝑥−3
5.
B. if the following function is continuous or discontinuous at ?
1. 𝑓(𝑥) =
4𝑥+5
9−3𝑥
(a) x=−1, (b) x=0, (c) x=3
2.𝑓(𝑥) =
6
𝑧2−3𝑧−10
(a)z=−2 (b)z=0 (c)z=5
B. Describe any discontinuities in the functions below:
1. y=x
2. y= x2
3. y=x3

8. ACTIVITY SHEET 9&10
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Solve for the following problems
1.Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x2
+ 1. Compute the following:
a. f(g(-3))
b. f(h(7))
c. (g◦h)(24)
2. Let f(x) = -3x + 7 and g(x) = 2x2
– 8. Compute the following:
a. f(g(x))
b. (g◦f)(x)
B.Describe the interval on which the function is continuous.
1.𝑓(𝑥) = 𝑥2
− 2𝑥 + 1
2. 𝑓(𝑥) = 3 − 2𝑥 − 𝑥2
3.𝑓(𝑥) =
𝑥
𝑥2−1
4. 𝑓(𝑥) =
𝑥−3
𝑥2−9
5. 𝑓(𝑥) =
1
𝑥2+1

9. ACTIVITY SHEET 11
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Evalute the following limits using Squeeze Theorem
1.lim
𝑥→0
𝑥2
𝑠𝑖𝑛
1
𝑥
2. lim
𝑥→0
𝑥4
𝑠𝑖𝑛
7
𝑥
3. lim
𝑥→0
𝑥2
𝑐𝑜𝑠
5
𝑥
4. lim
𝑥→0
𝑥2
cos(10𝑥)
5. lim
𝑥→0
𝑥𝑠𝑖𝑛𝑥
6. lim
𝑥→0
𝑥2
sin (12𝑥)
7. lim
𝑥→0
1−𝑐𝑜𝑠𝑥
𝑠𝑖𝑛𝑥
8. lim
𝑥→0
sin (3𝑥)
sin (4𝑥)

10. ACTIVITY SHEET 12
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Differentiate the following function with respect to x.
1.y= 5
2. y=5x18
3.𝑦 = 4𝑥5
+ 𝑥
4.𝑓(𝑥) = 4𝑥4
− 5𝑥 − 3
5. 𝑓(𝑥) = 3𝑥5
− 6𝑥2
+ 2𝑥 − 16
6. 𝑓(𝑥) = 𝑥4
− 3𝑥2
+ 6𝑥 − 3
7. 𝑓(𝑥) = 13𝑥5
− 6𝑥2
+ 13
8. 𝑓(𝑥) = 4𝑥3
− 18𝑥 + 3
9. 𝑓(𝑥) = (2𝑥 + 1)2
10. 𝑓(𝑥) = 𝑥3
+ 6𝑥
11. 𝑓(𝑥) = −7𝑥2
− 2𝑥 + 3
12. 𝑓(𝑥) = 4𝑥3 − 12𝑥 − 7
13. 𝑓(𝑥) = 2 + 8𝑥 − 3𝑥2
14. 𝑓(𝑥) = 3𝑥2
− 11𝑥 + 7
15. 𝑓(𝑥) = 12𝑥3 − 𝑥 − 25
B.Find the functions below for the given value of x:
1.
𝑥3−2
𝑥2 ; x=2
2.
2𝑥 −7
𝑥
; x= - 3
3. 𝑓(𝑥) = 6𝑥2
+ 6𝑥 − 36 ;x=-2

11. ACTIVITY SHEET 13
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Find the derivative of the following functions(do not simplify)
1.f(x)=(3𝑥2
+ 7)(4𝑥 − 1)
2. 𝑓(𝑥) = (4𝑥3
− 9)(7𝑥)
3. 𝑓(𝑥) = (14𝑥 − 2)(3𝑥2 + 8)
4. 𝑓(𝑥) = (3𝑥2 − 2𝑥)(𝑥 + 1)
5. 𝑦 = (2𝑥3
− 9𝑥)(8𝑥2
− 2𝑥 − 3)
6. 𝑦 = (12𝑥2
− 5𝑥)(15𝑥3
)
7. 𝑦 = (8𝑥 − 3)(3 − 4𝑥3
)
8. 𝑦 = (𝑥3 − 4𝑥)(2𝑥 + 1)
B.Find the derivative of the following functions. Simplify the numerators
1.𝑦 =
7𝑥−1
12+4𝑥
2. .𝑦 =
13𝑥−2
2𝑥3+8
3. .𝑦 =
3𝑥2−5
12+2𝑥
4. .𝑦 =
4𝑥3−2𝑥
𝑥3+1
5. .𝑦 =
3𝑥2−𝑥
𝑥2−7
6. .𝑦 =
2𝑥2−5𝑥
5𝑥3
7. .𝑦 =
𝑥−2𝑥3
𝑥2−7𝑥
8. .𝑦 =
8𝑥−3𝑥3
4−5𝑥2

12. ACTIVITY SHEET 14&15
Name:______________________________________________
Section: _____________________
Subject: M105 CALCULUS WITH ANALYTIC GEOMETRY
Instructor: Ms. Marjorie B. Malveda
A.Find the derivative of each given function (use chain rule)
1.𝑦 = (8𝑥 − 3)3
2. 𝑦 = (𝑥3
+ 5𝑥)2
3. 𝑦 = (6 − 8𝑥2)3(2 − 5𝑥)
4. 𝑦 = (7𝑥 + 3)4
(5𝑥2
− 5)
5. 𝑦 = (6 − 8𝑥2
)3
(2 − 5𝑥)
B.Find the derivative of the following functions using implicit
differentiation:
1.4𝑦 + 5𝑥 = 10
2. 7𝑥 − 2𝑦 = −12
3. 𝑥3
+ 5𝑦 = 𝑥
4. 𝑥2
− 5𝑦3
= 2 − 𝑥
5. 3𝑦2
− 4𝑥2
= 𝑦 + 2𝑥
C.Use the quotient rule to prove the derivative of the following
trigonometric functions
1. tan x
2. cot x
3.sec x
4.csc x
5.𝑦 = 𝑠𝑒𝑐4𝑥
6. 𝑦 = 𝑡𝑎𝑛3𝑥 − 𝑐𝑜𝑡3𝑥
7. 𝑦 = 𝑐𝑜𝑡5𝑥 + 𝑐𝑠𝑐5𝑥
8. 𝑦 = 𝑡𝑎𝑛𝑥 + 𝑐𝑜𝑡𝑥
9. 𝑦 = 4𝑠𝑒𝑐𝑥 − 2𝑐𝑠𝑐𝑥
10. 𝑦 = 𝑠𝑒𝑐𝑥(𝑡𝑎𝑛𝑥)