CLASS X-IGCSE INTERNATIONAL MATH (0607)
HOLIDAYS HOME-WORK (2024-25) Estimate Time: 3 hours
Dear Students
We will be using this module to consolidate our understanding of graphs of non-linear functions, using
Geogebra applets and the GDC and its follow up exercises. We have dealt with linear functions, their
anatomy and problem solving. We have even explored and interpreted some real-life situations which use
linear functions. We will use this module to have a hands-on to explore non-linear functions and revise the
concepts covered in class before the summer break. This will give you confidence in approaching questions
based on graphs. The last segment also includes a mixed bag of practice questions to revise the topics
covered so far.
Assessment Objectives for this module are as follows:
Graph the following polynomials and tabulate your observations
Task 1: a) Exponential growth v/s Linear Growth and Linear Equation Anatomy
Use the applets https://www.geogebra.org/m/CVMPHDfd and https://www.geogebra.org/m/vs5wy4qw
Try out the above functions on your GDC too.
Answer the following questions:
Q1. What is the general form of the equation of a straight line? ……………………………
Q2. How can we tell the slope a line by looking at its equation? Explain.
………………………………………………………………………………………………………………..
Q3. How can we tell the y-intercept of a line by looking at its equation? Explain.
……………………………………………………………………………………………………………….
Task 2: a) Exponential Functions Anatomy b) Exponential Functions: Graphs
Interact with the applet https://www.geogebra.org/m/v8c8xjrc by dragging the TWO LARGE POINTS.
Then answer the questions that follow when you graph the exponential function 𝒚 = 𝒂𝒙−𝒉 + 𝒌
Q4. What does the parameter ‘a’ do to the graph? How does it affect it? Explain
……………………………………………………………………………………………………………..
Q5. What does the parameter ‘h’ do to the graph? How does it affect it? Explain
………………………………………………………………………………………………………………
Q6. What does the parameter ‘k’ do to the graph? How does it affect it? Explain
………………………………………………………………………………………………………………
Q7. Does the graph of the exponential function ever cross the dashed horizontal line (the axis in this case)?
Explain how you know it does OR how you know it does not.
…………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………
……………………………………………………………………………………………………
Now for task (b) just explore the applet https://www.geogebra.org/m/YK6pcUsB and think over the
questions based on it. Use the sliders carefully and analyze its impact on the graph.
Task 3: Exponential Growth & Decay (Illustrated Meaning-Extend your understanding)
Whenever a quantity increases by a certain percentage per unit time, this quantity is said to grow
exponentially. Whenever a quantity decreases by a certain percentage per unit time, this quantity is
said to decay exponentially. Interact with the applet https://www.geogebra.org/m/UNnfwuhQ for a few
minutes, then answer the questions that follow. You can check your answers too within the applet.
Task 4: Quiz: Graphing Exponential Functions (Create a sketch- Extend your understanding))
Interact with the applet https://www.geogebra.org/m/GMvvpwrm#material/zybgawza and sketch the given
exponential function. Make sure your horizontal asymptote , y-intercept are correct. Check your answer
using the button provided. Feel free to make mistakes. Just ensure you get it correct and clear your concept
with gradual attempts. It includes transformations too, so be careful !
Task 5: Quadratic Functions Anatomy
Interact with the following applets and answer the questions given below. Attempt the MCQs given in the
applet and check your answer. The specific applet needs to be explored for the questions mentioned
alongside.
https://www.geogebra.org/m/jyhek3te (Q8)
https://www.geogebra.org/m/txghkjfp (Q9-Q10)
https://www.geogebra.org/m/dcdhs6rw (Q11-Q13)
Q8. For the graph of 𝑦 = 𝑎𝑥 2 what happens when 𝑎 = 0? Explain.
…………………………………………………………………………………………………………………
Q9. Suppose we graph the quadratic function 𝑦 = 𝑎𝑥 2 + 𝑐. What does the parameter 𝒄 do to the graph?
Explain.
…………………………………………………………………………………………………………
Q10. Suppose we graph the quadratic function 𝑦 = 𝑎𝑥 2 + 𝑐. What does the parameter 𝒂 do to the graph?
Explain.
………………………………………………………………………………………………………………
Q11. Suppose you graph the quadratic function 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘. What does the parameter 𝒌 do to the
graph? Explain.
………………………………………………………………………………………………………………
Q12. Suppose you graph the quadratic function 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘. What does the parameter 𝒉 do to the
graph? Explain.
………………………………………………………………………………………………………………
Q13. Suppose you graph the quadratic function 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘. Explain how changing the value of
𝒂 affects the graph. Be specific
……………………………………………………………………………………………………………
Task 6: Sketching graphs of quadratic functions
Interact with the applet https://www.geogebra.org/m/munejsfy to move the LARGE POINTS to sketch the
graph of the quadratic function given. Press the CHECK button to check your graph. Try this exercise for at
least 3 quadratic functions by clicking on NEW PROBLEM.
Task 7: Graphing Quadratic functions- Axis of symmetry
For the quadratic function given in the applet https://www.geogebra.org/m/x5enavtv , enter its axis of
symmetry. Then graph it using the LARGE 3 POINTS. Try this exercise for at least 3 quadratic functions by
clicking on NEW PROBLEM.
Task 8: Now complete the table below to summarize your understanding of graphing quadratic functions.
You may use Desmos / Geogebra graphing calculator/ GDC to verify your responses.
Rough
Quadratic Function Sketch of
Graph
y = 3x 2
1
y = − x2
2
𝑦 = 𝑥² − 7𝑥 + 10
Sign of a
in
ax2+bx+c
and its
effect on
the
sketch
Point(s) of
intersection
with y axis
(also known
as the y
intercept)
Point(s) of
intersection
with x axis
(also known as
the x
intercept)
Turning Point of
the graph using the
vertex form
Quadratic Function
𝑦 = −𝑥² + 7𝑥 − 10
y = x 2 − 8 x + 13
y = − x 2 − 8 x − 13
y = ( x − 3) 2 + 1
𝑦 = (𝑥 − 3)2 − 1
Rough
Sketch of
Graph
Sign of a
in
2
ax +bx+c
and its
effect on
the sketch
Point(s) of
intersection
with y axis
(also known
as the y
intercept)
Point(s) of
intersection with
x axis (also
known as the x
intercept)
Turning Point of the
graph using the vertex
form
Task 9: Match the appropriate graphs with each equation
The first equation is the general form of a quadratic function y =  ax 2 + bx + c ; the second equation
is the factorized form y = ( x − a)( x − b) and the third equation is the completed square form
𝑦 = (𝑥 − 𝑝)2 + 𝑞. Complete the equations as required in all three forms and justify yourself the
relation between the sign of a in the first form of the equation and the direction of the parabola;
second form of the equation and the zeroes; and the third form of the equation and the coordinates
of the point where the parabola bends.
Task 10: Understanding Quadratic graphs (Sort)
Q14. Match the numbers with the appropriate alphabet in the card sort activity. Color the equation box with
the sketch box with the same colour , if they match. (NON- CALC)
Task
11:
LET’S EXTEND OURSELVES – CUBIC POLYNOMIALS
Visit and study the following link http://www.purplemath.com/modules/polyends.htm
Visit each of the linked sections on the top of the page namely End Behavior, Zeroes and their multiplicities,
Flexing, Turnings & “bumps”, Graphing. After going through each, answer the questions that follow.
Practice Sheet
Do the following questions on notepad sheets
Q1. State whether true or false giving reasons.
Q2.
Q3.
Q4. Use your GDC to answer the questions.
a) Plot the function
b) Use your GDC to
c) On the same screen , plot 𝑦 = 3𝑥 − 2
𝑤ℎ𝑒𝑟𝑒 − 1 ≤ 𝑥 ≤ 3.5
𝑥3
d) The equation 𝑦 = 2 − 3𝑥 − 1 = 3𝑥 − 2 can be written in the form 𝑥 3 + 𝑎𝑥 + 𝑏= 0. Find the values
of 𝑎 𝑎𝑛𝑑 𝑏.
Answer (d) (ii) a= ………………. and b= ……………………….
Question 5:
Use your GDC to find the other solution.
Answer (iii) x=,…………. [1]
What can you say about the asymptotes of this function? (Use your GDC)
……………………………………………..END OF MODULE ……………………………………