GENERAL AND SPECIFIC COMPETENCIES IN MATHEMATICS IV
(Advanced Algebra, Trigonometry and Statistics)

A. Functions
1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function
1.2 Differentiate a function from a mere relation
* real life relationships
* set of ordered pairs
* graph of a given set of ordered pairs
* vertical line test
* given equation
1.3 Illustrate the meaning of the functional notation f(x) 1.4 Determine the value of f(x) given a value for x
B. Linear Functions
1. Demonstrate knowledge and skill related to linear functions and apply in solving problems
1. Define the linear function f(x) = mx + b
2. Given a linear function Ax + By = C, rewrite in the form f(x) = mx + b and vice versa 3. Draw the graph of a linear function given the following: * any two points

* x and y intercepts
* slope and one point
* slope and the y-intercept
4. Given f(x) = mx + b, determine the following: * slope
* trend: increasing or decreasing
* x and y intercepts
* some points
5. Determine f(x) = mx + b given:
* slope and y-intercept
* x and y intercepts
* slope and one point
* any two points
6. Solve problems involving linear functions
C. Quadratic Functions
1. Demonstrate knowledge and skill related to quadratic functions and apply these in solving problems
1.1 Identify quadratic functions f(x) = ax2 + bx + c
1.2 Rewrite a quadratic function ax2 + bx + c in the form f(x) = a(x-h)2 + k and vice versa
1.3 Given a...

...Level 1/Level 2 Certificate
Mathematics
Specification
Edexcel Level 1/Level 2 Certificate in Mathematics
(KMAO)
First examination June 2012
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...Name _______________________________________ Score ______________________
Section __________________________
REVISING IN MATHEMATICS IV
A.Y. 2014 - 2015
(Science Class)
General Directions: Analyze the following statements then write the correct answer.
I. MULTIPLE CHOICES
Directions: Read the following test items carefully. Write the letter of the correct answer.
1. Which of the following is a polynomial function?
a. P(x) = 3x-3 – 8x2 + 3x + 2 c. P(x) = 2x4 + x3 + 2x + 1
b. P(x) = x3 + 4x2 + – 6 d. G(x) = 4x3 – + 2x + 1
2. What is the degree of the polynomial function f(x) = 5x – 3x4 + 1?
a. 2 c. 4
b. 3 d. 5
3. What will be the quotient and the remainder when y = 2x3 – 3x2 – 8x + 4 is divided by
(x +2)?
a. q(x) = 2x2 – 7x + 6 , R = -8
b. q(x) = 2x2 – 7x + 6, R = 8
c. q(x) = 2x2 – 7x – 6, R = -8
d. q(x) = 2x2 – 7x - 6 , R = 8
4. If f(a) = 2a3 + a2 + 12, what will be the value of f(a) at a = -2?
a. 1
b. -1
c. 0
d. 2
5. What must be the value of k so that when f(x) = kx2 - x + 3 divide by (x + 1) and the remainder is 5?
a. 2
b. -2
c. 0
d. 1
6. What must be the value of k in the function f(x) = x4 + x3 – kx2 – 25x – 12 so
that (x – 4) is a factor?
a. -12
b. -13
a. 13
b. 12
7. What is the remainder when f(x) = x4 + 3x2 + 4x – 1 divided by (x – 1)?
a. 7
b. -7
c. 6
d. 5
8. Which of the following binomial is a factor of f(x) = x3 – x2 – 5x – 3?
a. x - 1
b. x + 2
c. x - 3...

...Collin Doyle
Mrs. Perino
Math 48A.01
11 January 2013
Homework 1.2: P. 19-21 #’s 23-24, 66-67, 70, 73, 74a-b, 76
23) Problem: Explain how to determine whether a parenthesis or a square bracket is used when graphing an inequality on a number line.
Solution: a. Parenthesis: indicate a range of values, open interval, I think of parenthesis as being the parent that is more open to given their child toys and bending the rules.
b. Brackets: has limits between two numbers, closed interval, I think of brackets as the stern parent who enforces the rules to the highest degree.
24) Problem: The three-part inequality a < x < b means “a is less than x, and x is less than b.” Which one of the following inequalities is not satisfied by some real number x?
A. -3 < x < 5 B. 0 < x < 4
C. -3 < x < -2 D. -7 < x < -10
Solution: D, because -10 is less than -7 and x is greater than -7 which also means that x is also greater than -10.
66) Problem: If f(3) = -9.7, identify a point on the graph of f.
Solution: (3,-9.7), f(3) is f(x) which means that 3 is the x-value and -9.7 is the y-value.
67) Problem: If the point (7,8) lies on the graph of f, then f(___) = ____.
Solution: f(7) = 8, this problem is the reverse of the problem before, you plug in the x-value (7) into x in f(x) and then plug in the y-value (8) in for the y.
70) Problem: Use the graph of y = f(x) to find each function value: a. f(-2), b. f(0),...

...values of t.
s is a complex algebra variable defined by: s = a +jω where j = sqrt(-1), so you will be partly using imaginary numbers.
The symbol i (j in electrical engineering) is used to represent √ -1. Therefore, for example, √(-4) = 2i. The number called i, or 1i , or xi are called purely imaginary numbers.
One use of the complex plane is known as the s-plane. It is used to visualize the roots of the equation describing a system's behavior (the characteristic equation) graphically. The equation is normally expressed as a polynomial in the parameter 's' of the Laplace transform, hence the name 's' plane.[1]
Complex plane using Argand diagrams show the z-plane, where z = x + iy and may use z-Transforms as well as the Laplace. In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. It can be considered as a discrete-time equivalent of the Laplace transform. This similarity is explored in the theory of time scale calculus. Through bilinear transformation, the complex s-plane (of the Laplace transform) is mapped to the complex z-plane (of the z-transform).
Z = a+ ib, = r e^itheta, a = real part of z, b = imaginary part of z, r = modulus of z, theta = argument of z, a & b are real numbers. While this mapping is (necessarily) nonlinear, it is useful in that it maps the entire jΩ axis of the s-plane onto the unit circle in the...

...Semi-Detailed Lesson Plan in Mathematics (Transformations)
Level: First Year High School
Subjects: Mathematics, Geometry, Transformations
I. Objectives:
A. To recognize Euclidean transformations.
B. To recognize reflections, translations, and rotations.
C. To prove theorems related to transformations.
D. To solve problems involving transformations.
E. To apply transformations to real-world situations.
F. To create designs using transformations.
II. Materials:
papers, protractor, ruler
tangram puzzle
worksheets
III. Procedure:
A. Presentation
Activity - Folding of Paper
The teacher will give an activity that involves the folding of paper and tracing of shapes.
B. Discussion
From the activity, the teacher will point out that geometry is not only the
study of figures but is also the study of the movement of figures.
Is the original figure congruent to the other figures?
How does the second image compare to the original figure?
C. Input
Definitions:
Transformations
Reflection
Rotation
Translation
Dilation
Rigid Motion
Theorems:
Theorem 18-1
Theorem 18-2
Theorem 18-3
Theorem 18-4
C. Discussion
The above definitions and theorems will be discussed and proved. The teacher will ask the student to give examples of transformations.
D. Activity
Tangram Puzzle
The students will form six groups. Each group is going to make images of animals using tangram puzzle and they will identify the...

...Contribution of India in mathematics
The most fundamental contribution of India in mathematics is the invention of decimal system of enumeration, including the invention of zero. The decimal system uses nine digits (1 to 9) and the symbol zero (for nothing) to denote all natural numbers by assigning a place value to the digits. The Arabs carried this system to Africa and Europe.
1) Aryabhata is the first well known Indian mathematician. Born in Kerala, he completed his studies at the university of Nalanda. In the section Ganita (calculations) of his astronomical treatise Aryabhatiya, he made the fundamental advance in finding the lengths of chords of circles, by using the half chord rather than the full chord method used by Greeks. He gave the value of as 3.1416, claiming, for the first time, that it was an approximation. He also gave methods for extracting square roots, summing arithmetic series, solving indeterminate equations, and also gave what later came to be known as the table of Sines. He also wrote a text book for astronomical calculations, Aryabhatasiddhanta. Even today, this data is used in preparing Hindu calendars. In recognition to his contributions to astronomy and mathematics, India's first satellite was named Aryabhata.
2) Brahmagupta is renowned for introduction of negative numbers and operations on zero into arithmetic. His main work was Brahmasphutasiddhanta, which was a corrected version of old...

...Why study Mathematics?
The main reason for studying mathematics to an advanced level is that it is interesting and enjoyable. People like its challenge, its clarity, and the fact that you know when you are right. The solution of a problem has an excitement and a satisfaction. You will find all these aspects in a university degree course.
You should also be aware of the wide importance of Mathematics, and the way in which it is advancing at a spectacular rate. Mathematics is about pattern and structure; it is about logical analysis, deduction, calculation within these patterns and structures. When patterns are found, often in widely different areas of science and technology, the mathematics of these patterns can be used to explain and control natural happenings and situations. Mathematics has a pervasive influence on our everyday lives, and contributes to the wealth of the country.
The importance of mathematics
The everyday use of arithmetic and the display of information by means of graphs, are an everyday commonplace. These are the elementary aspects of mathematics. Advanced mathematics is widely used, but often in an unseen and unadvertised way.
• The mathematics of error-correcting codes is applied to CD players and to computers.
• The stunning pictures of far away planets sent by Voyager II could not have had their...