SUBDOMAIN 212.1 - NUMERACY, ALGEBRA, & GEOMETRY Competency 212.1.2: Solving Algebraic Equations - The graduate solves algebraic equations and constructs equations to solve real-world problems. Introduction: An important element of learning is to connect mathematical concepts with physical concepts. Graphical representations of mathematical functions will allow you to visualize the meaning and power of mathematical equations. The power of computer programs and graphing calculators provide a more thorough connection between algebraic equations and visual representation, which will increase appreciation and understanding of mathematical language. In this task, you will be making connections between algebraic equations and graphical representations. Task: A. Complete the following graphs: 1. Graph the following values on a single number line. • Value 1: 1 • Value 2: 0 • Value 3: –6 • Value 4: 3/4 • Value 5: –1.7 2. Graph the following points on a single coordinate plane. Make sure to include labels for each quadrant of the coordinate plane. • Point 1: (3, –2) • Point 2: (0, 0) • Point 3: (–1, 7) • Point 4: (3, 5) • Point 5: (–4, –5) 3. Graph the following functions on separate coordinate planes. • Function 1: y= 2x − 1 • Function 2: y= (–3/4)x + 5 • Function 3: y= x2 − 4 • Function 4: y= –3x2 − 6x − 5 a. In each graph, label each axis of the coordinate plane. Additionally, label each intercept as “x-intercept” or “y-intercept” and include the ordered pair. • Whenever applicable, label the vertex as “vertex” and include the ordered pair. B. When you use sources, include all in-text citations and references in APA format. Note: Please submit all graphics and equations in *.pdf (Portable
Students solve equations, evaluate algebraic expressions,
solve and graph linear equations and linear inequalities, graph lines, and solve systems of linear
equations and linear inequalities. These concepts and skills serve as a foundation for subsequent
coursework. Applications to real-world problems are integrated throughout the course. This course is the
first half of the college algebra sequence, which is completed in Algebra 1B.
TOPICS AND OBJECTIVES
Real Numbers and Algebraic Expressions
Specification – What students need to learn:
1 Algebra & functions
1.1 The rules of indices
Laws of indices for all rational exponents. The equivalence of and should be known.
1.1 Algebraic Expression Ext Qs
1.2 Indices & Surds
Use and manipulation of surds.
1.3 Rationalising the denominator
Students should be able to rationalise denominators.
1.3 Surds & Indices Ext Qs
Algebraic manipulation of polynomials, including expanding brackets and collecting like…
ACCUPLACER MATH REVIEW SHEETS
The Accuplacer exam is a branching exam. This means that when you miss a problem, it will branch to a lower level
problem. When you get a problem right, the test then gives you a slightly more difficult problem. In this fashion, this
test is very accurate in determining your placement into our DMAT/MATH program.
The first exam that you will be given will be the Elementary Algebra test. Depending on your score, you will then take
either the Arithmetic (to place you…
my linear function for both the men and the women’s scatter plots (Shown on Page
3) start from 1 and increases infinitely. This is because the “domain” represents the number of
Olympic events held after 1944 and the Olympic events, so far, will continue until the end of time,
therefore the domain will not have an end to it as well.
The Range of the linear function for the men’s scatter plot (Shown on Page 2 and 3) is
anything below or equal to 10.3, and the range of my linear function for the…
1. Solve each equation below, if possible, using any strategy. State the strategy you used for each part. Be sure
to check your solutions (Remember: solving strategies may include graphing, algebraic strategies, etc.!)
a. 4 8x 2 8
b. 3 4x 8 9 15
5 1 4x
2. The function graphed at right is y (x 3)2 5 . Use this graph
(x + 3)2 − 5 = 4. (Hint: What did the 4 in the
to solve the equation
equation replace? How did the graph help…
Absolute Value Function- An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line. The absolute value parent function, written as f(x) = |x|
Constant of Variation- The ratio between two variables in a direct variation or the product of two variables in an inverse variation. In the direct variation equations = k and y = kx , and the inverse variation equations xy = k and…
INTRODUCTION TO FUNCTIONS
-The independent variable goes on the x-axis, and the dependent variable on the y-axis
eg. Time – x-axis and Distance – y-axis
-A function is a rule that gives a single output number for every valid input number
-The graph of y=mx+b is a straight line with slope m and y-intercept b.
-slope is Rise/Run
-Constant Slope Property
-The slope of all segments of a line are equal.
-Properties of a Linear Function
-The equation y=mx+b represents a linear function.
ACT One, Larch , OBJ
CCS, CSP, Petri Nets
Finite State Machines
Types of Formal Methods
Description of the operations that can be perform on a system, and the relationships between operations. More specifically: A signature part which de nes the syntax of operations (what parameters they take and return); An equations part, which de ne the semantics of the…
design a novel controller for an automated robotic arm. A discrete Proportional Integral Derivative
(PID) control technique is being used to replace the complex electronic circuitry, which would greatly reduce the cost
and size of the controller. Function is derived for mathematical modeling of the system through which the stability of the
system can be evaluated prior to fabrication.looptune to tune a multi-loop controller for a 4-DOF robotic arm manipulator.
The recent rapid…