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…
Being one the most astounding formulas in mathematics, Euler’s identity is popularly called God’s equation. Some people also go as far as calling it the mathematical equivalent of Da Vinci's Mona Lisa or Michaelangelo's David.
Named after Leonhard Euler, the formula establishes the deep relationship between trigonometric functions and complex exponential functions.
According to the formula, for any real number x,
In the above formula, e is the base of the natural logarithm…
即 (-d[A]):(-d[B]):d[G]:d[H]=(-dnA ):(-dnB ):dnG :dnH =a : b : g : h
Sample Exercise：The decomposition of N2O5 proceeds according to the equation：
4NO2(g) + O2(g)
If the rate of decomposition of N2O5 at a particular instant in a reaction vessel is 4.2×10−7
mol · dm−3 · s−1，what is the rate of appearance of (a) NO2； (b) O2?
1 d[N 2 O5 ]
d[NO 2 ]
“The Cold Equations”
Question: Who should be blamed for the deaths of the miners/surveyors and the riots on frontier planet?
Marilyn Lee Cross John Barton The Company
Broke the law
Signs said “keep out”
Delayed Barton’s missions
Destroyed company property
Persuaded him to dump
medicine…jeopardized the lives of
Doesn’t care about others…is selfcentered
Goes on to the ship even though
she knows she shouldn’t (thought
there would be a fine which shows
that she knew she didn’t…
Solving Equations and Inequalities
One of the main goals in this course is to help students develop techniques for solving a wide variety of equations and inequalities, which in turn can be used to model real-life situations. This module will focus specifically on linear equations and inequalities.
An equation can be written in many different ways and still be the same equation. For example:
3x + y = 4 original equation
y = −3x…
Chemical Reactions and Equations
The “Chemical Reactions and Equations” lab was to observe physical and chemical properties associated with chemical reactions, to make note of/document the evidence of the chemical reaction, to practice balancing equations, to predict the products that form from a reaction, and to have an understanding; did the elements bond, break apart, or did they switch partners in the reaction (determine what happened to the reactant/s as they formed new product/s)…
reaction is performed. Most
often an increase in the concentration of the reactants also increases the rate of reaction. Likewise an increase in temperature will increase the rate of the reaction in accordance with the activation energy (Arrhenius Equation). In this lab we will examine both factors to determine the order of a reaction and the activation energy.
The Rate Law and Order of Reaction
Since the reaction rate is often dependent on the concentrations of the reactants the rate law is…
For Supervisor’s use only
Level 1 Mathematics, 2004
90147 Use straightforward algebraic
methods and solve equations
9.30 am Thursday 11 November 2004
Check that the National Student Number (NSN) on your admission slip is the same as the number at the
top of this page.
You should answer ALL the questions in this booklet.
You should show ALL working.
If you need more space for any answer, use the page provided at the back of this booklet and clearly
Math Study Guide
Solve each equation for x using any method learned in class.
(1) If there is no solution, then say so. Write your answers using complex numbers if needed.
Show/Explain your work.
(2)Solve each equation for x using algebra.
If there is no solution, then say so. Write your answers using complex numbers if needed.
(3) Simplify each of the following as much as possible.
Note 1. Diﬀerential Equations
= F (x, y). If F (x, y) =
it is called a separable equation and can be solved by the method of separation of
h(y) dy = g(x) dx.
• A ﬁrst order diﬀerential equation has the form
• A ﬁrst order linear diﬀerential equation is of the form
+ P (x)y = Q(x). To
solve the equation, we multiply both sides of the equation by the integrating factor
I(x) := e
P (x) dx
. The equation becomes
I(x)y = I(x)Q(x)