1. Steve Greer sgreer@hrsb.ca hrsbstaff.ednet.ns.ca/sgreer
University Prep Math
Steve Greer
hrsbstaff.ednet.ns.ca/sgreer
Course Outcomes
By the end of the course, students should be able to
Solve linear equations
Solve a system of equations
Identify linear, quadratic and exponential patterns
Algebraically find the equation of each type of pattern
Graph linear and quadratic functions
Transfer between the 3 forms of a quadratic
Solve quadratic equations by factoring, completing the square or by using the quadratic root formula
Solve for the vertex of a quadratic
Solve exponential equations using common bases and logs
Solve logarithmic equations
Solve simple probability problems
Use permutations and combinations to solve problems involving probability

2. University Prep Math Phrase or Term Definition Example A variable
The letter which stands for a number that can change.
‘x’ in 2x-6 is a variable. Its value could be 4, or -6, or any other number.
A function
The relationship between two variables.
y = 2x is a relationship between two variables (x and y). In this case, the function says “y is always twice as much as x”.
Evaluating an expression
Finding out what the value of the expression is when you know the value of the variable.
Evaluate: 4x-1 when x = 3.
We plug in a 3 wherever we see an ‘x’ and follow the order of operations.
Phrase or Term
Definition
Example
Phrase or Term
Definition
Example
A variable
The letter which stands for a number that can change.
‘x’ in 2x-6 is a variable. Its value could be 4, or -6, or any other number.
Phrase or Term
Definition
Example
A variable
The letter which stands for a number that can change.
‘x’ in 2x-6 is a variable. Its value could be 4, or -6, or any other number.
A function
The relationship between two variables.
y = 2x is a relationship between two variables (x and y). In this case, the function says “y is always twice as much as x”.

3. Order of Operations: When to do what
B E D M A S I V S ON DD I T ON R A C K E T S X P ON E N T S U B T R A C I ON U L T I P A C ON

4. “Evaluating an Expression” examples
Evaluate the following expressions given the value of the variable stated.
7x-3 if x = (x-2) if x = 4
5r -7t -6 if r = 2 and t = t2 +5t -9 if t = 2
3x(x-2) + x/2 if x = if j =3
Answers:

5. Find the root of each equation. 1) 5(x-4) = 10 2) 8w – 2 = -42
Phrase or Term
Definition
Example
Solving an equation or finding the roots.
Finding out what the value of the variable is when you know what the expression equals. This is the opposite as evaluating the expression.
Root – the value of the variable that makes the equation true.
Solve for ‘x’.
3x-4 = 8
We will “undo” BEDMAS
Answers:
) -5
3) 11
4) 10/6 = 1.67
5) ) -3
Find the root of each equation.
1) 5(x-4) = 10 2) 8w – 2 = -42
3) ½ (g+1) = 6 4) 3x + 6 = 9x – 4
5) 6)

6. Where do these functions come from?
We have worked with a few expressions and a few equations but what do they mean? Let’s look out how our every day lives use functions all the time!

7. Linear Function: Temperature
The temperature in Dallas, Texas is 940F. What is that temperature in degrees Celsius?

8. Here’s a graph showing the relationship between the two temperature measurements.
If we can describe this graph mathematically, we can calculate the temperature in Dallas. We need the
EQUATION OF A LINE

9. y = mx+b describes ANY (straight) line.
THE EQUATION OF A LINE
This equation has two parts. The slope, which is given the symbol ‘m’ (DUH!) and the y-intercept, given the symbol (you guessed it) ‘b’
y = mx+b describes ANY (straight) line.

10. THE EQUATION OF A LINE
PART 1: The slope of a line is a number value indicating how steep the line is.
Each of these lines is as steep as the others. They have the same slopes.

11. THE EQUATION OF A LINE
PART 2: The vertical (y) intercept is the point where the line crosses the vertical (y) axis.
These lines share the same vertical intercept. But they each have a different slope.

12. THE EQUATION OF A LINE
Each distinct line has a specific slope and a specific y-intercept. If these are defined, then we can find every point on the line.
Finding slope:
The slope indicates how much change there was in the dependant variable (y) for every change in the independent variable (x).
Mathematically, that means to find the CHANGE in the ‘y’ variable and divide it by the CHANGE in the ‘x’ variable.
Slope: Δy / Δx
We can use two points on the graph to calculate the slope, or we can identify it as a RATE OF CHANGE given in the question.

13. Finding the slope.

14. THE EQUATION OF A LINE
Each distinct line has a specific slope and a specific y-intercept. If these are defined, then we can find every point on the line.
Finding the y-intercept
EVERY y-intercept can be given in the form (0,y). This means that if we let x = 0, we can get the y-value and thus the y-intercept.
Mathematically, that means to find the VALUE of the ‘y’ variable when the ‘x’ variable has a value of 0.
Let’s find the y-intercept of our equation.

15. USING THE EQUATION OF A LINE
Our equation is F = 9/5C + 32
We know the value of “F”, the number of degrees Fahrenheit. We want to know “C”, the number of degrees Celsius. So we need to solve the equation for C.

16. (34.4,94)

17. Cell Phone Bill – A function
What are two variables involved in cell phone use?
We can find a relationship between the cost of the bill and the time of usage.
Which variable depends on the other?
Let’s say that it costs 20 cents per minute and that you are always charged a monthly fee of $7.00.
Questions: 1) What is the function?
2) If you talked for 45 minutes, what will your bill be?
3) If your bill is $37.40, how many minutes were you on the phone?

18. Substitution and Elimination
We will now look at the situation where we compare two linear equations. This can help us figure out when two cell plans cost the same amount, for instance.
We can use elimination or substitution to solve a system of equations.
A set of equations that have common variables. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
For example: If 3x + 4 = y, there are an infinite number of solutions to this equation.
BUT if 3x + 4 =y AND -7x-1 =y, then none of those solutions work. That is, they don’t satisfy BOTH equations.
(1,7) or (0,4) or (-1/3,3) or (-100,-296) to name a few

19. So what is the solution to
3x + 4 =y and -7x-1 =y?
If both 3x + 4 and -7x-1 are equal to ‘y’, they must be equal to each other.
3x+4 = -7x – 1
5 = -10x
x = -0.5
We can now use this value in either of the original equations to solve for y:
y= 3 (-0.5) +4
y= 2.5
OR y = -7(-0.5) -1
y = 2.5
This is the ONLY x value that will give us the same y value in each equation
The same!

20. Substitution Practice
Ex. What values of x and y satisfy both of these equations? 3x + 2y = 11 and 5x – 3y = 31
Solve one equation for one of the variables.
3x + 2y = 11
2y = 11-3x
y = (11-3x)/2
5x – 3[(11-3x)/2] = 31
Now solve for x.
Substitute this expression into the other equation.
5x – 33/2 +9x/2 =31
10x/2 +9x/2 = /2
19x/2 = 62/2 + 33/2
19x/2 = 95/2
19x = 95
X = 5
y = (11-3(5))/2
Y = -4/2 = -2

21. Substitution Practice
Ex. What values of x and y satisfy both of these equations? 3x + 2y = 11 and 5x – 3y = 31
Let’s double check our answer. The solution x = 5 and y = -2 will work in both equations
3(5) + 2(-2) = 11
= 11
11= 11
5(5)-3(-2) =31
= 31
31 = 31
Both are true statements!

22. Elimination Practice
To eliminate one of the variables, we may need to multiply an equation by a factor before we add or subtract the equations.
Ex. Solve this system of equations using elimination.
6h + 3f = -3
9h -2f = -11
Let’s subtract the equations.
-3h + 5f = 8
Still two variables…this didn’t help!

23. Elimination Practice
To eliminate one of the variables, we may need to multiply an equation by a factor before we add or subtract the equations.
Ex. Solve this system of equations using elimination.
6h + 3f = -3
9h -2f = -11
Let’s add the equations +
Let’s subtract the equations.
15h+ f = -14
Still two variables…this didn’t help!

24. Elimination Practice
To eliminate one of the variables, we may need to multiply an equation by a factor before we add or subtract the equations.
Ex. Solve this system of equations using elimination.
6h + 3f = -3
9h -2f = -11 2( 3( )
Let’s subtract the equations.
Let’s add the equations
Now they become
12h + 6f = -6
27h – 6f = -33
Let’s multiply the first equation by 2 and the second equation by 3 so that both have the term ‘6f’. +
Now we can add them to eliminate ‘f’
39h = -39
h = -1
To find ‘f’ simply plug -1 for h into either equation.
6(-1) + 3f = -3
-6 + 3f = -3
3f = 3
f = 1

25. Word problem example
A certain Math textbook costs $10 more than 3 times the amount of an English book. Together, they total $140 before taxes. Calculate the price of each book.
E = price of English book
M= price of Math book
10+3E + E = 140
10+4E = 140
M =10+3E
M + E = 140
4E = 130
E = 130/4
E = 32.5
M =107.5

26. Solve these systems using substitution:
x- 3y = -25 2) 5x + 9y = -2 3) 2x -4y = 15
4x + 5y = x +4y = -1
Solve these systems using elimination:
4) 3x +5y = -9 5) x = 2y + 1 6) x + y = 950
2x - 3y = x – 9y = x y =
Answers:
(-4,7) 2) (0.5, -0.5) 3) (1,-3)
4)(2,-3) 5) (9, 4) 6) (250, 700)