## 5 Keys to Your Math 10 Success

Here are 5 things that will help you in Ms. Pahlevanlu’s math 10 class.

1. Do the blog posts. Yes they’re not that interesting but it’s best not to let them accumulate.

2. Listen. Ms. P’s lessons are really not hard to follow and don’t usually take that long. So at least pay attention so you don’t have to re-learn the lesson later.

3. Don’t stress. As the daily homework is not checked it is up to you how prepared you want to be. So don’t over-exert yourself doing extra practice if you don’t need it.

4. Ask for help if you need it. Ms P is very approachable and you have lots of class time to get the help you require.

5. Study. The tests aren’t ridiculously challenging bu to succeed or obtain the mark you would like you will need to study or have a general knowledge of what you are learning.

## Week 15 – Slope

The slope of a line segment is the steepness of the line. It is the ratio of the rise (vertical) over the run (horizontal).

Horizontal lines have a slope of 0, and vertical lines have an undefined slope.

In math, slope is represented by the letter m.

Slope Formula: The slope of a line can be determined even without the graph as long as you have the two points and the slope formula. The formula is as follows:

M= $\frac{y2-y1}{x2-x1}$

Example: Determining the slope of points A (4,5) and B (2,1)

## Week 14 – Distance Formula

This week in math we learned about the distance formula in regards to relations and how to determine the length of a line segment.

The distance formula works as follows:

This may look complicated however it is really just the Pythagorean theorem with the line segment lengths formulas plugged in.

The following diagram shows the Pythagorean theorem well:

Example: Determining the length of A (3,4) to B (8, -2)

## Week 13 – Domain and Range

This week in math 10 we learned about the domain and range of a relation. The domain of a relation is all possible values that can be used as the input of the independent variable and the range is all possible values that can be used as the output of the dependent variable.

Also when working with graphs, remember that x-values = input values, therefore x-values = domain, and y-values = output values and y-values = range.

When using brackets there are two different sets with two different meanings:

Closed brackets: Equal to –  [ ]

Open brackets: Not equal to – ( )

Example: When working with graphs or ordered pairs, the domain and range can be determined by listing the inputs and outputs.

Ordered pairs:

(1,3), (-2,4), (3,5), (7,8),

D: {1, -2, 3, 7}

R: {3, 4, 5, 8}

## Week 12 – Intercepts

This week in math we learned about intercepts. Intercepts are the points on the graph where the line touches either the x or y axis. You can also find the x or y intercepts given a equation. This is done by replacing either the x or y values with zero and solving for x or y.

To find the x intercept, you replace the value of y in your expression with zero. If you are finding the y intercept, you replace the value of x with zero. Then solve the expression.

Example equation: 3x + 2y = 24

X- intercept:

3x + 2(0) = 24

3x = 24

x= 8

X-intercept = (8, 0)

Y- intercept:

3(0) + 2y = 24

2y = 24

y = 12

Y-intercept = (0, 12)

## Week 11 – Factoring Polynomial Expressions

This week in math we learned about the steps for factoring polynomial expressions. These steps can be remembered using the acronym CDPEU. It’s not necessary to remember it but if it works for you, use it.

C – Common Factors

D – Difference of squares

P – Patterns within the polynomial

E – Easy – Is the leading coefficient 1 and is the expression easy to factor

U – Ugly – The expression is not easy to factor and will require further work

Also always remember to fully factor/simplify your expressions.

Example: 8$x^4$ + 10$x^2$-3

(4$x^2$ -1) (2$x^2$ + 3)

This can then be simplified to:

(2x + 1) (2x – 1) (2$x^2$ + 3)

## Week 10 – Difference of squares

This week in math we looked over the difference of squares, a a concept we discovered in week 9 where you use the method as a way of skipping the distributive method while evaluating your expression.

The method works as follows:

(a+b) (a-b)

= $a^2$ + ab – ba – $b^2$

= $a^2$$b^2$

This can be used to work backwards as well, when factoring expressions.

Example:

75$x^2$$y^2$ -3

First we remove the common factor,

3 (25$x^2$$y^2$ -1)

Then we factor.

3 (5xy – 1) (5xy + 1)

## Week 9- Recognizing Polynomial Patterns

This week in math 10 we learned how to recognize patters within polynomial expressions and evaluate them. These patterns can be remembered and then applied to skip over distributive property steps and evaluate the expressions quicker.

The patterns:

(a+b) (a-b)

= $a^2$ + ab – ba – $b^2$

= $a^2$$b^2$

$(a+b)^2$ = (a+b) (a+b)

= $a^2$ + ab + ba + $b^2$

= $a^2$ + 2ab + $b^2$

$(a-b)^2$ = (a-b) (a-b)

= $a^2$ -ab -ba + $b^2$

= $a^2$ -2ab + $b^2$

## Week 8- F.O.I.L

This week in math 10 we learned about multiplying polynomials, distributive property, and the acronym FOIL.

The acronym FOIL stands for First terms, Outside terms, Inside terms, and Last terms. This is in regards to which terms you multiply and in what order, before you combine like terms.

Distributive property (FOIL) with binomials would look like: (a+b) (c+d) = ac + ad + bc + bd.

Example: In this expression, you begin by multiplying 3x and 2x, the FIRST terms, then 3x and 5, the OUTISDE terms, then 2 and 2x, the INSIDE terms, and finally 2 and 5, the LAST terms.

## Week 7 – Calculating unknown angles (theta)

This week in math we learned how to calculate unknown angles of triangles given the sine, cosine and tangent ratios. The easiest way to remember these is the acronym SOH CAH TOA. The first letter stands for the ratio, and the second and third letters represents what lengths you put into the expression. When the expression is written, the second letter is in the numerator, and the third goes in the denominator.

To use the ratios you have to have your triangle labelled correctly. Then you can use the opposite, adjacent, and hypotenuse lengths to find your angle. These are the lengths represented by O, A, and H in SOH CAH TOA.

Example: In the triangle (see below) angle x is our unknown angle. Because we have at least 2 side lengths, we can find it. In this case the opposite and adjacent lengths will be used, so the tangent ratio will be the one we use. Then you simply set up the equation: $tan^-1$ (5/6), and plug it into your calculator. This gives us roughly 39.8° which will be rounded to 40°.