Category Archives: Math 11

Final Blog Post! – Math 11

Posted on by

The top 5 things I learned in math was to: simplify radicals, solve for X using the quadratic formula, use the 2 special triangles, derive equations to solve for a variable (cosine law), and graph quadratics.

1. Simply Radicals

Simplifying radicals is a key topic that I learned. It is taking a radical and making it mixed to make it simpler.

2. Solving Quadratic Equations

Another important thing I picked up is solving quadratic equations using the quadratic formula. This formula is great for finding the roots of an equation like ( ax^2 + bx + c = 0 ).

3.The two special triangles the 45°-45°-90°/ the 1-1-Root 2triangle and the 30°-60°-90°/ the 1-Root 2- 3 triangle – are really useful in trigonometry. They have unique properties that make finding the lengths of sides pretty straightforward when you know the angles.

4. The Cosine Law is super handy for solving triangles when you know two sides and the included angle, or all three sides. To find the angle of a triangle with the 3 sides, we use C= cos-1(a^2+b^2-c^2/2ab)

5. Graphing quadratic functions has been another key skill. The standard form of a quadratic function is ( y = ax^2 + bx + c ). Graphing these functions involves finding the vertex, axis of symmetry, and intercepts.

Week 15 – Math 11

Posted on by

This week in math, we learned how to find the rotational angles of a reference angle in each quadrant. First, the reference angle always come off of the x axis.

Example: refθ=30

First, label each reference angle.

Next, label each rotational angle.

Finally, find the rotational angles.

q1= 30

q2= 150

q3= 240

q4= 330

 

 

Week 14 – Math 11

Posted on by

This week in math, we learned how we can solve fractional equations using multiple different  methods. The first method included cross multiplying. The other one included putting all the numbers over the same denominator.

Example:

Cross multiply

\frac{1}{9}+\frac{1}{x}=\frac{4}{9}

First, you collect the like terms to one side.

\frac{1}{x}=\frac{3}{9}

Then, simplify and cross multiply.

\frac{1}{x}=\frac{1}{3}

x=3

Like denominators

\frac{1}{9}+\frac{1}{x}=\frac{4}{9}

First, you put everything over the same denominator.

\frac{x}{9x}+\frac{9}{9x}=\frac{4}{9x}

Then, collect like terms.

\frac{9}{9x}=\frac{3}{9x}

Next, multiply both sides by the denominator.

9=3x

Lastly, divide both sides by the coefficient.

x=3

Knowing that there are more than just one way to solve the same problem allows us to be able to solve in the most efficient way depending on the person. It allows us to have flexibility and also be able to solve using which way might be easier for the specific question.

Week 13 – Math 11

Posted on by

This week in math, we learned how to simplify rational expressions.

Example:

\frac{4x^{2}+28x+48}{2x^{2}+2x+12}

First we need to see if there are any numbers that we can pull out of the expressions. Here, we pull out 4 from the top and 2 from the bottom.

\frac{4\left ( x^{2}+7x+12 \right )}{2\left ( x^{2}+5x+6 \right )}

Next, we factor the expressions.

\frac{4\left ( x+3 \right )\left ( x+4 \right )}{2\left ( x+3 \right )\left ( x+2 \right )}

Then, we cancel out any similarities. Here, we canceled out (x+3) from the top and bottom. We also simplify 4 over 2 to 2 over.  1

\frac{2\left ( x+4 \right )}{1\left ( x+2 \right )}

And now we have our answer!

Week 10 – Math 11

Posted on by

This week, we learned how to find an equation of a function using the vertex and one point on the line. We then were about to put the equation into standard form.

Example 1:

Vertex= (3,-4)

Point= (4,1)

y=a(x-3)^2-4

*note: the vertex is put into the equation  The x value, 3 is made negative and put into the equation with the 4 stays negative.

Next, input the point we were given into the x and y spots in the equation, then solve for a.

(1)=a(4-3)^2-4

1=a-4

5=a

Then take your a value and complete the equation.

y=5(x-3)^2-4

Then to put it into general form, we must expand the equation.

y=5(x-3)(x-3)-4

y=(5x-15)(x-3)-4

y=5x^2-15x-15x+45-4

y=5x^2-30x+41

Example 2:

Vertex=(7,-6)

Point= (9,-4)

y=a(x-7)^2-6

-4=a(9-7)^2-6

-4=a4-6

2=a4

1/2=a

y=1/2(x-7)^2-6

=1/2(x-7)(x-7)-6

=(1/2x-7/2)(x/1-7/1)-6

=1/14x^2-7/2x-7/2x+49/2-6

=1/14x^2-14/2x-37/2

y=1/14x^2-7x-37/2

Week 12 – Math 11

Posted on by

This week in math, I learned how to write an inequality in interval notation. Interval notation is a notation of the x intercepts of an inequality.

Example: x^2 + x – 6<0

(x+3)(x-2)<0

x1=-3

x2=2

-3<x<2

Interval notation: (-3,2)

Example: x^2+9x+8≤0

(x+8)(x+1)≤0

x1=-8

x2=-1

-8≤x≤-1

Interval notation: [-8,-1]

Square brackets are for “greater than/less than or equal to“, round brackets are for “less than/greater than.”

 

Week 11 – Math 11

Posted on by

This week in math, we learned how to graph inequalities. When we have an equation, the line may be linear.

For example y=2x-5

This is a linear line. When we use a greater than/less that sign, an area of the graph is shaded in.

Example; y\leq 2x-5

When y is less than x, the shaded part goes towards the bottom of the graph and vice versa.

Example; y\geq2x-5

When we graph a system of 2 inequalities, our answer will but in the spot that is shaded twice.

Example; y<-x+1 and y>\frac{1}{2}x-2

Extra fact!

What its greater than/less than or equal to, then the line is solid because it includes that line value. If it is dotted, that means its is just greater than/less than.

Week 7 – Math 11

Posted on by

This week in math, I learned how to use the quadratic formula. The Quadratic formula is ax^{2}+bx+c=0. To find the value of X, you input the values of the letters into this formula. {\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}},}

For example:

4x^{2}-12x+3=0

a=4

b=-12

c=3

So,

equation

Then,

equation

equation

equation Then divide by 4.

equation

 

I chose to right about the quadratic formula because I tend to understand concepts more when there is a distinct formula that I need to use. I do better when there is one correct way to do things and not multiple different paths. I am very excited to see how this unit turns out for me.

 

Week 6 – Math 11

Posted on by

This week in math, we started our next unit. We learned how to factor trinomials using the area method.

Example:

3x^2 + 14x+ 15

9x+5x=15x so this is what the square would look like.

This is the easiest way for me to solve a trinomial because I am able to visualize what the answer would be.