Week 17 in Prec 11

After having the winter break, we came back to school in week 17. In the new week, we learnt the    Trigonometry. The primary trig ratios are “sin”, “cos”, “tan”.

In the any triangles, we can find these three values for each angle, we have learnt the simple in math 10, so the important thing in this unit are Sine Law and Cosine Law.

For the sine law, if we know one angle and its opposite line and a side line, or we know two angles and the opposite line of one of them, we can use the sine Law.

This is the cosine law, in fact, there are three functions for each angle, we can use this one to change into the other two. If we know three line or one angle and its two adjacents, we can use the cosine Law.

And in the end, we have biggest angles in this unit, so the symbol of three ratios will change.

For the quadrant 1, sin, cos and tan are all positive; and the Q2, sin is positive, cos and tan are negative; tan is positive , sin and cos are negative in the Q3; in the end, cos is positive, tan and sin are negative in the Q4. It make a sentence: All students take calculate(ASTC). Easy to remember!

Top1: chapter8, absolute value and reciprocal functions

Top2: chapter6, trigonometry

Top3: chapter3, solving quadratic equations

Top4: chapter1, sequences and series

Top5: Chapter4, analyzing quadratic functions

 

Week 15 in prec 11

This week we learnt the chapter Rational Expressions and Equations.

For each expression:

1. Factor the numerator and denominator.

2. Identify the non-permissible values of the variables.

3. Divide the numerator and denominator by their common factors.

This is the normal steps in solving the expressions, like this example:

Frist, we should factor it into \frac{9(2+x)(2-x)}{(x-2)(x-3)}

and we can cancel the x-2, but here we should cancel into -1 because they and opposite number,

we will get \frac{-9(2+x)}{(x-3)}, but don’t forget the non-permissible, here the x can’t equal to 2 and 3, because we can’t divide by zero.

Week 14 prec 11

We finished the ch8 in the week 14.

For the absolute value equations, the key thing is the x-intercepts, we should find the x-intercepts first when we doing these questions, after we find the x-intercepts, we turn the negative part over the x-axis. 

For the reciprocals functions, we should remember the shape of the two functions, and the asymptotes of the reciprocals functions the the x-intercepts of the original functions, for the special one, quadratic function, we have three shapes. Because the quadratic functions can have no x-intercept. 

Week13 in prec 11

This week we learnt the ch8 ABsolute value and Reciprocal Functions.

I think the most important thing in this topic is to find the part we need to “change”, it’s hard, but also easy when you can factor it practically.

In this two examples, one is the linear and the other is parabola. We need to change both of their negative part into positive , the point that change is the x-intercept , after we find the x-intercept ,we can change it. Remember what we change is absolutely symmetry to the origin part.

Week 12 in Prec11

In the week 12, we learnt the chapter 5 graphing inequalities and systems of equation. I think it’s easy to graphing because you just need to graph the equation and the area you need, the hardest point is to find the area you need. I have a easier way to find it instead to find a test point.

First , of course you need the graphing of the function. 

And there are 4 points I graph out , they are all “above” the functions which are not we need to calculate. And what we need is the black areas, when the points are “above” the function , they are greater than the function, the points are “below” the function,they are less than the functions. So now we have the answer, the black area are all “below” the functions, so they are all less than the functions.

prec 11 week 11

When we calculate the inequality, for my experience , if the symbol is greater(linear and going up), the area is on the left; on the contrary , is on the right.

 

if it’s quadratic equation(opens up), if the symbol is greater , the area is inside the function; on the contrary, is  outside the function.

WEEK 10 in prec 11

This Saturday is the Remembrance Day, and this is my first Remembrance Day in Canada , so let’s make a moment of silence for them first.

So next week I think we will have the mid-term exam. In this week we had review all the knowledge we learnt before. 

We had the problems-self-made in this week. = =

 

 

Week 9 in prec 11

Next week we will have a quiz in quadratic function, so this week’s main job is to review the knowledge and build them up.

in the picture told us the importance of the three forms:

Standard form(vertex form), general form and the factored form.

We can get a lot of message from these three forms, we can get the vertex from the standard form, the x-intercept from the factored form, and the y-intercept from the general form. We can also change them into each one to get the more message.

After that, we can lists the messages we get and then to do the problems, just remember the vertex is the most important , but not always, if you can find the intercepts, that’s also work.

And the complete the square! This help us change the three forms into each other.

 

Week 8 in Prec 11

In week 8, we learned the analyzing quadratic functions.

First of all , we should find the vertex out. It’s the most important thing in a quadratic function, and then, we should find out the x-intercept if necessary. It can help us to figure out the rough shape of the quadratic functions.

We have three forms:standard form, general form and factored form.

y=a(x-p)^2+q can tell us the vertex; y=ax^2+by+c can tell us the y-intercept is c; and the y=a(x-x_{1})(x-x_{2}) can tell us the x-intercept if it has.

After we have found three or more points besides the vertex, we can draw it , use smooth curves.