Practice final

Hi all,

Here is the practice final exam: 115final15_prac

This is basically a study guide, so the way to use it is to expand it into several types of problems. For example, when you do the linear equation problems, make sure to do some problems in section 2.3; when you solve quadratic equations, check your homework from section 1.3.

When doing these problems, make your sheet on the side, write down the methods you use, write down what was hard for  you. We will go over these problems in class tomorrow, and bring any questions you have for me!

 

Review of week 13 and preview of last week

Hi all,

One week left! Next week, we will finish up with trig functions and review for the final exam.

Last week, we talked about trig functions, in terms of ratios of length in a right triangle. Make sure to have the definitions of those trig functions and their relations written down on your sheet!

On Thursday, we looked at some applications of trig functions in right triangles. We can classify the information given to us as two categories: either angle relations or length relations. If you know one acute angle, you can find the other one by a+b=90 degrees; if you know two edges, you can solve for the last one by the Pythagorean theorem. The things that connect these two kinds of information are the trig functions, and you would often use trig functions to solve angle from edge and vice verse.

There are two types of information given in general: one angle and one edge, or two edges. Notice you will always need at least one edge in order to solve a triangle (similar triangles are of different size, but have the same angles!)

Next week, we will finish up the introduction of trig functions in the coordinate plane. It will be similar to trig functions in right triangles, but now it is easier to describe the vertices, etc. On Thursday, we will review for the whole semester.

Test 3 correction is due Tuesday and no later than that! 

Review of week 11/12 and preview of week 13

Hi all,

Hope you had a great Thanksgiving! In week 11, we reviewed for the test and had our test 3 on Thursday. Remember to regrade for more points!

On Tuesday, we started talking about angles, degrees and triangles, these will be the basis for trig functions, starting from next week.

For what we learned on Tuesday, make sure you understand how to compute complementary and supplementary angles, how to compute the length of edges in a right triangle. Similar triangles are triangles of the same shape, and always have the same angles. Therefore their corresponding edges have lengths of a fixed ratio.

Next week, we will introduce trig functions in right triangles and Cartesian planes. In right triangles, they are really just ratios of the length of edges.

Alright, that is it for now. Let me know if you have more questions!

Review of week ten and preview of week eleven (Test on Thursday, Nov 19)

Hi all,

Last week we talked about quadratic functions and exponential/log functions.

The quadratic function has two forms: general form and standard form. Standard form gives more information about the function: whether it opens up or down, where the vertex is, where the x-intercepts are (if there are any). If given general form, we complete the square to get the standard form. In applications of quadratic functions for example, vertex gives information about the maximum or minimum of the function, depending on the sign of leading coefficient.

On Thursday, we did more computation on completing the square and briefly introduced exponential and log functions. For exponential and log functions, make sure you know how to evaluate the functions and have a general image of the graphs of the functions in your head (x and y intercepts, domain and range of the functions, if the function increase or decrease?).

Next week, we will review on Tuesday and have test 3 on Thursday. I will write a practice test and bring the practice test on Tuesday for you to work on. For now, review your homework problems and redo the problems we did in class (self diagnose quiz and exercises)

There is no homework due next week, so use your time to review for the test!

Let me know if you have any questions!

Review of week nine and preview of week ten

Hi all,

Last week, we talked about linear functions and lines and started with quadratic functions on Thursday. This week, we will finish with quadratic functions and start talking about exponential and log functions.

Linear functions represent lines on the plane, and are determined by two pieces of information: slope and an intercept, two points, slope and a point, etc. Any two points on the line can give you the slope (sometimes undefined as the line is vertical!). If the slope is positive, the linear function increases as x increases; if the slope is negative, the function decreases as x increases; if the slope is zero, the function does not increase or decrease. Setting y=0 give the x-intercept and setting x=0 gives the y-intercept. These are all information that helps you plot the graph of the line.

Quadratic functions are of the shape y=ax^2+bx+c, and setting y=0 gives the x-intercept(s) if any exists! We have seen last week, that the quadratic equation ax^2+bx+c=0 can have two distinct solutions, one solution or no solution. These three situations correspond to two x-intercepts, one x-intercept or no x-intercept in the graphs of our parabolas. In the process of looking for x-intercepts, we learned three methods: factoring, quadratic formula or completing the square. This coming Tuesday, we will keep using completing the square, as it gives more information: vertex. Vertex gives information on the maximum or minimum of the function and where the max/min is attained. We will also see some applications of quadratic functions in modeling.

Alright, that is it for now. Sorry for the late sum up, let me know if you have any questions!

Review of week eight and preview of week nine (homework in separate post)

Hi all,

Last week we had our second test and talked about the coordinate system, next week we will talk about lines in the coordinate system and quadratic equations.

The coordinate system is a powerful tool to combine algebra with geometry: pairs of points, distances and equations are all presented on the coordinate plane with explicit pictures. We have plotted some pictures on Thursday, and you have seen the general way of plotting graphs of functions: take some arbitrary values of x and compute the corresponding y values from the function, plot those dots in your plane and connect them. The examples we did in class on Thursday are all linear functions, next week we will see some quadratic functions.

Tests will be handed out to you next Tuesday, make sure to do corrections! If you want to talk about any of the problems, come for help! The corrections are due Nov 17.

Homework problems are posted in a separate post, don’t forget to do them!

Alright, have a good weekend, see you next week!!