Today is the last day of the Fall semester and it is our final exam day.

If your kid is unable to come to school today, you can download the exam below. Have him/her do it at home. This is a close-book exam, with one hour and 20 minutes.

http://blog.newtonchineseschool.org/wangweidong/files/2012/01/Math-7-Fall-Final-Exam-2012.pdf

We started Chapter 10 with polynomials today and we covered polynomial addition, substraction, and multiplication.

For adding and substracting two polynomials, it is important to add/substract the same degree terms. For multiplying two polynomials, one uses the distributive property and multiplies each term out. For multiplying two binomials, there is an easy way to help student remember: FOIL, which refers to the First terms, the Outer terms, the Inner terms, and the Last terms:

(ax + b)(cx + d) = acx^2 + adx + bcx + bd

There are some special products of polynomials that students should memorize:

(a + b)(a – b) = a^2 – b^2

(a +/- b)^2 = a^2 +/- 2ab + b^2

For home work, visit the following link:

http://blog.newtonchineseschool.org/wangweidong/files/2012/01/Math7_Fall_HW_L14.pdf

We went over word problems for quadratic function/equation.

There are severla types of such problems:

• Questions with area
• Questions with droppoing/throwing object in the air
• Questions with maximum/minimum values
• Questions with right triangles
• Questions with consecutive numbers

In all cases, we need to read carefully from the question, gather the givens, draw a picture to help us understand the problem, label the unknown, and write out equations. Then solving it should be easier as we can always use the formulae to do so.

We went over several such problems in the classroom together. For the homework (below), finish them all.

http://blog.newtonchineseschool.org/wangweidong/files/2012/01/Quadratic-Equation-Word-Problems.pdf

Today’s topic is quadratic inequalities and comparing three different models (linear, exponential, and quadratic).

Like other inequalities we have learned, we want to be able to graph a quadratic inequality. Three steps will get you there:

1. Graph the quadratic equation. If the inequality has an equal sign in it, use solid line. Otherwise use dashed line.
2. Pick a point that is not on the graph and test it with the original inequality.
3. Shade the solution area with the test result from Step 2. If the test result is true, the point is in the solution region, shade the region that contains the point. Otherwise, shade the other region.

So far we have learned three data models that can be used to express the relationships for a set of points: linear, exponential, and quadratic.

For linear model, the delta of two consecutive values should be constant. That is, for y = mx + b, y(x+1) – y(x) = m.

For exponential model y = C(1+/-r)^t, we know the ratio of two consecutive values should be contact. That is, y(t+1)/y(t) = 1+/-r.

If neither linear nor exponential relationship can be established, you can try quadratic model.

For homework, visit the following link:

http://blog.newtonchineseschool.org/wangweidong/files/2011/12/Math7_Fall_HW_L12.pdf

We don’t have school for the following two weeks and I will see you on 1/8/2012. Have a wonderful holidays.

Today we talked about the generic formulae for solving a quadratic equation of ax^2 + bx + c = 0

x= (-b +/- sqrt(b^2-4ac))/(2a)

We did exercise of using the formulae to solve some quadratic equations.

We further talked about the real life example of throwing an object, with the following mode:

h = -16t^2 +vt + s

where s is the initial height in feet, v is the initial speed (ft/s), t is the time, and h is th height at t time. When throwing an object upward, v has a positive value; when throwing the object downward, v has a negative value.

The terms inside the radical in the formulae is called discriminant. We talked about the application of the discriminant, and use it to determine how mnay solutions to get.

We further related the formulae to the graphing, and the relationship between the solutions and the x-intercepts.

For homework, visit the following link:

http://blog.newtonchineseschool.org/wangweidong/files/2011/12/Math7_Fall_HW_L11.pdf

Today we covered section 9.3 and 9.4, about graphing a quadratic function and how to solve a quadratic equation with graphing.

We talked about the shape of a quadratic function, a parabola, how to use the value of a to determine whether the u-shaped parabola opens up (when a > 0) or opens down (when a < 0). We have the formulae to find the x value of the vertex: x = – b/2a. We talked about how to find the y value at the vertex. We talked about the axis of symmetry, which is the vertical line passing through the vertex.

As the shape of a parabola is a U-shape, when it opens up, there is a minimum value of the y at the vertex. Similarly, when it opens down, there is a maximum value of y at the vertex.

Students are still uncomfortable working with letters like a, b, c (representing constands) in place of specific numbers, as in y = ax^2 + bx + c. When I ask them with a specific number, they will give me an answer. But if I ask with something with a/b/c, they look at me, puzzled. This takes time, as they are still getting into algebra.

To graph a quadratic function y = ax^2 + bx +c, follow the following steps:

1. Find the vertex with the formulae, find its y value;

2. Make a table with the vertex in the middle, do one side (as the other side is symmetric), +1, +2, +3, find the corresponding y values.

3. Connect those points with a smooth curve.

The solution to a quadratic equations, also called roots, are x-intercepts on the graph. So to solve a quadratic equation with graphing:

1. rewrite the equation into the form of ax^2 + bx +c = 0

2. Graph the quadratic function y = ax^2 + bx + c

3. Find the x-intercepts. These are your solutions.

4. Check the answer algebratically.

Below is the link to the homework for today:

http://blog.newtonchineseschool.org/wangweidong/files/2011/12/Math7_Fall_HW_L10.pdf

Feel free to contact me for any question.

Today we started the new chapter on quadratic equations and functions.

We started with talking about square roots. Every postive real number has two square roots, one positive square root and one negative square root. The square root of 0 is 0, and the square root of a negative number does not exist.

We talked about perfect squares, those are numbers whose square roots are integers, or quotients of integers.

We looked at the simple form of a quadratic equation of x^2 = d. It has 2 solutions, +/- sqrt(d), if d > 0; it has 1 solution 0, if d = 0; it has no solution if d < 0.

We then focused on radical simplification. A radical is in its simplest form if:

a. There is no perfect square factors, other than 1 in the radical;

b. There is no fraction in the radical;

c. There is no radical in denominators.

So today’s homework is about solving simple quadratic equations in the form of x^2 = d, and to simply radicals.

Homework here: http://blog.newtonchineseschool.org/wangweidong/files/2011/11/Math7_Fall_HW_L9.pdf

Today’s topics are exponential growth functions and exponential decay functions.

An exponential growth function can be written as the following:

y = C(1+r)^t

where t represents time, r is called growth rate (r > 0), 1+r is called growth factor, C is in the initial value.

A good example to help understand the exponential growth function is the simple bank annual interest. r will be the annual interest rate, t represents number of year, C is the initial deposit, and y is the total amount after t years.

Similarly, an exponential decay function can be written as the following:

y = C(1-r)^t

where t represents time, r is called decay rate (1 > r > 0), 1-r is called decay factor, C is the initial value.

A good example would be car losing value as 10% per year.

This lesson finishes the chapter 8. Next time we will do a review of what we have learned in the first 6 lessons, to get ready for the mid term exam two weeks from now, on 11/6.

Here is the homework:

http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L6.pdf

Dear Parent/Student:

Today we first went over the exponential functions again as some students found that part of the homework difficult. We then continued our Exponents study with section 8.3 and 8.4. We further talked abut the division properties of exponents:

a^m / a^n = a ^ (m-n), a <> 0 and

(a / b)^m = a^m / b^m, b <> 0

We did some exercises on simplifying expressions with exponents. I think students are still not good at dealing with negative exponents and how to make a negative exponents positive with: (a /b) ^ (-m) = (b / a)^m. This takes practice to get better.

We then talked about scientific notation where a positive number can be represented as C*10^n, where 1<= C < 10, and n is an integer. We talked about how to convert from a decimal number to a scientific notation number and vice versa, how to do multiplication and division with scientific numbers.

Below is this week’s homework:

http://blog.newtonchineseschool.org/wangweidong/files/2011/10/Math7_Fall_HW_L5.pdf