June 14

# Week 17 — Math10

This week we learned two ways to solving systems of Linear Equations, they are

• Substitution
• Elimination

Substitution

(an algebraic method of finding solution for systems by substituting one equation into the other)

Step: 1. Choose the simpler equation and express one variable in terms of the other.

2. Substitute the expression from step 1 into the other equation.

3. Solve the single variable equation.

4. Substitute the solution from step 3 into the equation in step 1 to find the variable.

Elimination

Steps : 1. If necessary, multiply each equation by a constant to obtain coefficients for x (or y) that are identical (except perhaps for the sigh.)

2. Add or subtract the two equations to eliminate one of the variables.

3. Solve the resulting equation to determine the value of one of the variables.

4. Substitute the solution into either of the original equations to determine the value of the other variable.

June 4

# Week 16–Math 10

My ‘aha’ moment in this week.

This question:

There is no number, you must feel confused, but do not worry. First, figure out what is the slope of the first equation:

Then figure out the slope of the second equation:

The question said they are parallel, so:

So the answer is A.

May 29

# week 15 — Math 10

This week I learnt chapter 9– Equations of Linear Relations.

My aha moment is I solved a difficult question.

The question is Determine the angle of elevation for the line segment CD, where C(9,4) and D(-5,-2).

(hint: slope = tan. ratio) First, we just figure out what is the slope:

And then, we use the tan. ratio to figure out what is the angle of the elevation.

Then I got the answer.

May 22

# Week 14–Math 10

This week I solve a difficult question.

Here is the question.

This question is about midpoint, the midpoint formula is:

The question also tells us the slope is -3, means m=-3/1, and the slope formula is m=(y2-y1)÷(x2-x1), so we could use the point (1,6) to figure our the other point. The question said “The other endpoint is on the x-axis” it means the other point must be (x,0). According those information above, we could have a equation:

Then we got the other endpoint is (3,0). Now we just use the midpoint formula before,

This is the final answer.

May 8

# Week 11–Math 10

This week we learnt the chapter 7 — Relations and Functions.  From this week’s classes, I got some hints.

• The variable has coefficient is the independent variable, so another variable is the dependent variable.
• Independent variable, input, and domain these words are the same meaning; Dependent, output, and range mean the same.
• The different ways a relation may be represented are: equation, the graph, the words, table of values, set of ordered pairs, mapping, function notation.
• Every time you need at least three points to graph.
• The discrete variables— data that is counted–there are only some points on the graph–can not interpolate as points in between– no meaning
• The continuous variable— data that is measured–there is a line on the graph, the points are connectedmeaning
• The equation has degree onelinear; The equation has more that two degrees or equal twono linear
• X-intercept => y=0, (x,0)
• Y-intercept=>x=0, (0, y)
• Every time you do the question like this “Determine the x- and y- intercepts of each equation.” at the end, you need answer as ordered pairs. If you meet a situation like this “-y^2=81” you can not figure it, you just write down no y-intercept.
• When you do the question like “State the domain and range for each relation.” if you see there is only dots on the graph, you just list their domains, remember “no repeat”; If the line is continuous, no end, you just write down — D={xER} or R={yER}; Every time the line is continuous, you need have this at the end, {xER}{yER}.
• Functions — input only has one output. But output can have two inputs.

April 24

# Week 10 — Math 10

This week  we learnt a easy way to check did we solve the questions right. It is:

Common?

Differences of  Squares?

Pattern?

• Easy (x^2)

For example: x^2+4x+3

• Ugly (ax^2)

For example: 2x^2+8x+8

When we started to do a question we need ask these questions to ourselves.

April 21

# “Patterns in Polynomials” — Math 10

In this unit we learnt some patterns.

From this example, If we use the ordinary method to solve this question must be use FOIL, that need to do lots of works, so we need a easier way t solve this question. In this diagram, we could find out the two parts that I circled are the same just different signs, so they cancelled out. What left? The x square and the number. So the first Pattern that we need to remember is

When we do the questions like this example next time, we could use this pattern to solve questions faster.

This is the second Pattern.

In this picture we can see there are two “2x”, is 4x just like 2 times 2 times x. So we could figure out a pattern to help us solves this type of questions faster.

Hint: (a-b)^2 is similar way to solve.

This is the third Pattern, I showed some examples in this picture. From these examples we could find out a pattern is:

When we got this pattern, we do some questions like x^2+8x +15 next time, we could easily solve it.

April 17

# Week 9– Math 10

This week we leant some interesting patterns. Just like the pictures show below.

This week we also learnt three formulas, they can help us to figure out questions quicker than before.

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

We just need to remember those formulas.

For example: (4-7x)(4+7x)

If you use the distributive property(FOIL), you need to write down: =4×4+4×7x-4×7x-7×7x=16-49x

If you use the formula, you just need one step.