Summary of Video

Video 1:

From that video, I think that we have to believe with our ability. We have to certain that we be able to doing something. If we have a dream, so we must sure that we can to reach our dream. Without assureance from our heart, we incable to doing we anxious and we dream. So, we must believe with our ability.

Video 2:

In second video, I am more know about mathematics. Mathematics learned geometry, trigonometry, ln x, significant figure, limit x approach boundlessly, exponent, integral e power x and from this video, I know that value of phi is 3,145…………

Video 3:

The third video show about mathematic problem solving.

For example :

The graph of f(x) = x + 1 if 2f(p) = 20. How value of f(3p)?

Answer:

2f(p) = 20

f(p) = 10

f(x) = x + 1

we substitution p to f(x) = x + 1 become f(p) = p + 1

f(p) = p + 1 = 10

p = 10 – 1 = 9

f(3p)????

3p = 3(9) = 27

f(x) = x + 1

f(3p) = 3p + 1 = 27 + 1 = 28

So value of f(3p) is 28

Video 4:

Video 4 about the properties of logarithm.

1. Log x to the base b equals y symmetry with b power y equal x

2. Log x to the base 10 equals Log x

3. Log x to the base natural numeral equasl Ln x (this natural logarithm)

Example :

1.Log 100 to the base 10 equals x. How value of x?

2. Log x to the base 2 equasl 3. How value of x?

3. Log 1 over 49 to the base 7 equals x. How value of x?

Answer :

1. Log 100 to the base 10 equals x, become 10 to the power of x equals 100, so x equal 2.

2. Log x to the base 2 equals 3, become 2 to the power of 3 equal x, so x equals 8.

3. Log 1 over 49 to the base 7 equals x, become 7 to the power of x equals 1 over 7 to the power of 2 in bracket. This similer with 7 to the power of x equals 7 to the power of minus 2, so x equal minus 2.

4. Log M times N in bracket to the base b equals Log M to the base 2 plus Log N to the base 2.

5. Log M over N in bracket to the base b equals Log m to the base 2 minus Log N to the base 2.

6. Log x to the power of n in bracket to the base b equals n times Log x to the base b.

Example:

How value of Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in square bracket to the base 3?

Answer:

Log x to the power of 2 times y plus 1 in bracket all over open bracket z to the power of 3 close bracket in bracket to the base 3

equals Log x to the power 2 times open bracket y plus 1 close bracket in square bracket to the base 3 minus Log z to the power 3 in bracket to the base 3

equals Log x to the power 2 to the base 3 plus Log open bracket y plus 1 close bracket to the base 3 minus Log z to the power 3 to the base 3

equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

So, Log x to the power of 2 times y plus 1 in bracket over open bracket z to the power of 3 close bracket in bracket to the base 3 equals 2 times Log x to the base 3 plus Log y plus 1 in bracket to the base 3 minus 3 times Log z to the base 3.

Video 5:

About Graph of Rational Function.

Example:

Draw a function of f(x) equals x plus 2 in bracket over x minus 1 in bracket

Answer:

f(x) = ( x + 2 ) / ( x – 1 )

even x = 1 we find f (x) = 3 / 0 ( this wrong and imposible ), so graph of f(x) not be able nudge line x = 1.

And not all rational fuction denominator can be zero..

Video 6:

Video 6 consist obout Trigonometry.

Sine (Sin), Cosine (Cos), and Tangents (Tan) are trigonometric ratios.

Ratio of Sin is opposite per hypotenuse (soh)

Ratio of Cos is adjoin per hypotenuse (cah)

Ratio of Tan is opposite per adjoin (toa)

The other trigomometric rations are represented as follows:

Secant (Sec) is one cos

Cosecant (Cos) is one sin

Cotangents (Cot) is one tan

For example:

If the right triangle ABC right angled at B where AB = 3 cm, BC = 4 cm, CA = 5 cm (hypotenuse). P is angle front of BC and Q is front of BA. How value of all trigonometric ratio?

Answer:

1. Sin P = opposite/hypotenuse = 4/5

Cos P = adjoin/hypotenuse = 3/ 5

Tan P = opposite/ adjoin = 4 /3

Cosec P = one sin = 5/ 4

Sec P = one cos =5/ 3

Cot P = one tan = 3/ 4

2. Sin Q = opposite/ hypotenuse =3/ 5

Cos Q = adjoin/ hypotenuse = 4/ 5

Tan Q = opposite/ adjoin = 3/ 4

Cosec Q = one sin = 5/ 3

Sec Q = one cos = 5 /4

Cot Q = one tan =4/ 3

My Diffucult Word to Express Mathematical Idea

Part I : (diffucult word)

1. abscissa
2. acute
3. altitude
4. apex
5. axis
6. chain process
7. circumscribed circle of triangle
8. common line
9. concorent
10. denominator
11. edge
12. intersection
13. intersects
14. is required
15. isosceles triangle
16. line segment
17. medians
18. midpoint
19. minimum extreme
20. modulus inequalities
21. obtained
22. obtuse
23. paralleling
24. perpendicular
25. plane
26. point
27. point of intersection
28. replaced
29. right triangle
30. satisfies
31. simultaneous equations
32. solid figure
33. statement
34. surds inequalities
35. surface area
36. the corresponding
37. the derivation
38. the properties
39. to determine
40. to the base
41. touches
42. truth table
43. vertex

Part II: (The meaning of difficult word)

1. abscissa : absis
2. acute angle : sudut lancip
3. altitude : garis tinggi
4. apex : puncak
5. axis : sumbu
6. chain process : proses berantai
7. circumscribed circle of triangle : lingkaran luar segitiga
8. common line : garis persekutuan
9. concorent : berpotongan di satu titik
10. denominator : penyebut
11. edge : rusuk
12. intersection : irisan
13. intersects : memotong
14. is required : diperlukan
15. isosceles triangle : segitiga samakaki
16. line segment : ruas garis
17. medians : garis berat
18. midpoint : titik tengah
19. minimum extreme : titik balik minimum
20. modulus inequalities : pertidaksamaan harga mutlak
21. obtained : mendapatkan
22. obtuse angle : sudut tumpul
23. paralleling : sejajar
24. perpendicular : tegak lurus
25. plane : bidang
26. point : titik
27. point of intersection : titik potong
28. replaced : diganti
29. right triangle : segitiga siku-siku
30. satisfies : memenuhi
31. simultaneous equations : sistem persamaan
32. solid figure : bangun ruang
33. statement : pernyataan
34. surds inequalities : pertidaksamaan bentuk akar
35. surface area : luas permukaan
36. the corresponding : bersesuaian
37. the derivation : penurunan rumus
38. the properties : sifat-sifat
39. to determine : menentukan
40. to the base : bilangan pokok
41. touches : menyinggung
42. truth table : tabel kebenaran
43. vertex : titik puncak

Part III : ( Application the difficult word in the sentence )

1. A rational of surds on the its denominator, such us .
2. ­^a log b = m, m is logarithm of b to the base a.
3. The value of x that satisfies log x = 2
4. The properties of parabol are has vertex at P of coordinate P = (-b/2a, -d/4a)
5. The equation of axis of symmetry in the line x = -b/2a that is the abscissa of the point T.
6. If ax² + bx + c = 0 is a quadratic equation, so the parabol intersects y axis at the point (0,3)
7. ax² + bx + c = 0, if a>0, we obtain minimum extreme.
8. The chain process can usually in problem solving of mathematic.
9. The parabol intersects x axis at one point that is the point (3,0), the parabol touches.
10. To determine a parabol is required at least three different point.
11. The derivation of formula is given as follows.
12. Find maximum area of a rectangle inscribed an isosceles triangle of sides a, a and b.
13. The roots do not change when the variable x replaced by y.
14. Simultoneous equations one linier and one quadratic.
15. Find point of intersection of the lines y = 2x – 7 and x-2y + 1= 0.
16. Equation of line that touches the parabol f(x) = -1/2 x² + 4x and perpendicular.
17. The example of surds inequalities is .
18. The standart procedure to solve modulus inequlities is by squaring both sides of equation.
19. Principally if any trigonometric ratio is given then we can determine the corresponding right triangle.
20. Find radius of circumscribed circle of triangle DEF.
21. Determine whether the triangle KMN (MN = 9cm, KM = 5 cm, NK = 7 cm) is acute or obtuse.
22. The three altitudes of a triangle are concorent.
23. The point D, E, F consectively are midpoint of BC, AC, AB.
24. Lines of BE, AD, CF are medians of triangle ABC.
25. Make the truth table of the statement ( W^Q ) v Q
26. Pyramid T. ABCD of base ABCD and of apex T.
27. If the point E lines on plane ABCD and perpendicular ABCD, then TE is called the altitude of the pyramid T.ABCD.
28. Cone one of solid figure.
29. Find volume of the largest cone inscribed a cube of edge 7cm.
30. If passing through the point A and B is drawn a straight line then length of the line segment AB is the the distance between the point A and point B.
31. In the cube ABCD.EFGH, the line BC is common line of planes ABCD and BCGF.
32. In the cube ABCD.EFGH the point M is the midpoint of BF. Show intersection of the plane passing through H, C, M in the cube.
33. Find surface area of the cube of edge 10cm.

diffucult word from: Asri Mulat Rahmawati (08301244036)

Mathematics Problem Solving and Mathematics Essence

Basicly?math problem is differented into 2 part :

1. Problem that related to the daily lives. Math can applied in our lives, incase in the economic sector, example : How many interest that the customer can get from the bank?
2. Math problem, example : How wide a long square is?, How wide a cicle that have radium 7 cm is?

In this case, math is used as tool, math is used as a way or tool to counting.

Mathematics problem solving also need skills , they are:

1. Logical, How can a mathematics problem be finished with our logical.
2. Organization
3. Classification, classification some math problems so that can be easier in solving them.
4. Identification, we have to can identifiying many problems, so we can solve them with the formula.

A student consided can solve a math problem if a student can:

1. Sure with their capability, student can solve that math problem well.
2. They can try the other way, but also a student can solve that problem with the other way from teacher, also their own way.
3. Hav a high curiosity. The student is not race with that problem only, but also a student want to solve the other problem that more difficult than the before problem, if a student ask to their teacher how to solve that problem.

Mathematics Essence

1. Mathematics as a communication tool

In this case math motivate student to know math caracters, motivate student to know math problems. Math to motivate a student to read and write a math problem. Math can used as information communication toll or idea, example : from the direct dialog or written, graphic, chart in explaining an idea, with chart or information table that want to be exlendee can be more clearly.

2. Mathematics as a problem solving

Math help students to solve math problem with their own way. Math also can motivate student to be logical, consistan thinked, so they can solve a problem with math way. Math motivate the student to be competent in solving problem. It also can help the student to know how and when they use mathematics tools as calculator, pecalipers, arch, ruller etc.

3. Mathematics as a investigation

Math can use as a tool to find the other way in math problem solving. It also motivate the student to appreciate the other’s discovery. It can motivate the student to find all problems in the math world.

4. Mathematics as a pattern investigation

It can motivate the student to the experiment with some ways.

If that all is can be understood by the teacher well, so it hoped math can be loved by all of student in the school. If the teach process is interesting so the student will think that math is interesting and it is not horror.