Test of English

1. How we get phi?
Circumference of a circle is a limit of polygon on its circle. Circumference of circle noticed by “s”. It has relationship with radius (r) , namely s divided two r equals phi (s:2r = phi)
Proportion s : 2r of circumference of a circle with radius is equal of all circle. Phi equals twenty two divided by seven or three point one four.
2. How we get abc formula?
Formula of quadratic equation is a square x plus bx plus c equals zero
Change koefisien x square to be x square plus bx divided by a plus c divided by a equals zero.
Miss the konstanta on left, so we get x square plus bx divided by a equals negative c divided by a.
Add both of the sides right and left with quadratic of a half koefisien, we get x square plus bx divided by a plus the square of b divided by 2a equals negative c divided by a plus the square of b divided by 2a.
Change side of left be perfect quadratic, so
the square of x plus b divided by 2a equals negative 4ac plus b square divided by four a square then x plus b divided by 2a equals the square root of negative four ac plus b square divided by four a square, after that we get x. x equals negative b divided by 2a plus minus one 2a the root of b square minus 4ac, finally, x equals negative b plus minus the square root of b square minus 4ac divided by 2a.
3. Determine the area which limited y equals x square and y equals x plus two
To find that solution, we can draw it but for the first, we should make table. We’ll use scalene number to convert x.
For example, if x is zero, y is zero
if x is plus minus one, y is one
If x is plus minus two, y is four
And if x is plus minus three, y is nine, etc

For the second equation, y equals x plus two
I’ll choose x is zero so that y is two. (zero,two)
If y is zero, x is negative two. (negative two, zero)
The next step is we search the intersection point,
x square equals x plus two, so we get x equals negative one or x equals two
The last step is we have to integral from negative one until two on x plus two minus x square. By counting the integral we get the area which limited by way equals x square and y equals x plus two
4. Determine the volume of cone
Most of the three dimension have a formula volume namely, base area multiplied by height. For example the formula of cube volume is cubic sides. It happened because the base of cube is square and it has congruen sides so the volume of cube id cubic sides. Meanwhile the volume of cube equals one third limas volume. Limas volume has similar with cone volume, it just difference in base. So the cone volume is one third area base multiplied by height of cone. Or one third multiplied by circle area multiplied by height of cone.
5. Prove that the sum of angle of scalene triangle is one hundred and eighty degree.
Triangle have three angles, and sum of the angle is one hundred and eighty degree. On Element’s Euclid book 1, propositions 1 27 through 1 32 establish the theory of parallels and prove that the sum of the angle of a triangle is equal to two right angles.
If we have the picture of triangle and we cut the three of angles. After that we arrange the piece of them, we’ll get straight line or the measure of angle is one hundred and eighty degree.
6. Determine the probability of sum number more than 6 from two dices by throwing once.
A dice has six sides namely, one , two, three, four, five, and six. There are two dices so there are thirty six probability. The question how many probability come sum of number more than six.
The probability are (one, six), (two,five),(two, six),(three,four), (three, five), (three, six), (four, three), (four, four), (four, five), (four, six), (five, two), (five, three), (five, four), (five, five), (five,six),(six,one), (six, two), (six, three), (six, four), (six, five), (six,six)
There are twenty one, so the probability come sum of number more than six is 21/36.
7. How we determine the equation which on ( ten, zero) and have segment of circle x square plus y square equals nine?
To solving this question, we use equation segment formula which follow point (a,b), namely x index once x plus y index once y equals the square of radius. So the equation can be searched by entering elements which known. x index one is ten, y index one is zero and the square of radius is nine.
By accounting the equation we can give solution that the equation is ten x minus nine equals zero.
8. How we prove the phytagoras ?
Imagine that!
I have drawn two pictures, the pictures were square. For the first square. It’s divided into six pieces, namely two squares and four right triangles congruent. The second square is divided into five pieces namely the square on the hypotenuse and four right triangles congruent. a, b, c are sides of square. c means hypotenuse. By subtracting equals from equals. It follows that the square on the hypotenuse is equal to the sum of the squares on the legs. It’s one of the proof to make sure that it’s right.
9. Determine the sum of two hundred odd number first!
Odd number is started from one, three, five, seven,…
The sum of odd number is one plus three plus five plus seven,…
Let’s we find the sum of the odd number with formula.
one plus three plus five equivalent with five plus three plus one, if we sum of them, the result is six plus six plus six, or six multiplied by n
So we can conclude that one plus three plus five equals (six plus six plus six) multiplied by two =nx6/2=a half multiplied by n(one plus four)=a half multiplied by n (a+un)
n means the many of odd number
a means first term
un means last term
Our duty is finding the solution for the sum of the odd number, two hundred first
so one plus three plus five plus…plus one hundred and ninety nine equals…
the difference from 1 to three is two, therefore we can find the value of n
un= one hundred and ninety nine
one hundred and ninety nine =a+(n-1)b
one hundred and ninety nine =1+(2n-2)
one hundred and ninety nine =2n-1
two hundred=2n
n=one hundred
The sum is a half multiplied by one hundred multiplied by (one plus one hundred and ninety nine)
a half multiplied one hundred multiplied by two hundred equals ten thousand
10. the step to draw the cube ( the element of cube known)
Before, let’s know about the elements of cube
· frontal plane means every parallel plane with drawing plane.
· Frontal line is every line or segment which located on frontal plane.
· Orthogonal line is every line which located perpendicular on frontal plane.
· Surut angle means the angle which located between horizontal frontal segment to right and orthogonal segment to behind.
· The compare of projection or compare of orthogonal means the propotion between length of the map with the real length.
For example:
Draw ABCDEFGH cube. Given, the length of side is 3 cm, ABFE is frontal plane, sudut simpang 30’ and proportion of projection is one third.
First, make AB segment which length 3 cm. At point A make angle of 30’,so there is AD segment the length of AD is one third multiplied by 3 cm equals one cm. Because the projection of ABCD parallelogram, then the base can be done. The middle of side is vertical segment, therefore E, F, G and H can be drawn.