From 18670260285d25b14921a89fae60089da334c921 Mon Sep 17 00:00:00 2001 From: altaf-creator Date: Mon, 25 Sep 2023 20:18:57 +0700 Subject: Unlocked website, added rationalising roots --- lessons/matematika/index.html | 70 ++++++ lessons/matematika/locked.html | 58 +++++ lessons/matematika/pangkat-akar/akar.html | 170 +++++++++++++ lessons/matematika/pangkat-akar/latihan.html | 167 +++++++++++++ lessons/matematika/pangkat-akar/pangkat.html | 139 +++++++++++ lessons/matematika/pangkat-akar/scientific.html | 69 +++++ .../quadratic-equation/finding-suitable.html | 117 +++++++++ lessons/matematika/quadratic-equation/index.html | 277 +++++++++++++++++++++ lessons/matematika/quadratic-function/index.html | 75 ++++++ 9 files changed, 1142 insertions(+) create mode 100644 lessons/matematika/index.html create mode 100644 lessons/matematika/locked.html create mode 100644 lessons/matematika/pangkat-akar/akar.html create mode 100644 lessons/matematika/pangkat-akar/latihan.html create mode 100644 lessons/matematika/pangkat-akar/pangkat.html create mode 100644 lessons/matematika/pangkat-akar/scientific.html create mode 100644 lessons/matematika/quadratic-equation/finding-suitable.html create mode 100644 lessons/matematika/quadratic-equation/index.html create mode 100644 lessons/matematika/quadratic-function/index.html (limited to 'lessons/matematika') diff --git a/lessons/matematika/index.html b/lessons/matematika/index.html new file mode 100644 index 0000000..4c800ec --- /dev/null +++ b/lessons/matematika/index.html @@ -0,0 +1,70 @@ + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + +
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+

Chapter 1 - Bentuk Pangkat dan Akar

+

Lesson 1: Exponent

+

Lesson 2: Root

+

Exercise 1

+

Lesson 3: Exponents Extended - Scientific Form of Decimals

+

Chapter 2 - Quadratic Equation

+

Main Lesson: Quadratic Equation - The Introduction

+

Chapter 3 - Quadratic Function (no it's not equation)

+

Main Lesson: Quadratic Function - The Introduction

+
+
+ + + + + diff --git a/lessons/matematika/locked.html b/lessons/matematika/locked.html new file mode 100644 index 0000000..c6384ec --- /dev/null +++ b/lessons/matematika/locked.html @@ -0,0 +1,58 @@ + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + +
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This lesson is locked.

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+ + + + + \ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/akar.html b/lessons/matematika/pangkat-akar/akar.html new file mode 100644 index 0000000..1bacf4c --- /dev/null +++ b/lessons/matematika/pangkat-akar/akar.html @@ -0,0 +1,170 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + + + +
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Definition

+ Root is the inverse of exponent. For example;
+
    +
  • 42 = 16, so 16 = 4
    • +
  • 52 = 25, so 25 = 5
    • +
  • 102 = 100, so 100 = 10
    • +
+ +

Simplifying Square Roots

+ You can simplify a root by factoring the root number another number that is rational. Or in other words, divide the root number by the perfect squares. For example; +
    +
  • + Simplify 60
    + 60 = 4 × 15 = 215
    +
    • +
  • + Simplify 48
    + 48 = 16 × 3 = 43
    +
    • +
  • + Simplify 125
    + 125 = 25 × 5 = 55
    +
    • +
+ +

Root Operations

+

Addition

+ Roots with coefficient can be added with another coefficient that have the same roots.
+ ac + bc = (a + b)c +
    +
  • 32 + 42 = (3 + 4)2 = 72
    • +
  • 5 + 35 = (1 + 3)5 = 45
    • +
+

Subtraction

+ Roots with coefficient can be subtracted with another coefficient that have the same roots.
+ ac - bc = (a - b)c +
    +
  • 73 - 43 = (7 - 4)3 = 32
    • +
  • 106 - 56 = (10 - 5)6 = 56
    • +
+

Multiplication

+ Roots can be multiplied with any other roots. If the root is the same as the other multiplied root, the root can be deleted (if you want to be faster).
+ ac × bd = (a × b)c × d +
    +
  • 2 × 5 = 10
    • +
  • 32 × 43 = (3 × 4)2 × 3 = 126
    • +
  • 25 × 35 = (2 × 3)(5) = 6(5) = 30
    • +
+

Division

+ Roots can be divided with any other roots.
+ ac ÷ bd = (a ÷ b)c ÷ d +
    +
  • + 86 ÷ 43 = (8 ÷ 4)6 ÷ 3 = 22 +
    • +
+ +

Rationalising Roots

+

We can rationalise or simplify a fraction with a root denominator. To rationalise a root, multiply the fraction with a fraction of opposite roots. For example:

+

Example 1:

+ + +

Example 2:

+ + +

Example 3:

+ + +
+
+ + + + + + diff --git a/lessons/matematika/pangkat-akar/latihan.html b/lessons/matematika/pangkat-akar/latihan.html new file mode 100644 index 0000000..6bdae1d --- /dev/null +++ b/lessons/matematika/pangkat-akar/latihan.html @@ -0,0 +1,167 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + +
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+

Pertanyaan

+
    +

    Pangkat

    +
  1. 8p2q × 2pq3
    2. +
  2. 641⁄2 + 811⁄3
    3. +
  3. 25 + 320 - 45
    4. + +

    Merasionalkan Akar

    +
  4. 4⁄5
    5. +
  5. 35⁄23
    6. +
  6. 5⁄3 - 2
    7. +
  7. 5 - 7⁄5 - 2
    8. + +

    Operasi Pangkat

    +
  8. (8p23)3 ÷ 2pq
    9. +
  9. (a1⁄3b1⁄3)6⁄(a2⁄3b4⁄3)9
    10. + +

    Persamaan Pangkat

    +
  10. 2x + 8 = 64
    11. +
  11. 162x + 3 = 32
    12. +
+

Jawaban

+
    +
  1. 16p3q4
    2. +
  2. + 641⁄2 + 811⁄3
    + = 64 + 381
    + = 8 + 381 +
    3. +
  3. + 25 + 320 - 45
    + = 65 + 320
    + = 65 + 34 × 5
    + = 65 + 322 × 5
    + = 65 + 3 × 25
    + = 65 + 65
    + = 125
    +
    4. +
  4. + 4⁄5
    + = 4⁄5 × 5⁄5 = 45⁄5 +
    5. +
  5. + 35⁄23
    + = 35⁄23 × 3⁄3
    + = 315⁄2 × 3
    + = 15⁄2 +
    6. +
  6. + 5⁄3 - 2
    + = 5⁄3 - 2 × 3 + 2⁄3 + 2
    + = 5(3 + 2)⁄(3)2 - (2)2
    + = 5(3 + 2)⁄3 - 2 = 5(3 + 2)⁄1
    + = 5(3 + 2) +
    7. +
  7. + 5 - 7⁄5 - 2
    + = 5 - 7⁄5 - 2 × 5 + 2⁄5 + 2
    + = (5 - 7) × (5 + 2)⁄(5)2 - (2)2
    + = 5 + 10 - 35 - 14⁄5 - 2 = 5 + 10 - 35 - 14⁄3 +
    8. +
  8. + (8p23)3 ÷ 2pq
    + = (24p2)3 ÷ 2pq
    + = 243 p6 ÷ 2pq
    + = 6912p5 ÷ q +
    9. +
  9. + = (a1⁄3b1⁄3)6⁄(a2⁄3b4⁄3)9
    + = + (a1⁄3)6 (b1⁄3)6 + ⁄ + (a2⁄3)9 (b4⁄3)9 +
    + = + a2 b2 + ⁄ + a6 b12 +
    + = a-4 b-10 +
    10. +
  10. + 2x + 8 = 64
    + = 2x + 8 = 26
    + = x + 8 = 6
    + = x = 6 - 8
    + = x = -2 +
    11. +
  11. + 162x + 3 = 32
    + = (24)2x + 3 = 26
    + = 28x + 12 = 26
    + = 8x + 12 = 6
    + = 8x = 6 - 12
    + = 8x = 6
    + = x = -6⁄8
    + = x = -3⁄4 +
    12. +
+
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+ + + + + + \ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/pangkat.html b/lessons/matematika/pangkat-akar/pangkat.html new file mode 100644 index 0000000..e8362dd --- /dev/null +++ b/lessons/matematika/pangkat-akar/pangkat.html @@ -0,0 +1,139 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + +
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+

Exponents

+ xn = x1 × x2 × ... × xn +

Examples

+
    +
  • 25 = 2 × 2 × 2 × 2 × 2 = 32
    • +
  • 57 = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78.125
    • +
+

Exponent Operations

+

Multiplication

+ ax × by = (a × b)x + y +
    +
  • 104 × 22 = (10 × 2)4 + 2 = 206
    • +
+

Division

+ ax ÷ by = (a ÷ b)x - y +
    +
  • 103 ÷ 24 = (10 ÷ 2)4 - 2 = 52
    • +
+

Exponent

+ (ax)y = ax × y +
    +
  • (22)3 = 22 × 3 = 26 = 64
    • +
+ +

Zero Exponent

+

a0 = 1

+

Examples

+
    +
  • 50 = 1
    • +
  • 70 = 1
    • +
  • 1000 = 1
    • +
  • 28,670 = 1
    • +
+

One Exponent

+

a1 = a

+

Examples

+
    +
  • 51 = 5
    • +
  • 71 = 7
    • +
  • 1001 = 100
    • +
  • 28,671 = 28,67
    • +
+

Fractional Exponent

+ +

x y⁄z = + zxy

+

Examples

+
    +
  • 5 1⁄2 = + 25
    • +
  • 7 2⁄3 = + 372
    • +
+

Small Note: 2x or x menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.
3x means cubic root.

+ +

Exponential Equation

+
    +
  1. 2x + 5 = 64
    + = 2x + 5 = 26 ↖ ubah ke bentuk 2 berpangkat (2x)
    + = x + 5 = 6
    + = x = 1 +
    2. +
  2. 16x + 2 = 32
    + = (24)x + 2 = 25
    + = 24x + 8 = 25
    + = 4x + 8 = 5
    + = 4x = 5 - 8
    + = 4x = -3
    + = x = -3⁄4 = -3⁄4 +
    3. +
+
+
+ + + + + + diff --git a/lessons/matematika/pangkat-akar/scientific.html b/lessons/matematika/pangkat-akar/scientific.html new file mode 100644 index 0000000..9394f6e --- /dev/null +++ b/lessons/matematika/pangkat-akar/scientific.html @@ -0,0 +1,69 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + +
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← Go back to Main Lesson

+ Firstly, lets use this equation.
+
+

Step-by-step

+
    +
  1. Find the factors of c, which in this equation, c = 30.
    2. +
  2. The factors of 30 are: +
      +
    • 1, 30
      • +
    • 2, 15
      • +
    • 3, 10
      • +
    • 5, 6
      • +
    +
    3. +
  3. Lets define that the first and second factors are y1, 2. To find the suitable factors for the equation, you need to check if; +
      +
    • , and
      • +
      • +
    +
    4. +
  4. Check for each of the factors. We end up with 5 and 6.
    5. +
  5. So, the answer is 5 & 6
    6. +
+

← Go back to Main Lesson

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Introduction

+ In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x + represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.[1] +

Formula / Format

+ ax2 + bx + c = 0 +

+ a, b, c = known numbers, where a ≠ 0
+ x = the unknown, or the root +

+

Exercises

+

Finding the roots with factorisation.

+
    +
  1. + +

    +

    + To find the answer, we need to find the factors of c that is suitable for b and c. What and how do I find the suitable factors?
    + The suitable factor for the equation are 2 and -3.
    + Then, insert each numbers to this formula: , where y is the factor.

    +

    +
    + So, the answer is +

    + +
    2. +
  2. +

    +
    + Factors: 2, 4
    +

    +
    +
    +
    +
    +

    + +
    3. +
+

Relation between Quadratic Equation and Algebraic Expressions

+

This is an algebraic expression → . You can turn that into a quadratic equation.

+ + +

Quadratic Equation's Root Operations

+

Finding Quadratic Equation with Roots

+

You can use the formula below to find a Quadratic Equation with 2 roots.

+ , where x1, 2 are the roots.
+

+ Example:

+ +

+ +

Quadratic Root's Mathematical Operations

+

Formulas

+

+

+

Examples

+
    +
  1. +

    Diketahui persamaan kuadrat , memiliki akar-akar persamaan kuadrat x1 dan x2. Jika x1 < x2, maka tentukan: +

      +
    1. x1 + x2
      2. +
    2. x1 × x2
      3. +
    +

    +
    +
      +
      2. +
      3. +
    +
    2. +
+ +

References

+
    +
  1. Quadratic Equation - The English Wikipedia, https://en.wikipedia.org/wiki/Quadratic_equation
    2. + +
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