From 81505edfecaea10fab2d68247a7b99645286a54f Mon Sep 17 00:00:00 2001 From: altaf-creator Date: Sun, 30 Jul 2023 20:23:36 +0700 Subject: Changed homepage, improved css and added roots, new notes (some not finished yet) --- lessons/matematika/pangkat-akar/akar.html | 112 ++++++++++++++++++++ lessons/matematika/pangkat-akar/latihan.html | 152 +++++++++++++++++++++++++++ lessons/matematika/pangkat-akar/pangkat.html | 34 +++++- 3 files changed, 294 insertions(+), 4 deletions(-) create mode 100644 lessons/matematika/pangkat-akar/akar.html create mode 100644 lessons/matematika/pangkat-akar/latihan.html (limited to 'lessons/matematika/pangkat-akar') diff --git a/lessons/matematika/pangkat-akar/akar.html b/lessons/matematika/pangkat-akar/akar.html new file mode 100644 index 0000000..b519d5e --- /dev/null +++ b/lessons/matematika/pangkat-akar/akar.html @@ -0,0 +1,112 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + + + +
+ + + + +
+
+

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 +
    +
  • + 12 ÷ 3 = 2 +
    • +
  • + 86 ÷ 43 = (8 ÷ 4)6 ÷ 3 = 22 +
    • +
+
+
+ + + + + + \ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/latihan.html b/lessons/matematika/pangkat-akar/latihan.html new file mode 100644 index 0000000..4aa75e7 --- /dev/null +++ b/lessons/matematika/pangkat-akar/latihan.html @@ -0,0 +1,152 @@ + + + + + + + + + + Al Azhar 9th Grade Lesson Notes + + + + + + + + + + +
+ + + + +
+
+

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 ba12 +
    + = 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. +
+
+
+ + + + + + \ No newline at end of file diff --git a/lessons/matematika/pangkat-akar/pangkat.html b/lessons/matematika/pangkat-akar/pangkat.html index f3af1a2..efba6e1 100644 --- a/lessons/matematika/pangkat-akar/pangkat.html +++ b/lessons/matematika/pangkat-akar/pangkat.html @@ -53,10 +53,20 @@

Exponent Operations

Multiplication

ax × by = (a × b)x + y +

Division

ax ÷ by = (a ÷ b)x - y +

Exponent

- axy = ax × y + (ax)y = ax × y +

Zero Exponent

a0 = 1

@@ -79,14 +89,30 @@

Fractional Exponent

x y⁄z = - z√(xy)

+ zxy

Examples

+

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. +
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