TIPS DAN TRIK CEPAT TKA MATEMATIKA 2025‼️ PASTI KELUAR!! | Mantappu Academy

Main ideas, concepts, and lessons

1. Tricks for fast problem-solving in Indonesian competitive exams

   • The video claims the same foundational techniques apply across TKA, SNBT/SMBT, PNS-style tests, Olympiads, and similar math questions.
   • The emphasis is on core “skills” that make solutions faster, easier, and quicker than conventional long methods.

2. Butterfly trick (fraction addition/subtraction)

   • Used when adding/subtracting fractions where a direct common denominator would be long.
   • The method involves creating a “butterfly-like” cross multiplication to combine terms efficiently.

3. Cross multiplication trick for algebraic equations with fractions

   • For fraction-form equations, convert to a cross-multiplication form.
   • Often described as: (top-left × bottom-right) = (top-right × bottom-left).

4. Solving systems (SPLDV) involving fractions via substitution of reciprocals

   • For systems that include fractions like 1/x and 1/y, the method is:
     • Treat 1/x = a and 1/y = b (replace reciprocals with new variables).
   • This converts the system into a more standard SPLDV form (linear equations in two variables).
   • After solving for a and b, convert back:
     • a = 1/x
     • b = 1/y

5. Average of large numbers using a reference (shifting technique)

   • Instead of summing large values directly, choose a reference number (example: 71).
   • Compute differences from the reference:
     • Each data value becomes (value − reference).
   • The average becomes:
     • reference + (average of the differences)
   • This reduces arithmetic errors and speeds calculation.

6. Inverse function concept trick

   • Focuses on using the concept of inverse, not necessarily computing the full inverse expression.
   • Key idea:
     • If you want f⁻¹(3), you solve f(x) = 3 and then interpret the resulting x as the inverse value.
   • Example idea shown:
     • For f(x) = x + 3, the inverse reasoning makes f⁻¹(x+3) = x.
   • For more complex functions, the video notes the inverse may require factoring/roots, but the proposed approach is to use inverse concepts to avoid full inverse computation.

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Methodologies / step-by-step instructions (detailed)

A) Butterfly trick for fraction addition/subtraction (fast combining)

• When adding fractions: set up numerator/denominator multiplication in a “cross” pattern rather than finding a common denominator normally.
• Core operational steps (as demonstrated):
  • Multiply the “diagonal” terms:
    • Example structure shown:
      • a/b + c/d → combine using cross products to get a single fraction.
  • For subtraction, do the same as addition but the sign changes (as described in the minus example).

B) Cross multiplication for fraction equations (algebra with fractions)

• Given an equation with fractions, set it up as a cross-multiplication:
  • (top-left × bottom-right) = (top-right × bottom-left)
• Then:
  • Solve the resulting equation for the variable.

C) Solving fraction-based SPLDV using reciprocal substitution (1/x, 1/y)

• Step 1: Identify reciprocals such as 1/x and 1/y.
• Step 2: Substitute:
  • Let 1/x = a
  • Let 1/y = b
• Step 3: Rewrite every term in the system using a and b:
  • Example conversion shown:
    • terms involving 1/x become terms in a
    • terms involving 1/y become terms in b
• Step 4: Solve the resulting SPLDV for a and b.
• Step 5: Convert back:
  • x = 1/a
  • y = 1/b
• Why this helps: it avoids messy direct cross-multiplication with large fraction denominators.

D) Average of large numbers using a reference number

• Step 1: List the data values.
• Step 2: Choose a reference number (example used: 71).
• Step 3: For each data value, compute its difference from the reference:
  • difference = value − reference
• Step 4: Sum the differences.
• Step 5: Compute:
  • average = reference + (sum of differences / n)
  • where n is the number of data points.
• Benefit: calculations involve smaller numbers (differences), reducing errors.

E) Inverse-function question trick via solving f(x)=k (without full inverse)

• Goal: compute f⁻¹(k).
• Step 1: Set:
  • f(x) = k
• Step 2: Solve for x.
• Step 3: The solution x equals f⁻¹(k).
• Important note from the video:
  • You don’t always need to find a closed-form inverse; you can use the inverse concept directly.
  • For complicated inverse forms, you might need factoring/roots, but the conceptual method remains: “plug k, solve for x.”

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Speakers / sources featured (as named in subtitles)

• Jal Polin (speaker/host; mentioned as “with me Jal Polin”)
• Billy Kurniawan (speaker/host; mentioned as “and I Billy Kurniawan”)
• Mantapu Academy / Mantapu Akademi (channel/brand; referenced throughout)