PASTI KELUAR‼️ BOCORAN SOAL TKA 2025, WAJIB PAHAM!! | Mantappu Academy

Main ideas / lessons (by topic)

1) Algebra problem (Level 2 Applications)

• Goal: Solve for specific values (especially the “first number”) from a word problem involving three variables.
• Key concept: Convert Indonesian/word statements into math equations (this translation skill is emphasized as crucial).
• Method shown:
  • Let the three numbers be (A), (B), (C).
  • Use the three statements as three equations since there are 3 unknowns.
  • Use elimination and substitution (and avoid over-solving).
• Example outcome (as explained):
  • From the first number’s condition, derive (B + C = 35).
  • Then compute (A = 5 + (B + C) = 40) (the narration is messy, but the intended logic is to use (B+C) to get (A) directly).

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2) Geometry mixed with equations (Triangle area via Pythagorean triple)

• Given: For triangle (ABC),
  • (A + B = 18)
  • (A + C = 25)
  • (B + C = 17)
• Key concept: Use the system to find the side lengths efficiently, then recognize a special triangle.

• Method shown:

  1. Add the three equations: [ (A+B) + (A+C) + (B+C) = 18+25+17 = 60 ] [ 2A + 2B + 2C = 60 \Rightarrow A + B + C = 30 ]

  2. Solve by substitution: [ C = 30 - 18 = 12 ] [ B = 30 - 25 = 5 ] [ A = 30 - 17 = 13 ]

• Special insight:

  • The sides are 12, 5, 13, which form a Pythagorean triple, so the triangle is right-angled.

• Area shortcut used:

  • Since it’s right: [ \text{Area}=\frac{1}{2}\times \text{base}\times \text{height} ]

  • Using legs 12 and 5: [ \text{Area}=\frac{1}{2}\cdot 12 \cdot 5 = 30 ]

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3) Trigonometry simplification using quadrant rules (quadrant-based memorization)

• Problem type: Evaluate an expression involving trig values using quadrant signs and symmetry.
• Given (as stated):
  • (\sin 240^\circ + \sin 225^\circ + \cos 315^\circ)
• Key concept: Be fluent with quadrant rules and angle transformations.
• Method emphasized:
  • Prefer memorized anchors 180° and 360° (rather than focusing on 90°/270°).
  • Determine the sign from the quadrant:
    • In Quadrant III, (\sin) is negative (and (\cos) is also typically negative).
    • In Quadrant IV, (\cos) is positive.
• Goal: Compute quickly using conversions and cancellation.
• Result they reach (stated):
  • Final simplified sum: (-\frac{\sqrt{3}}{2})

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4) Statistics (ratio of counts using weighted average)

4a) Average age + ratio of teachers vs lecturers

• Given:
  • Combined average age (teachers + lecturers): 42
  • Average age of teachers: 39
  • Average age of lecturers: 47
• Question: ratio (#\text{teachers}:#\text{lecturers})

• Method shown:

  • Let:
    • Teachers = (G)
    • Lecturers = (D)
  • Convert averages to totals:
    • Teacher total age = (39G)
    • Lecturer total age = (47D)

  • Combined average: [ 42(G+D)=39G+47D ]

  • Rearrange: [ 42G+42D=39G+47D ] [ 42G-39G=47D-42D ] [ 3G=5D ]

  • Therefore: [ \frac{G}{D}=\frac{5}{3} ]

• Conclusion:

  • Teachers : lecturers = 5 : 3

4b) Mean/average transformation trick (statistics without full solving)

• Given mean condition:
  • Mean of ((a-2)), ((b+3)), ((c+5)) is 6
• Then asked:
  • Mean of ((a+4)), ((b+6)), ((c-1))

• Method emphasized:

  • Mean = (sum of three terms) / 3

  • From the first mean: [ \frac{(a-2)+(b+3)+(c+5)}{3}=6 ] [ a+b+c+6=18 \Rightarrow a+b+c=12 ]

  • For the second mean: [ \frac{(a+4)+(b+6)+(c-1)}{3}=\frac{(a+b+c)+9}{3} ] Substitute (a+b+c=12): [ \frac{12+9}{3} = 7 ]

• Conclusion:

  • The second mean equals 7

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5) Functions: Domain and range with root and fraction constraints

Domain of ( f(x)=\sqrt{\frac{x}{2-x}} )

• Key concept: Domain includes only values of (x) that keep the function:
  1. Defined under the square root (radicand (\ge 0) for real outputs)
  2. Valid in denominators (denominator (\ne 0))
• Method shown (inequality-based):
  1. Apply root constraint: radicand (\ge 0)
  2. Apply fraction constraint: denominator (\ne 0)
  3. Combine constraints by splitting the number line into intervals around critical points (zeros where numerator/radicand hits 0 and where denominator hits 0).
  4. Test a sample value from each interval to see where the radicand is nonnegative.
• Additional emphasis:
  • Even if a root condition seems satisfied at a boundary, it can still fail if the denominator becomes 0.

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6) Bonus probability idea (comment-based discussion)

• Setup:
  • From 10 people: 3 men and 4 women selected for roles chairman, secretary, treasurer.
• Probability question asked:
  • “Chances of being elected as a male chairman or female secretary.”
• Instruction:
  • The presenter does not solve it on the video; viewers are asked to discuss solutions in the comments.

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Methodology / instruction lists explicitly presented

A) How to handle algebra word problems with 3 variables

• Translate each sentence into a mathematical equation.
• Assume variables for the three unknowns (e.g., (A, B, C)).
• Build 3 independent equations for 3 variables.
• Use elimination/substitution to solve.
• If only one variable is asked, derive it without necessarily fully solving everything.

B) How to quickly compute trig expressions

• Memorize transformations and key angles based on 180° and 360°.
• Use quadrant rules to determine the sign of (\sin) or (\cos).
• Convert angles relative to 180°/360° (instead of relying on 90°/270°).
• Simplify and look for cancellations to speed up.

C) How to solve “average + ratio” in statistics

• Let counts be variables (e.g., (G) for teachers, (D) for lecturers).
• Convert each average into a total:
  • average (\times) count (=) total.
• Use the combined average to create a total equation:
  • combined average (\times) (total count) (=) sum of totals.
• Solve for the ratio (\frac{G}{D}).

D) How to avoid heavy solving with mean problems

• Start from the mean definition:
  • (\text{mean}=\frac{\text{sum}}{3})
• Use the first mean to find (a+b+c).
• Substitute into the second expression’s sum, then divide by 3.

E) How to determine the domain for functions with roots and fractions

• Identify constraints:
  • Square root requires radicand (\ge 0) (for real numbers).
  • Any fraction requires denominator (\ne 0).
• Convert constraints to inequalities.
• Find critical points (where radicand/numerator becomes 0 and where denominator becomes 0).
• Split the number line into intervals and test sign using a sample point in each interval.
• Intersect all valid conditions to get the final domain.

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Sources / speakers (identified in subtitles)

• Jerom Polin
• Billy Kurniawan
• “Mantapu Akademi / Matapok Academy” channel (program/brand; no other individual sources named)