[KOMPLIT NO.1-25] SOAL GLADI TKA SMA 2026 MATEMATIKA WAJIB | SOAL ASLI TKA SMA 2025 MTK WAJIB #TKA

Summary

The video is a lesson-by-lesson review of 25 questions from the 2025 Indonesian high-school TKA compulsory/general mathematics exam, intended as preparation for the 2026 exam. The instructor demonstrates how to translate word problems and diagrams into mathematical models, select the right formula, and check whether answers satisfy the question’s conditions.

Questions and Main Methods

1. Sets and set operations

   • List each set’s members before applying the operations: (A={1,2,3,4,5}), (B={0,2,4,6,\ldots}), and (C={2,3,5,7}).
   • Find the intersection (A\cap B={2,4}), then take its union with (C).
   • The result is ({2,3,4,5,7}).

2. Exponent rules

   • Rewrite powers so expressions have the same base: (8=2^3) and (9=3^2).
   • Apply the power-of-a-power rule, then subtract exponents when dividing like bases.
   • The expression simplifies to (\frac{4}{3}).

3. A defined binary operation

   • Simplify the operation’s numerator using ((a-b)^2=a^2-2ab+b^2); the operation becomes (\frac{a^2+b^2}{a+b}).
   • Substituting the given value produces (a^2-5a-6=0), whose roots are (6) and (-1). Since (a) is nonnegative, use (a=6).
   • Thus, the claim that (a) is a multiple of 3 is true, the claim that it is prime is false, and the stated operation involving 6 and 0 is true.

4. Linear-function word problem

   • Substitute the target temperature increase, (y=0.7), into (y=0.02x-39.9).
   • Solve for (x); the predicted year is 2030.

5. Course fees and discounts

   • Use the 50th registrant’s discounted payment of Rp180,000 and (y=0.9x) to infer an initial course fee of Rp200,000.
   • The instructor concludes that all four later students can afford the course: their available funds exceed the normal fee, even before considering achievement-based discounts.

6. Arithmetic sequences

   • The first row has 400 sheets and the second has 550, so the common difference is 150.
   • Apply (U_n=a+(n-1)d): the fifth row has 1,000 sheets.
   • The instructor also reminds viewers to know the arithmetic-series sum formula.

7. Repeated percentage decrease

   • A 20% daily reduction means each day’s level is 80% of the previous day’s.
   • Starting at 13 mg/dL, the levels reach roughly 6.66 on day 4 and 5.32 on day 5.
   • Those are below 7 but not below 5, so the patient feels comfortable but is not yet clinically cured on days 4 and 5.

8. Graphing a system of inequalities

   • Find the equations of the boundary lines from the plotted points, then test a point inside the shaded region to determine each inequality’s direction.
   • The resulting system is (x-2y\geq -4), (x+y\leq2), and (y\geq0). The instructor selects option B.

9. Three-variable linear equations

   • Represent the prices of roses, lilies, and carnations with variables and translate the three bouquet compositions into equations.
   • Instead of solving for every flower price, add the equations and compare the resulting expression with the requested bouquet.
   • The requested combination costs Rp115,000.

10. Angles - Use equal vertically opposite angles and linear pairs that sum to (180^\circ). - The pairs identified as guaranteed to form (180^\circ) are statements 3, 4, and 5.

11. Parallel planes in a room diagram - Identify the bookshelf’s plane, then rule out walls parallel to it and surfaces that are not walls. - The schedule board can go on faces BCGF and ADHE.

12. Similar trapezoids and the Pythagorean theorem - Use similarity ratios to find missing trapezoid dimensions, then use right triangles and the Pythagorean theorem. - The required side (LM) is (8\sqrt5) cm.

13. Garden layout and Pythagorean triples - Turn the illustration into a right trapezoid and find its sloping side. The relevant right triangle has legs 150 cm and 360 cm, giving a hypotenuse of 390 cm. - Divide 390 by each pot diameter to check the plant-spacing statements: the counts are 26 for ginger, 15 for turmeric, and 13 for galangal. The instructor marks only the turmeric statement true. - The instructor recommends recognizing common Pythagorean triples, including 5–12–13.

14. Reflection and rotation - Work through the transformations in order: reflect across (y=1), then rotate (180^\circ) about the origin. - Use the transformation formulas to recover the original point from the image; the point is (B=(4,3)).

15. Decorative strings in a rectangular prism - Use the midpoint of the ceiling edge and form a right triangle with sides 3 m and 4 m. - Each string is 5 m, so two strings use 10 m. From a 20 m roll, 10 m remains.

16. Perimeter of a clock ornament - Find the straight sides with the Pythagorean theorem, use the semicircle formula for the curved edge, and add the boundary lengths. - One ornament has perimeter 191.4 cm; two require 382.8 cm of thin wood.

17. Data sufficiency for a kite’s perimeter - Use the kite-area formula and the given diagonal to determine the other diagonal. - The area statement alone and the side-length statement alone are each insufficient, but together they allow the sides—and therefore the perimeter—to be determined. - The answer is option C: both statements together are sufficient, while neither alone is.

18. Packing boxes in a truck - Compare the two permitted box orientations by dividing the truck-bed dimensions by the corresponding box dimensions and rounding down to whole boxes. - The better orientation holds 360 boxes.

19. Cylinder surface area and sticker cost - Since the stickers cover the cylinder’s curved surface, calculate (2\pi rh), then multiply by eight decorations. - At 300 cm² per sheet, 8,800 cm² requires rounding up to 30 sheets. - At Rp9,000 per sheet, the minimum cost is Rp270,000.

20. Trigonometric ratios - Interpret the given cosine as adjacent side over hypotenuse, then use the Pythagorean theorem to find the remaining side lengths. - Checking the proposed ratios shows that the first two statements are false and the tangent statement is true: (\tan\beta=\frac{3\sqrt7}{7}).

21. Reading a graph - Check each statement against the relevant school’s line and years, looking for increases, decreases, or constant values. - The instructor identifies statements 1 and 4 as correct.

22. Arranging market stalls - Treat the required sequence with trader C between A and D as a single block. - There are two possible internal orders, A–C–D and D–C–A. For each, the block and the other two traders can be arranged in (3!=6) ways. - Total arrangements: 12.

23. Mean, median, and constraints - Use the mean of 6 to find that the two unknown values sum to 15. - Combine the median and range conditions to determine their possible values, then assess whether each statement must be true. - The first statement is false; the second and third are true.

24. Probability of drawing an empty envelope - Add the envelopes containing prizes or items: (15+12+10+8=45). - Of 60 envelopes, (60-45=15) are empty, so the probability is (15/60=\frac14).

25. Probability after earlier draws - Let (a) be the number of prize slips taken by the four people before Ani. Blank slips are returned, so they do not reduce the total. - Set the probability of Ani drawing a prize, (\frac{10-a}{15-a}), equal to (\frac23). Solving gives (a=0). - Therefore, the previous four people must all have drawn blank slips.

Overall Lessons

• Translate definitions, diagrams, tables, and word problems into mathematical notation before calculating.
• Choose formulas that match the structure of the question: set operations, exponent laws, linear equations, sequences, similarity, the Pythagorean theorem, trigonometry, or probability.
• In statement-checking questions, distinguish between something that is possible and something that is guaranteed.
• For geometry and packing questions, account for orientation, boundaries, and whole-unit constraints. For materials sold by area or sheet, round up when necessary.

Speakers and Sources

• Speaker: One instructor/narrator from the Ar-Raihan tutoring channel, presenting the lessons and worked solutions. No other speakers are clearly featured.
• Sources: The instructor’s worked examples are based on the 2025 SMA TKA compulsory/general mathematics questions, including their diagrams, graphs, tables, and problem statements. The video also includes brief practice prompts, but those prompts are not worked through in the provided subtitles.