PAKET 1 NO. 28-35 || 'BOCORAN SOAL' ASLI TKA MATEMATIKA WAJIB 2026 DARI PUSMENDIK

Summary

The video works through questions 28–35 from a mandatory TKA mathematics practice set. The instructor demonstrates probability, volume, geometric sequences, percentage calculations, grouped-data statistics, and spatial geometry. The solutions rely on identifying the relevant quantities in each question and applying the appropriate formula.

Question 28 — Probability Without Replacement

A school selects two band groups at random: first a boys’ group, then a girls’ group. The calculation uses 6 boys’ groups and 4 girls’ groups, for a total of 10 groups.

• Probability the first selection is a boys’ group: (\frac{6}{10}).
• After that selection, 9 groups remain, including 4 girls’ groups. Probability the second selection is a girls’ group: (\frac{4}{9}).
• Since both events must happen, multiply: [ \frac{6}{10}\times\frac{4}{9}=\mathbf{\frac{4}{15}}. ]

The transcript’s opening description of the number of boys’ groups is inconsistent, but its calculation uses six.

Question 29 — Composite Volumes and Capacity

The problem asks whether a 220-liter cheese supply can meet an order if packages are filled to 75% of their volume.

• Package A: Add the volumes of its cylinder and cone:
  • Cylinder: (160\pi\text{ cm}^3)
  • Cone: (32\pi\text{ cm}^3)
  • Total: (192\pi\text{ cm}^3)
  • At 75% capacity: (144\pi\approx452.16\text{ cm}^3)
• Package B: Add the volumes of its box and pyramid:
  • Total package volume: (768\text{ cm}^3)
  • At 75% capacity: (576\text{ cm}^3)

For 150 A packages and 200 B packages, the filled volumes total about 67.8 L + 115.2 L = 183 L. Since this is less than 220 L, the supply is sufficient and the proposed filling rule can be used.

Question 30 — Geometric Sequence and Cumulative Load

The support-point loads form a geometric sequence: (0.5, 1, 2,\ldots) tons, with first term (a=0.5) and ratio (r=2). The instructor uses the geometric-series sum:

[ S_n=\frac12(2^n-1). ]

• Through the sixth support point: (S_6=31.5) tons. A 32-ton supply is enough.
• Through the seventh: (S_7=63.5) tons, so 31.5 additional tons beyond the available 32 tons would be needed—not 30 tons.
• Through the fifth point: (S_5=15.5) tons. From a 32-ton supply, 16.5 tons would remain.
• If the concrete’s cumulative load limit is 20 tons, the fifth-point total is below the limit, but the sixth-point total exceeds it.

Question 31 — Comparing Potential Tourist Markets

The question compares estimated tourist counts by multiplying each country’s tourist total by the relevant percentage.

• Australia: Surfing tourism is (20\%) of 120,000, or 24,000.
• Japan: Culinary tourism is (70\%) of 40,000, or 28,000. Thus, Australia’s surfing market is not larger.
• Malaysia: The body-care market is (90\%) of 65,000, or 58,500.
• China: The culinary market is (60\%) of 85,000, or 51,000. Malaysia’s estimated market is larger.
• For shopping tourism, Japan’s (30\%) of 40,000 is 12,000, while China’s (40\%) of 85,000 is 34,000. China’s estimate is larger.

The main lesson is to translate each percentage claim into a comparable number before judging whether it is true.

Question 32 — Finding a Missing Frequency from the Mode

The salary data are grouped into intervals, with one frequency unreadable. Since salaries are expressed in millions, the stated mode of Rp15.75 million is treated as 15.75.

• The modal class has a lower boundary of 13.5 and a class width of 3.
• Its frequency is 24; the preceding frequency is (x), and the following frequency is 18.

• Substitute these values into the grouped-data mode formula: [ 15.75=13.5+3\frac{24-x}{(24-x)+(24-18)}. ]

• Solving gives (x=6).

The instructor emphasizes identifying the modal class and its neighboring frequencies before applying the formula.

Question 33 — Probability of Drawing a Particular Prize

Anto draws from the remaining prize coupons. The instructor counts 4 Jakarta–Kuala Lumpur tickets remaining out of 36 coupons:

[ P=\frac{4}{36}=\mathbf{\frac19}. ]

The explanation stresses tracking which prizes have already been taken and using the remaining total as the denominator.

Question 34 — Relationships Between Lines in a Cube

The instructor evaluates claims about cube edges and lines:

• (AD) and (FG) are parallel, not perpendicular.
• (BC) and (EH) are identified as parallel.
• The transcript says (EF) and (CG) do not meet; its follow-up description of their relationship is unclear. With standard cube labeling, those two lines are skew, so the audio’s suggestion that they are perpendicular may be inaccurate.

Question 35 — Order of Operations with Fractions

The expression is evaluated by doing multiplication before addition:

• (\frac74\times\frac8{21}=\frac23), after cancelling common factors.
• Then: [ \frac14+\frac23=\frac3{12}+\frac8{12}=\mathbf{\frac{11}{12}}. ]

The video announces question 36 at the end, but the subtitles do not include its solution.

Speakers and Sources Featured

• Speaker: One unnamed instructor/presenter, speaking on behalf of the Ruang Tentor channel.
• Source mentioned: The Pusmendik TKA simulation website is identified in the introduction as the source of the practice questions.