Prediksi TKA Matematika 2026 (Part 1)

Summary

This video covers 10 practice problems from the SMP TKA Mathematics Package A, providing step-by-step explanations for each. Topics include calculating total costs with promotions, estimating bus rental expenses, determining days of the week, solving proportion problems, computing fuel consumption, adjusting workforce for project completion, rationalizing irrational fractions, and calculating areas of geometric shapes. Each problem is carefully broken down with clear reasoning, showing both the method and the final answer. The tutorial emphasizes practical strategies for tackling SMP-level math questions efficiently, making complex concepts accessible and helping students build confidence in problem-solving and exam preparation.

Takeaways

• 😀 Raka receives a discount on his purchase in a marketplace promotion by getting one of the cheapest items free when buying five items.
• 😀 The total cost of purchasing two headsets and three wireless mice is Rp314,000, and after applying the discount, the final amount to be paid is Rp266,000.
• 😀 A school rents two buses for a study tour, with each bus costing Rp1,875,000. The total rental cost for two buses is Rp3,750,000, and the estimation is slightly higher than Rp3,500,000.
• 😀 To determine the day of the week for a future date, such as April 8, the total days until the date are calculated, with a method using modulo 7 to find the correct weekday.
• 😀 The correct weekday for July 1, 2023, is a Saturday, while the statements in the multiple-choice options help verify the correct answer.
• 😀 In a ratio problem, the total money of Andi, Badu, and Citra is determined using a given ratio of 5:3, with the amount of Rp300,000 representing the difference between Andi and Citra's money.
• 😀 Joshua travels a distance of 150 km with an average speed of 60 km/h in 2.5 hours. The fuel consumption for the trip is calculated based on the ratio of 1.5 L of fuel per 45 km, resulting in 5 liters of fuel needed.
• 😀 A construction project initially planned for 30 days with 14 workers will require additional workers if delays occur, such as a 3-day pause. The solution uses a ratio-based approach to calculate the required number of workers.
• 😀 A renovation project initially planned for 80 days with 10 workers can be completed faster if additional workers are added, as shown through a calculation using the inverse relationship between workers and time.
• 😀 Rationalizing expressions with square roots involves multiplying both the numerator and denominator by the conjugate to eliminate the square root from the denominator, as demonstrated with a sample problem.

Q & A

How is the total cost calculated for Raka's purchase when a marketplace promotion applies?

First, calculate the total cost of each type of item: 2 headsets at Rp85,000 each equals Rp170,000, and 3 mice at Rp48,000 each equals Rp144,000. The total is Rp314,000. The promotion gives a discount equal to the cheapest item, which is Rp48,000. Subtracting this gives the final payment: Rp314,000 - Rp48,000 = Rp266,000.

How can you estimate the total cost for renting buses for a school trip?

Determine the number of buses needed (2 buses for 89 students if each bus holds 45). Multiply the rental price per bus (Rp1,875,000) by the number of buses: 2 x Rp1,875,000 = Rp3,750,000. This is an estimate slightly above Rp3.7 million.

Given that April 8 falls on a Wednesday, how can you determine the weekday of a later date, like July 1?

Count the total days from April 8 to July 1. April has 30 days, so 30-8=22 remaining in April. Add May's 31 days and June's 30 days: 22 + 31 + 30 = 83 days. Divide 83 by 7 to find the weekday cycle: 83 ÷ 7 = 11 weeks and 6 days. Counting 6 days forward from the last known Wednesday, July 1 falls on a Wednesday.

How do you find the total money of Andi, Badu, and Citra if their ratio is 5:3 and the difference between Andi and Citra is Rp300,000?

Let the total parts be 5+3=8, but to include Badu we consider total ratio sum as 15. The difference of Andi and Citra is 2 parts = Rp300,000. Therefore, 1 part = Rp150,000. The total sum is 15 parts = 15 x Rp150,000 = Rp2,250,000.

How is the fuel requirement calculated for Joshua's trip?

Joshua travels at 60 km/h from 6:50 to 9:20, taking 2.5 hours. The distance is speed x time = 60 x 2.5 = 150 km. If 1.5 L fuel covers 45 km, then required fuel = 150 x 1.5 ÷ 45 = 5 L.

How do you determine the additional workers needed to complete a house repair project on time?

If 14 workers can complete the project in 30 days, after 6 days with a 3-day halt, 21 days remain. Using the inverse proportion formula: required workers = (24 days x 14 workers) ÷ 21 days = 16 workers. Additional workers needed = 16 - 14 = 2.

How do you verify the time required when workers are added to a project?

Use the inverse relationship between workers and time. For 10 workers finishing in 80 days, adding 6 workers (total 16) reduces the time to 10 x 80 ÷ 16 = 50 days. If fewer workers are added, recalculate proportionally.

What is the process of rationalizing a fraction with a square root in the denominator?

Multiply both numerator and denominator by the conjugate of the denominator. For example, for 12/(3+√3), multiply top and bottom by (3-√3). Simplify using distributive property, combine like terms, and reduce if possible.

How do you calculate the area of a parallelogram when the sides involve square roots?

Use the formula Area = base x height. For a base of 3+2√2 m and height 3√2-2 m, multiply: (3+2√2) x (3√2-2). Simplify using distributive property and combine like terms: area = 5√2 + 6 m².

How do you simplify an expression like (2√8)/(1+√2) by rationalization?

Multiply numerator and denominator by the conjugate (1-√2). Expand numerator and denominator using distributive property, simplify square roots, and combine terms. The simplified form becomes -4√2 + 8 in this example.