Prediksi Soal Asesmen Sumatif Akhir Tahun Matematika Kelas 8 Tahun 2025 (Part 1)

Summary

In this educational video, Om Ali Suud explains a series of mathematics problems related to circles and algebra for 8th-grade students. He covers a range of topics such as calculating angles in circles, finding areas of sectors, and understanding the properties of various geometric shapes. The tutorial also touches on algebraic expressions and linear equations. Throughout, Om Ali offers clear explanations and step-by-step solutions for each problem, aiming to help students understand the concepts and prepare for their upcoming exams. The video concludes with an invitation to continue with more problems in the next part.

Takeaways

• 😀 The video starts with a greeting and introduction to the topic of predicting questions for the End-of-Year Mathematics Assessment for 8th grade students.
• 😀 The first question discusses identifying parts of a circle, including the yellow area (called a 'tembereng') and line segment OD (called an 'apotema').
• 😀 In the second question, the relationship between central and inscribed angles is explained: the central angle is twice the size of the inscribed angle that subtends the same arc.
• 😀 The third question involves calculating the value of X using the relationship between central and inscribed angles.
• 😀 The fourth question explains how to calculate the measure of angle CDB based on the given angle AOC and the properties of the circle.
• 😀 Question 5 discusses supplementary angles formed by two intersecting chords, with the sum of opposite angles being 180°.
• 😀 In question 6, the area of a sector (juring) is calculated using the formula involving the central angle and radius of the circle.
• 😀 The seventh question covers how to calculate the area of a shaded region in a circle by subtracting the area of a square (belah ketupat) from the area of the circle.
• 😀 Question 8 introduces the concept of comparing the lengths of two arcs using the proportion of their central angles.
• 😀 Question 9 applies the Pythagorean theorem to calculate the length of a tangent line between two gears of different radii.
• 😀 The final question in the transcript discusses identifying linear equations in two variables from a set of provided equations, with the correct answers being equations 1 and 4.

Q & A

What is the term used for the yellow area in the diagram where OD is a radius of the circle?

The yellow area is called a 'tembereng,' and the line OD is referred to as the 'apotema.'

What is the correct relationship between the central angle and the inscribed angle on the same arc?

The central angle is twice the size of the inscribed angle, not the other way around.

How do you calculate the value of X in the equation 3x + 10 = 70?

First, subtract 10 from both sides, resulting in 3x = 60. Then, divide by 3, giving X = 20 degrees.

What is the angle CDB if the central angle AOC is 80 degrees and AB is a diameter?

The angle CDB is 50 degrees. The total angle of the circle is 180 degrees, so the remaining angle is 100 degrees, and half of it gives the inscribed angle of 50 degrees.

How do you calculate the sum of angles A and D if the opposite angles of a cyclic quadrilateral add up to 180 degrees?

To find angle A, subtract 116 degrees from 180, giving 64 degrees. To find angle D, subtract 75 degrees from 180, giving 105 degrees. The sum of angles A and D is 169 degrees.

What is the area of a sector with a central angle of 60 degrees and a circle diameter of 28 cm?

The area of the sector is approximately 102.67 square centimeters. This is calculated by using the formula for the area of a sector and simplifying the expression.

How do you find the area of the shaded region between a circle and a rhombus with a diagonal of 20 cm?

The area of the shaded region is calculated by subtracting the area of the rhombus from the area of the circle. The circle's area is πr², and the rhombus's area is 1/2 * diagonal1 * diagonal2.

How do you calculate the length of a chord (busur) given the angle and the radius of a circle?

The length of the chord can be calculated by using the ratio of the central angle to the total circle angle (360 degrees) and applying this ratio to the arc length. In the case provided, the length of the chord CD is 14.67 cm.

How do you calculate the length of the tangent line between two gears with radii 3 cm and 8 cm, with the centers 13 cm apart?

To calculate the length of the tangent line, apply the formula for the distance between two external tangent lines: √(distance² - (r1 - r2)²), which results in 12 cm.

Which of the following represents a linear equation in two variables?

The correct linear equation in two variables is the one with variables x and y, such as equation 1. Equations involving squares of variables (like quadratic equations) are not linear.