45 Essay Questions for Grade 8 Mathematics, First Semester, Merdeka Curriculum 2025 and Exam Answer Key

The Shiro CoprPelajar class 8 can now access 45 mathematics essay questions for the first semester of the 2025 Merdeka Curriculum, complete with the latest answer keys as study materials for exam preparation.

These questions are compiled based on the core materials listed in the latest Merdeka Curriculum and are designed to test in-depth conceptual understanding.

Equipped with clear answer explanations, this set of questions is suitable for preparing for daily tests, mid-term tests, and final term tests.

This article comes as a practical solution for students, teachers, and parents looking for up-to-date math problem references.

All questions are written in an essay format that trains students' critical thinking skills.

Immediately listen and utilize these questions as effective learning companions in the era of the Merdeka Curriculum.

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8th Grade Math Problem

A. Rational and Irrational Numbers

1. Explain the difference between rational and irrational numbers!

Answer: Rational numbers can be expressed as a/b, where a and b are integers and b ≠ 0. Irrational numbers cannot be expressed as a/b, for example √2, π.

2. Is √49 a rational number? Explain your reason.

Answer: Yes, because √49 = 7, and 7 is an integer (rational).

3. Convert 0.75 into the simplest fractional form!

Answer: 0.75 = 75/100 = 3/4.

4. Is 0.333... a rational number? Explain!

Answer: Yes, because 0.333... = 1/3.

5.    Express √50 in the simplest form!

Answer: √50 = √(25×2) = 5√2.

B. Algebraic Operations

6. Simplify: 3x + 2x - 5 + 7!

Answer: 3x + 2x - 5 + 7 = 5x + 2.

7. Calculate the value of: (2x - 3)(x + 4)!

Answer: 2x⊃2; + 8x - 3x -12 = 2x⊃2; + 5x - 12.

8. If a = 3 and b = -2, calculate the value of a⊃2; + 2ab + b⊃2;!

Answer: 9 + 2(3)(-2) + 4 = 9 - 12 + 4 = 1.

9. Factorize: x² + 7x + 10!

Answer: (x + 2)(x + 5).

10. Simplify 5(x - 2) - 3(x + 4)!

Answer: 5x - 10 - 3x -12 = 2x - 22.

C. Linear Equations and Inequalities

11.    Solve: 2x - 5 = 11.

Answer: 2x = 16 ⇒ x = 8.

12. Determine the solution set of: 3x + 7 < 19

13. If 4x + 1 = 2x + 9, what is the value of x?

Answer: 2x = 8 ⇒ x = 4.

14. Write the inequality for: "twice a number plus 5 is less than 17"!

Answer: 2x + 5 < 17>

15. A number, when multiplied by 3 and then reduced by 4, gives 11. Determine the number!

Answer: 3x - 4 = 11 ⇒ x = 5.

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D. Relations and Functions

16. What is meant by a function in mathematics?

Answer: A function is a relation that maps each member of the domain to exactly one member of the codomain.

17. Given f(x) = 2x - 3. Calculate f(5)!

Answer: f(5) = 2(5) - 3 = 10 - 3 = 7.

18. Determine the domain of the function f(x) = √(x - 2).

Answer: x ≥ 2.

19. If f(x) = x⊃2; - 4x + 3, determine the value of f(2)!

Answer: 4 - 8 + 3 = -1.

20. Is the relation {(1,2), (2,3), (1,4)} a function? Explain!

Answer: No, because 1 is paired with two values (2 and 4).

E. Coordinate System

21. Determine the coordinates of the point resulting from the translation (x, y) → (x+2, y−3) for point A(3, 4)!

Answer: (5, 1).

22.    State the quadrant of the point (-4, 6)!

Answer: Quadrant II.

23. Calculate the distance between point A(1,2) and B(4,6)!

Answer: √[(4−1)² + (6−2)²] = √[9 + 16] = √25 = 5.

24. What is meant by the x-axis and y-axis?

Answer: The x-axis is the horizontal line, and the y-axis is the vertical line in the Cartesian coordinate system.

25. Describe which axis the point (0, -5) is on?

Answer: Y-axis (because x = 0).

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F. Plane Figures and Geometric Transformations

26.    State the formula for the area and perimeter of a rectangle!

Answer: Area = p × l, Perimeter = 2(p + l).

27. Calculate the area of a triangle with a base of 10 cm and a height of 12 cm!

Answer: ½ × 10 × 12 = 60 cm⊃2;.

28. If the length of the side of a square is 7 cm, what is the perimeter and area?

Answer: Circumference = 4×7 = 28 cm, Area = 7×7 = 49 cm².

29. Determine the type of triangle with side lengths 5 cm, 5 cm, and 8 cm!

Answer: Isosceles triangle.

30. A parallelogram has a base of 8 cm and a height of 5 cm. Calculate its area!

Answer: 8 × 5 = 40 cm².

31. What is meant by rotation in geometric transformation?

Answer: Rotation is the movement of a shape around a specific point by a certain angle.

32. Determine the image of the point (4, -2) if rotated 90° clockwise around the origin (0,0)!

Answer: (2, 4).

33. Explain the difference between dilation and reflection!

Answer: Dilation is the enlargement or reduction of a shape, reflection is the mirroring.

34. The triangle ABC is reflected over the y-axis. If A(3, 2), then what is its image?

Answer: A’(-3, 2).

35. A square with side length 6 cm is dilated with a scale factor of 2. Determine the length of its image's side!

Answer: 6 × 2 = 12 cm.

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G.    Mixed Problems

36. Solve: (x + 3)(x - 3)!

Answer: x⊃2; - 9.

37. The factors of x⊃2; - 6x + 9 are ...?

Answer: (x - 3)².

38. If f(x) = 3x + 2 and g(x) = x - 1, calculate f(g(4))!

Answer: g(4) = 3, f(3) = 3(3) + 2 = 11.

39. Determine the gradient of the line passing through the points (2,3) and (6,7)!

Answer: (7 - 3)/(6 - 2) = 4/4 = 1.

40.    The graph y = 2x + 1 intersects the y-axis at which point?

Answer: Point (0, 1).

41. Express 1/8 in decimal form!

Answer: 0.125.

42. Determine the solution set of: -2x + 5 ≥ 1.

Answer: -2x ≥ -4 ⇒ x ≤ 2.

43. Are all prime numbers rational numbers?

Answer: Yes, because prime numbers can be written as a/b, for example 7 = 7/1.

44.    Draw the graph of y = x⊃2;! Mention its symmetry properties.

Answer: Symmetry with respect to the y-axis.

45. What is the general form of a quadratic function and mention its graph!

Answer: y = ax⊃2; + bx + c; its graph is a parabola.

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