These 20 multiple-choice questions are carefully designed to help Grade 8 students master key concepts in two important mathematics topics: Operation of Algebraic Expressions and Reduction and Enlargement of Figures. Each question not only reinforces their understanding of fundamental skills such as simplifying, factoring, and solving expressions but also builds their ability to apply scale factors to real-world geometric problems.
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Practicing these types of questions is highly beneficial as it mirrors the format and difficulty of national examinations, ensuring that students are well-prepared, confident, and capable of tackling similar problems under exam conditions. With the added visual diagrams, students are encouraged to develop stronger problem-solving strategies and visual reasoning, both critical skills for success in standardized math assessments.
How to answer the Questions
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1. Simplify: \( (3x + 5) - (2x - 7) \)
2. Expand: \( (x + 2)(x - 5) \)
3. Factorize: \( x^2 + 5x + 6 \)
4. Simplify: \( 4x - 2(3x - 5) \)
5. Find the perimeter of a rectangle enlarged by a scale factor of 3, original perimeter = 12 cm.
6. Expand: \( (2x-3)(x+4) \)
7. A triangle with sides 3 cm, 4 cm, 5 cm is reduced by a scale factor of \( \frac{1}{2} \). What is the hypotenuse?
8. Simplify: \( (5x^2 - 2x) + (3x^2 + 7x) \)
9. A figure enlarged by a scale factor of 2 will have an area multiplied by:
10. Expand and simplify: \( (x-2)(x+2) \)
11. Simplify: \( (6x^2 - 3x) - (2x^2 + 5x) \)
12. The area of a square becomes 9 times larger after enlargement. What is the scale factor?
13. Factorize: \( x^2 - 9 \)
14. If the sides of a figure are reduced by a scale factor of \( \frac{1}{3} \), by what factor is the area reduced?
15. Simplify: \( (2x+5)(3x-4) \)
16. If the scale factor between two similar figures is 4, by what factor is the volume enlarged?
17. What happens to the volume of a cube when its sides are enlarged by a scale factor of 2?
18. Simplify: \( (3x-2)^2 \)
19. Find the new area if a rectangle with area 20 cm² is enlarged by a factor of 3.
20. A rectangle's dimensions are enlarged by a factor of 5. What happens to its perimeter?
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