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.
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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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