grade 8 sample only Factoring_ProblemSolving_Quiz.pptx

grade 8 sample only Factoring_ProblemSolving_Quiz.pptx

1. Question A rectangle has area x² + 5x + 6. If the length is (x+2), what is the width? A. x+2 B. x+3 C. x+5 D. x+6

2. Answer & Explanation ✅ Correct Answer: B Factor: x²+5x+6 = (x+2)(x+3). Width = x+3.

3. Question A garden has an area of 2x² + 7x + 3. If one side is (x+1), find the other side. A. 2x+3 B. 2x+1 C. x+3 D. x+2

4. Answer & Explanation ✅ Correct Answer: A Factor: 2x²+7x+3 = (x+1)(2x+3). Other side = 2x+3.

5. Question A school earned x² + 8x + 12 pesos from ticket sales. If each ticket costs (x+2) pesos, how many tickets were sold? A. x+6 B. x+4 C. x+12 D. x+8

6. Answer & Explanation ✅ Correct Answer: A Factor: x²+8x+12 = (x+2)(x+6). Tickets sold = x+6.

7. Question A rectangular garden has area x² − 16. If one side is (x−4), what is the other side? A. x+4 B. x−4 C. x+16 D. x−16

8. Answer & Explanation ✅ Correct Answer: A x²−16 = (x−4)(x+4). Other side = x+4.

9. Question A ball is thrown upward. Its height is modeled by h = −t² + 5t. When will the ball hit the ground? A. 0 s and 5 s B. 1 s and 4 s C. 2 s and 3 s D. 5 s only

10. Answer & Explanation ✅ Correct Answer: A Solve −t²+5t=0 → t(−t+5)=0 → t=0, t=5.

11. Question The product of two consecutive integers is n² + n. Which factorization represents this? A. n(n+1) B. (n−1)(n+1) C. n(n−1) D. (n+2)(n−2)

12. Answer & Explanation ✅ Correct Answer: A Two consecutive integers: n and n+1. Product = n²+n.

13. Question The area of a square is 9x². What is the perimeter of the square? A. 12x B. 18x C. 24x D. 36x

14. Answer & Explanation ✅ Correct Answer: A Side = √(9x²) = 3x. Perimeter = 4(3x)=12x.

15. Question The product of two numbers is x²+5x+6. If one number is (x+2), what is the other number? A. x+2 B. x+3 C. x+6 D. x+5

16. Answer & Explanation ✅ Correct Answer: B Factor: x²+5x+6=(x+2)(x+3). Other number = x+3.

17. Question A farmer has a triangular lot with area A=½(x+2)(x+6). Expand and simplify. A. ½(x²+8x+12) B. ½(x²+4x+12) C. ½(x²+2x+6) D. Prime

18. Answer & Explanation ✅ Correct Answer: A (x+2)(x+6)=x²+8x+12. Multiply by ½.

19. Question The length of a rectangle is (x+5) and the width is (x+2). Its area equals the area of a square with side (x+3). Find x. A. 2 B. 3 C. 4 D. 5

20. Answer & Explanation ✅ Correct Answer: None (x+5)(x+2) = x²+7x+10; (x+3)² = x²+6x+9. Equating: x²+7x+10 = x²+6x+9 → x=−1 (no positive solution).