# GRADE 8 SAMPLE MATH CHALLENGE QUESTIONS AND ANSWERS

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**Write equation of the line in ax+by+c=0. Time: 1 hr**

1. Simplify and express in positive exponent: (a^{-1}b^{2}c^{-5})^{4.}

2. What is the solution set of 2x-1>6?

3. Mary is 24 years old. John is half the age of Mary. How old is John?

4. What are the roots of 6x^{2}+x-2=0?

5. Solve for x: 5/(x-3) = (x+2)/(x-3)+3

6. What is the degree of equation 2x^{2}y-3xy+y^{2}=0

7. Simplify: (3-√2)/( √3-√2)

8. Give the product of (x-y)(x^{2}+xy+y^{2}).

9. Factor completely 2x^{5}-10x^{4}+8x^{2}.

10. Solve the equation: 2√x=√(x+27)

11. What is the conjugate of 1-√3?

12. Find the sum of x/(x^{2}-9) + (x+1)/(x^{2}-4x+3).

13. Find the solution set of 2x-y=4 and x+2y=-1.

14. The sum of 2/3 of the number and ¾ of the number is 51. Find the number.

15. Find the sum of equation 2x^{2}-3x+1.

16. For what value of K such that the lines 2x-ky=2 and x-2y=4 become parallel lines.

17. One factor of x^{2}+kx-2=0 is -1. Find the other root.

18. Find the maximum value of 1-3x-x^{2}.

19. Find the solution set of 2x^{2}+3x-2<0

20. Find the solution set of │2x-1│>3

21. Find the vertex of y=x^{2}-3x-6.

22. Find the perimeter of rectangle if the length is (2x-1) m and the width is (x+4) m.

23. For what values of m is (m-2)/(m+3) equal (m+1)/(m-1) ?

24. Find the equation of the line through (2,1) and (3,-2).

25. What is the slope of equation 2x-3y=4?

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### Dan

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