# Grade 8 Sample Math Challenge Question Part 3

These Questions are based on k+12 curriculum   Time: 1 Hour

1. What is the range of equation ax+by+c=0?
2. What is the remainder when x2-3x+2 is divided by x-2?
3. What is the slope of the line with 2 and -3 as its x and y intercept respectively?
4. The line 2x-3y +12=0 intersects  x-axis at (a,b). What is a+b?
5. The sum of two numbers is 39. The larger number is one more than the smaller number. What is the larger number?
6. What is the positive root of equation 2x2+5x-3=0?
7. What is the range of y=2x2+5x-3?
8. For what value ok k will 3x-5y-10=0 and 6x-10y+k=0 be dependent?
9. For what value of k will make 3x-5y-10=0 and 6x-ky+k=0 be parallel?
10. Factor completely: $8x^3-27$
11. What is the domain of $y=\sqrt{1-2x^2}$
12. What is the range of equation in  #11?
13. Find a quadratic equation with integral coefficients if one root is $2-\sqrt{3}$
14. Rationalize: $\displaystyle\frac{2 \sqrt{7} + \sqrt{3}}{3\sqrt{7} - 5\sqrt{3}}$
15. A motorist drove 240 km. If he had gone 20 kph faster , he could have made his trip in one hour less time, how fast did he drive?
16. If y varies inversely as the square root of x and y=6 when x=4. Find x when y=9.
17. Solve for x:  $\sqrt{11-x} - \sqrt{x+6} = 3$
18. In how many ways can we arrange 5 students in a round table?
19. There are 20 people inside the room. Each person made a handshake with each other once. How many possible handshakes happened?
20. How  many 6-digit license  plates can be made with 3 letters and 3 numbers(repetition is allowed)?
21. A pair of fair dice was tossed once, what is the probability of getting a sum of an odd number?
22. Five fair coins are rolled once, what is the probability of getting exactly 3 heads?

For #23-25 use the following data:

Given the scores for 10 students participated in Division Elimination Round of Math Challenge out of 50-item test are the following.

30, 32, 35, 32, 31, 46, 41, 42, 25, 33

23. What is the mean of the scores?

24. What is the median score?

25. What is the mode of the scores?