Category Archives: Grade 8 math challenge questions


This is the part 4 of free mtap reviewer for grade 8. It is also advisable to review reviewers for grade 7. Check this page to check all available reviewers for grade 8. Most of the topics here is already been discussed in this blog. If you want to know the tutorials. Use the custom search engine on the upper right part and type the keyword. I personally include some hints so that you will know what to find.

1. Evaluate: 67^2-66^2 (hint : Use sum and difference of two squares factoring)

2. What is the coefficient of x^3y^5 in the expansion of (x+y)^8? ( Hint: Binomial Theorem)

3. The length of a rectangle is 5 more than twice the width. If the perimeter is  58cm. What is the area of the rectangle?

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Sample Math Challenge Problems for Grade 8 – Orals

Disclaimer: This is not the official reviewer for the upcoming Metrobank -Mtap-Dep-Ed Math Challenge problems for division orals. These problems are created to somehow help students to enhance their speed and accuracy and familiarize some questions. We all don’t know what will be the questions. The more  problems we solve is the better math person we are. Have fun with these problems.


  1. What is the slope of the line with equation 3x-2y+4=0?
  2. If 26 increased by 4 times a number gives the same result as 1 increased by 9 times a number. What is the number?
  3. The sum of two numbers is 10 and their difference is 4. What is their product?
  4. Evaluate:  500^2 - 499^2
  5. Jane has 3 pairs of blouse,3 pairs of pants and 2 pairs of shoes. How many possible ways are there for her to choose an outfit?
  6. What are the roots of 15x^2-22x+8=0?
  7. In triangle ABC, \angle{A} >  \angle{B} > \angle{C}. What is the longest side of the triangle?
  8. For what value of k will make 2x-ky+1=0 parallel to x-y+1=0?
  9. The term that refers to an opinion or conclusion formed on the basis of incomplete information.
  10. The ratio of blue balls to white balls is 1:2, the ratio of the white balls to red balls is 3:4. What is the ratio of the blue balls to red balls?


  1. How triangle can be formed if two sides have lengths 12 and 21 and the third side has an even length?
  2. How many positive integral divisors 72 have?
  3. If 3^x+3^x+3^x=3 what is the value of x?
  4. Find the domain of the function f(x) = \sqrt{4-x^2}
  5. What is the coordinate of the center of a circle x^2+y^2-2x+4y-1=0 ?



  1. Find the value of \sqrt{5\sqrt{5\sqrt{5\dots}}}
  2. Find the sum of the series \displaystyle\frac{1}{1x2}+\displaystyle\frac{1}{2x3}+\displaystyle\frac{1}{3x4}+\ldots +\displaystyle\frac{1}{2013x2014}
  3. Rationalize: \displaystyle\frac{1}{\sqrt{2}+\sqrt{3}-\sqrt{5}}
  4. John drove 80 km downhill with a speed of 40 kph and went back at the speed of 10kph. What is John’s average speed?
  5. The ratio of the angles of quadrilateral is 2:3:4:6. What is the measure of the largest angle?

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?


Answer Key