Time: 1hour Source: 2011 Metrobank -MTAP-Dep-Ed Math Challenge 1st Year

1. What value will 3x^{2} + x +1 be multiplied to get 6x^{3} +5x^{2} +3x+1?

2. Solve for a from the equation 2a+1 = a – 1/2

3. Solve the inequality 2x-1 > 3-x.

4. Jose got scores of 90, 85, 82, 76 in the four exams. What grade must he get in the fifth exam to have an average of 84% or better?

5. The unit digit of a number is one more than twice the tens digit. If the digits are reversed the resulting number is 45 more than the original number. What is the original number?

6. Given the points A(0,0), B(4,0), C(2,4), D(-2,4). What figure is ABCD if the points are plotted and connected in order?

7. Which of the following is are functions? a. x^{2}+2y^{2} = 25 b. x^{2}+2x +y^{2} = 25 c. x^{2}+x+2y^{2}+8=0 d.

8. What is the range of the function? ?

9. What is the domain of the function ?

10. What is the slope of the line passing through P_{1}(3,2) and P_{2}(-4,1)?

11. What is the x-intercept of the line 2x-5y+8=0?

12. The x- and y-intercept of the line are 2 and -5 respectively. Write the equation of the line.

13. Two vertices of a square located in the first quadrant are at (0,0) and (0,4). Where are the other two vertices?

14. What is the product of (3x+2y)(x-3y)?

15. Completely factor (a^{4}-b^{4})

16. Factor 27x^{3}-48xy^{2}.

17. What is the greatest common factor of 27a^{5}b^{3}c^{2} and 9a^{3}b^{5}c^{3}?

18. Factor 3ac +3ad + 2cb + 2db.

19. Simplify:

20. Multiply

21. Simplify:

22. Find the biggest of the three consecutive odd numbers such that the product of the second and the third is greater than the square of the first by 110.

23. The sum of two numbers is 24 and their product is 143. Find the numbers.

24. Solve for x and y: 2x +3y = 7, 4x – 5y =25.

25. A boat travels 1 1/3 hours to go 20 km downstream and 2 2/9 hours to return. Find the rate of the boat in still water.