# 4th year Practice Math Challenge Questions and Answers Part II

Direction: Write all equation of the line in standard form. Time: 1 hour

1. What is the greatest integer function of 4.6?

2. The sum of the complement and twice the supplement of an angle is 111°. What is the angle?

3. What is the period of y=tan2x?

4. What is the range of y=log(x^2 – 4)?

5. Find the equation of the line though (2,-3) and perpendicular to 3x-4y-1=0.

6. A pair of fair dice is toss once, what is the probability of getting a prime sum?

7. PT is tangent to circle O and a secant intersect the same circle at points A and B.PT = X , PB=9, PA=(x-2). How long is PT?

8. Find the equation of the line with slope of ½ and x-intercept of 3.

9. The line x-2y+1=0 intersect the circle x^{2}+y^{2}=28 at two points. What the slope of the line joining these two points?

10. Solve for n: (2^{3n})(4^{n})=(1/2)^{n-4}

11. What is the inverse function of y=log_{4}(x-2)?

12. In a math contest represented by different schools, each school sent 3 participants; everyone has to make a handshake with each other. If there were 105 handshakes happened. How many schools participated in the said contest?

13. What is the maximum number of diagonals can be drawn in a regular dodecagon?

14. The minimum value of y=2x^{2}+kx+3 is 1. What is/are the value(s) of K?

15. I have two sticks with lengths of 6 cm and 10 cm. I have a third stick measuring 20 cm. If I want to create the largest triangle out of three sticks. How long will I need to cut off from the third stick?

16. What is the median of the following data? {82,89,85,90,93,96,89,88}

17. For what value(s) of y is the graph of y=16-x^{2} above x-axis?

18. Evaluate: 8+4+2+1+. . . . .

19. The area of the rectangle is 4 more than its perimeter. If the length is 2 more than the width. What is the dimension in meters?

20. What is the positive root of 2x^{2}-x-3=0?

21. Three of the roots of the equation 2x^{4}+ax^{2}+bx+c=0 are -1, 2, and -3. What is b?

22. How many pairs of positive integral solution in x+y=10?

23. A regular hexagon is inscribed in a circle. Another regular hexagon circumscribes the same circle. What is the ratio of the area of the smaller hexagon to hexagon circle?

24. How long after 3 o’clock will the minute hand and hour hand be together for the first time?

25. 5 fair dice is toss once, what is the probability that exactly three four’s will show up?

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### Dan

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