# 4th Year Math Challenge Practice Questions and Answers

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

1. Which of the following is/are function/s;                                                                                                                a.) x=y-4                b.)x=y2-1             c.) y=x2+2            d.)x2+y2=25
2. The sum of the supplement and complement of an angle is 228°. Find the measure of the angle.
3. ABCD is a quadrilateral inscribed in a circle. If angle A is 25°. What is the measure of angle C?
4. Solve for x in the following equation: $\displaystyle{\frac{2x-3}{3x-2}=\frac{6x-1}{9x+1}}$
5. Find the sum of the roots of m-3x-2x2=0 where m is a real number.
6. What is the range of function f(x)=2x-1 in the domain [-2,2]?
7. What is the minimum value of y=2x2-3x+2?
8. What the domain of y=log4(x2-1)?
9. If f(x)=2x2-1 and g(x)=x-1. What is f◦g?
10. What is the system of equations 2x-y=1 and x-2y=2?
11. Find the shortest distance between the point (2,3) and x-2y-4=0.
12. Find the equation of the line through (3,4) and parallel to 2x+y-4=0.
13. Find the equation of the line though (3,4) whose slope is twice the slope of 3x-2y-5=0
14. Triangle ABC is right angle at B and inscribed in circle O. If the legs of the triangle are 3 and 4. What is the area of the circle?
15. What is the remainder when f(x)=99x99+98x98+97x97+ . . . + 2x2+x is divided by x-1?
16. For what value/values of k does the equation y=3x2-kx+3 has real and distinct roots?
17. Find the equation with integral coefficient whose roots are the reciprocal of the roots of 2x2+3x-1.
18. A pair of fair dice was tossed once. What is the probability that a sum of 6 is obtain?
19. The ratio of the sides of two regular hexagons is 4:5. What is the ratio of their areas respectively?
20. What is the positive root of x2-4x-2=0?
21. The sum of the number and 3 less than twice the number is 15. What is the number?
22. What is the inverse function of f(x)=(x-2)/(2x+1)?
23. Find the solution set of x2-5x+6<0
24. Find the solution set of │2x-3│<7
25. The perimeter of the rectangle is 24 cm. If the length is two more than the width, what is the area of the rectangle?