# 4th Year Math Challenge Practice Questions and Answers

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

- Which of the following is/are function/s; a.) x=y-4 b.)x=y
^{2}-1 c.) y=x^{2}+2 d.)x^{2}+y^{2}=25 - The sum of the supplement and complement of an angle is 228°. Find the measure of the angle.
- ABCD is a quadrilateral inscribed in a circle. If angle A is 25°. What is the measure of angle C?
- Solve for x in the following equation:
- Find the sum of the roots of m-3x-2x
^{2}=0 where m is a real number. - What is the range of function f(x)=2x-1 in the domain [-2,2]?
- What is the minimum value of y=2x
^{2}-3x+2? - What the domain of y=log
_{4}(x^{2}-1)? - If f(x)=2x
^{2}-1 and g(x)=x-1. What is f◦g? - What is the system of equations 2x-y=1 and x-2y=2?
- Find the shortest distance between the point (2,3) and x-2y-4=0.
- Find the equation of the line through (3,4) and parallel to 2x+y-4=0.
- Find the equation of the line though (3,4) whose slope is twice the slope of 3x-2y-5=0
- 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? - What is the remainder when f(x)=99x
^{99}+98x^{98}+97x^{97}+ . . . + 2x^{2}+x is divided by x-1? - For what value/values of k does the equation y=3x
^{2}-kx+3 has real and distinct roots? - Find the equation with integral coefficient whose roots are the reciprocal of the roots of 2x
^{2}+3x-1. - A pair of fair dice was tossed once. What is the probability that a sum of 6 is obtain?
- The ratio of the sides of two regular hexagons is 4:5. What is the ratio of their areas respectively?
- What is the positive root of x
^{2}-4x-2=0? - The sum of the number and 3 less than twice the number is 15. What is the number?
- What is the inverse function of f(x)=(x-2)/(2x+1)?
- Find the solution set of x
^{2}-5x+6<0 - Find the solution set of │2x-3│<7
- The perimeter of the rectangle is 24 cm. If the length is two more than the width, what is the area of the rectangle?

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