# 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?

Click here for the answer key. Good luck!

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### Dan

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