Grade 8 Sample Math Challenge Question Part 3 What is the range o f equation ax+by+c=0? What is the remainder when x2-3x+2 x 2-3x+2 is divided by x-2? What is the slope of the line with 2 and -3 as its x and y intercept respectively? The line 2x-3y +12=0 intersects intersects x-axis at (a,b). What is is a+b? The sum of two numbers is 39. The larger number is one more than the smaller number. What is the larger number? What is the positive root of equation 2x2+5x -3=0? What is the range o f y=2x2+5x-3? For what value ok k will 3x-5y-10=0 3 x-5y-10=0 and 6x-10y+k=0 be dependent? For what value of k will make 3x-5y-10=0 and 6x-ky+k=0 be parallel? Factor completely: 8x2-27 What is the domain of y=\sqrt{1-2x^2} What is the range of equation in in #11? Find a quadratic equation with integral coefficients if one root is 2-\sqrt{3} Rationalize: \displaystyle\frac{2 \sqrt{7} + \sqrt{3}}{3\sqrt{7} - 5\sqrt{3}} A motorist drove 240 km. If I f he had gone 20 kph faster , he could have made his trip in one hour less time, how fast did he drive? If y varies inversely as the t he square root of x and y=6 when x =4. Find x when y=9. Solve for x: \sqrt{11-x} - \sqrt{x+6} \sqrt{x+6} = 3 In how many ways can we arrange arr ange 5 students in a round table? There are 20 people inside the room. Each person made a handshake with each other once. How many possible handshakes happened? How many 6-digit license license plates can be made with 3 letters letters and 3 numbers(repetition numbers(repetition is allowed)? allowed)? A pair of fair dice was tossed once, what is the probability of getting a sum of an odd number? Five fair coins are rolled once, what is the probability of getting exactly 3 heads? For #23-25 use the following data:
Given the scores for 10 students participated in Division Elimination Round of Math Challenge out of 50item test are the following.
30, 32, 35, 32, 31, 46, 41, 42, 25, 33
23. What is the mean of the scores?
24. What is the median score?
25. What is the mode of the scores?
GRADE 8 SAMPLE MATH CHALLENGE QUESTIONS AND ANSWERS Write equation of the line in ax+by+c=0. Time: 1 hr
Simplify and express in positive exponent: (a-1b2c-5)4. What is the solution set of 2x-1>6? Mary is 24 years old. John is half the age of Mary. How old is John? What are the roots of 6x2+x-2=0? Solve for x: 5/(x-3) = (x+2)/(x-3)+3 What is the degree of equation 2x2y-3xy+y2=0 Simplify: (3-√2)/( √3-√2) Give the product of (x-y)(x2+xy+y2). Factor completely 2x5-10x4+8x2.
Solve the equation: 2√x=√(x+27) What is the conjugate of 1-√3? Find the sum of x/(x2-9) + (x+1)/(x2-4x+3). Find the solution set of 2x-y=4 and x+2y=-1. The sum of 2/3 of the number and ¾ of the number is 51 . Find the number. Find the sum of equation 2x2-3x+1. For what value of K such that the lines 2x-ky=2 and x-2y=4 become parallel lines. One factor of x2+kx-2=0 is -1. Find the other root. Find the maximum value of 1-3x-x2. Find the solution set of 2x2+3x-2<0
Find the solution set of │2x-1│>3 Find the vertex of y=x2-3x-6. Find the perimeter of rectangle if the length is (2x-1) m and the width is (x+4) m. For what values of m is (m-2)/(m+3) equal (m+1)/(m-1) ? Find the equation of the line through (2,1) and (3,-2). What is the slope of equation 2x-3y=4?
Practice Math Challenge Questions for Third Year ( Geometry ) Part 1 Posted on December 27, 2013 by Dan
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0 Direction: All answers must be exact. Use pi as pi. Time: 1 hour
The supplement of the complement of an angle is 142°. Find the angle. Two sides of a triangle are 10 and 12. How many different triangles can be made out of these sides? In parallelogram ABCD, AB//CD, AD//BC. AB=(2x-5) cm, BC= (3x-11) cm, AD= (2x-1) cm. How long is CD? ABCD is a cyclic quadrilateral. The measure of angle A is three times the measure of angle C. Find the measure of angle A. ABC is right angle at B and inscribed at circle O. AB=3 cm, BC= 4 cm, What is the area of circle O? The diagonal of a square measures 4 cm, what is the perimeter of the square? The sum of interior angle of a regular polygon is 1260°. How many sides the polygon has? What are the maximum points of intersection if we have 6 lines? The number of diagonals of a regular polygon is 35. How many sides the polygon has? ABCD is a square with an area of 100 cm2. E is the midpoint of AB. What is the area of triangle DEC? The surface area of a sphere is 144pi cm2. What is the vo lume of the sphere? The measure of the base angle of an isosceles triangle is twice measure of the vertex angle. What is the measure of the vertex angle? Find the area of an equilateral triangle if it altitude is 10 cm? Solve for x: 2: 8-x = 4:9 The ratio of the areas of two similar pentagons is 25:49. If the perimeter of the smaller pentagon is 25 cm, what is the perimeter of the larger pentagon?
ABCD is a right trapezoid with AB//CD. Angle A=angle D= 90°, angle C= 30°.AB= 6 cm, CD= 10 cm. What is the area of trapezoid? ABCD is a square. A smaller square is drawn by connecting the midpoints of the larger square. What is the ratio of the area of smaller square to the larger square? A secant PAB is intersects the circle O at A and B such that PA>PB. PT is a tangent line to the same circle such that PT= 2PB, PA=8. How long is PT? What is the equation of the line through (2,1) and parallel to 3x-2y-6=0? What is the circumference of a circle with an area of 20pi cm? In parallelogram ABCD, AC meets BD at O. Suppose OA= 3x-2, OC= 13-6x, OB = 3x+2, find OD. The ratio of the angle of quadrilateral is 2:3:4:6. Find the measure of the smallest angle. Circles O1 and O2 are externally tangent at point P, and have radii 2 cm and 4 cm, respectively. Points A and B, both different from P, are chosen on O1 and O2 respectively, such that A,P, and B are collinear. If AB=4cm, How long is PB? Find the volume of a cube with a diagonal of 24 cm. Find the area of a circle inscribed in a square with an area of 64 cm2
Practice Math Challenge Questions for Grade 7 Part 2 Posted on January 13, 2014 by D an
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0 Time: 1hour
Source: 2011 Metrobank -MTAP-Dep-Ed Math Challenge 1st Year
By what value will 3x2 + x +1 be multiplied to get 6x3 +5x2 +3x+1? Solve for a from the equation 2a+1 = a - 1/2 Solve the inequality 2x-1 > 3-x. 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? 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? 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? Which of the following is are functions? a. x2+2y2 = 25 b. x2+2x +y2 = 25 c. x2+x+2y2+8=0 d. y=\sqrt{3x-5} What is the range of the function? y=\sqrt{x}? What is the domain of the function y=\displaystyle\frac{x^2+2}{x-2}? What is the slope of the line passing through P1(3,2) and P2(-4,1)? What is the x-intercept of the line 2x-5y+8=0? The x- and y-intercept of the line are 2 and -5 respectively. Write the equation of the line. Two vertices of a square located in the first quadrant are at (0,0) and (0,4). Where are the other two vertices? What is the product of (3x+2y)(x-3y)?
Completely factor (a4-b4) Factor 27x3-48xy2. What is the greatest common factor of 27a5b3c2 and 9a3b5c3? Factor 3ac +3ad + 2cb + 2db. Simplify: \displaystyle\frac{3x^2+5x-2}{(9x^2-1)(x^2-4)} Multiply \displaystyle\frac{6x}{3x-7}x\displaystyle\frac{9x-21}{21}
÷ \displaystyle\frac{x^2}{25}
Simplify: \displaystyle\frac{x-1}{x-5} + \displaystyle\frac{2x+3}{x-5} - \displaystyle\frac{3x^2+1}{x^2-25} Find the biggest of the three consecutive odd numbers such that the product of the second and the t hird is greater than the square of the first by 110. The sum of two numbers is 24and their product is 143. Find the numbers. Solve for x and y: 2x +3y = 7, 4x – 5y =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.
By what value will 3x2 + x +1 be multiplied to get 6x3 +5x2 +3x+1? Solve for a from the equation 2a+1 = a - 1/2 Solve the inequality 2x-1 > 3-x. 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? The unit digit of a number is o ne 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? 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? Which of the following is are functions? a. x2+2y2 = 25 b. x2+2x +y2 = 25 c. x2+x+2y2+8=0 d. y=\sqrt{3x-5} What is the range of the function? y=\sqrt{x}? What is the domain of the function y=\displaystyle\frac{x^2+2}{x-2}? What is the slope of the line passing through P1(3,2) and P2(-4,1)? What is the x-intercept of the line 2x-5y+8=0? The x- and y-intercept of the line are 2 and -5 respectively. Write the equation of the line. Two vertices of a square located in the first quadrant are at (0,0) and (0,4). Where are the other two vertices? What is the product of (3x+2y)(x-3y)? Completely factor (a4-b4) Factor 27x3-48xy2. What is the greatest common factor of 27a5b3c2 and 9a3b5c3? Factor 3ac +3ad + 2cb + 2db. Simplify: \displaystyle\frac{3x^2+5x-2}{(9x^2-1)(x^2-4)} Multiply \displaystyle\frac{6x}{3x-7}x\displaystyle\frac{9x-21}{21}
÷ \displaystyle\frac{x^2}{25}
Simplify: \displaystyle\frac{x-1}{x-5} + \displaystyle\frac{2x+3}{x-5} - \displaystyle\frac{3x^2+1}{x^2-25} 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.
The sum of two numbers is 24and their product is 143. Find the numbers. Solve for x and y: 2x +3y = 7, 4x – 5y =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.
