Mtap 1st Year

Time: 1 Hour

Source: 2011 Math Challenge 1st Year

1. What is the name of N = {1, 2, 3, 4, 5 …} ? 2. Round 434.243 to the nearest ten. 3. What is the greatest common factor of 48 and 60? 4. What is the greatest common multiple of 48 and 60? 5. What rational number is between 1/5 and 1/7? 6. Which is bigger 11/13 or 13/15? 7. What is $latex 2 1/3+3 1/7–4 2/3? 8. Evaluate 2 1/3×3/4÷1/3 9. Change to scientific notation 0.000261. 10.To which subset of the set of all real number does \sqrt{3} belong? 11.Peter has a small farm measuring 240 m by 310 m. how many hectares of land does peter own? 12.A cylindrical water tank has a diameter of 1 m and a height of 1.25 m. what is the capacity in liters? 13.Two numbers are in the ration of 3:5. Their sum is 88, what is the bigger number? 14.A picture is 20 cm by 60 cm. If ts enlarged so that its shorter side becomes 30 cm, what is the area of the resulting picture? 15.Evaluate the expression 3x2 + 4x2 – x at x=2. 16.Simplify 2(x2 +1) +3(x+1)2 -3x. 17.Simplify 2(x2+x-1) – 3(x-2)2 18.Multiply (a2+b) by (a-b) 19.Evaluate ( │-14│-│-26│ + 36)÷(│-16│ -│-10│) 20.A piece of cartolina is 20 cm by 60 cm. If it is enlarged so that its shorter side becomes 30 cm, what is the area of the resulting picture? 21.A small passenger plane flew a distance of 54 km in 70 minutes what was the speed in kilometers per hours to the nearest km? 22.What is the sum of 50 counting numbers 1+2 +3+ . . .+49 + 50? 23.Four consecutive odd numbers are added. If the smallest of the 4 is 2×-5, what is their sum? 24.An edge of a cube is x+3 cm. what is its volume? 25.What is the remainder if 3x2-2x+2 is divided by x-2?

Answer key

Time: 1hour Year

Source: 2011 Metrobank -MTAP-Dep-Ed Math Challenge 1st

1. What value will 3x2 + x +1 be multiplied to get 6x3 +5x2 +3x+1? 2. Solve for a from the equation 2a+1 = a – 1/2 3. Solve the inequality 2×-1 > 3-x. 4. 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? 5. 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? 6. 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? 7. 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} 8. What is the range of the function? y=\sqrt{x}? 9. What is the domain of the function y=\displaystyle\frac{x^2+2}{x-2}? 10. What is the slope of the line passing through P1(3,2) and P2(-4,1)? 11. What is the x-intercept of the line 2x-5y+8=0? 12. The x- and y-intercept of the line are 2 and -5 respectively. Write the equation of the line. 13. Two vertices of a square located in the first quadrant are at (0,0) and (0,4). Where are the other two vertices? 14. What is the product of (3x+2y)(x-3y)? 15. Completely factor (a4-b4) 16. Factor 27x3-48xy2. 17. What is the greatest common factor of 27a5b3c2 and 9a3b5c3? 18. Factor 3ac +3ad + 2cb + 2db. 19. Simplify: \displaystyle\frac{3x^2+5x-2}{(9x^2-1)(x^2-4)}

20. Multiply \displaystyle\frac{6x}{3x-7}x\displaystyle\frac{9x-21} {21}\div\displaystyle\frac{x^2}{35} 21. Simplify: \displaystyle\frac{x-1}{x-5} + \displaystyle\frac{2x+3}{x-5} \displaystyle\frac{3x^2+1}{x^2-25} 22. 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. 23. The sum of two numbers is 24 and their product is 143. Find the numbers. 24. Solve for x and y: 2x +3y = 7, 4x – 5y =25. 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.

1. Simplify: (2-\frac{1}{2}) + (3-\frac{1}{3}) + (4-\frac{1}{4}) 2. Let A=\{a,b,c,d,e\}, B=\{a,e,I,o,u\}, and C=\{e,f,g,h,i\}. Find (A\cap B)\cup(B\cap C) 3. Write \displaystyle\frac{1}{50000000} in scientific notation. 4. Nonoy left Butuan City to drive to Cagayan de Oro City at 6:15 PM and arrived 9:15 PM. If he average 80 kph and stopped 30 minutes for dinner, approximately how far is Cagayan de Oro from Butuan? 5. Simplify: (1-\frac{1}{2})^2-(1+\frac{1}{2})^2 6. Let the universal set U be \{1,2,\ldots,20\} If S=\{2,4,6,8,10,12\}, E=\ {3,6,9,12,15,18\} and T=\{15,16,17,18,20\} find (S\cup U\cup E\cup T) 7. What is the product of two consecutive odd numbers if the larger number is 3a-4? 8. Two angles are supplementary. One angle is 24° less than the other. What is the complement of the smaller angle? 9. Simplify: \displaystyle\frac{\frac{2}{3}+\frac{5}{6}}{\frac{4}{5}-\frac{1}{3}} 10. Kristine receives a basic monthly salary of Php 18 000 plus a commission of 12% of her total sales. In her recent monthly payday, she received Php 21 600. How much was her sale last month? 11. Simplify: (x+1)(x-2)-(x+2)(x-3)+(x-3)(x-4)-(x+4)(x-5) 12. How many two-digit prime numbers are there whose units digit is greater than the tens digit? 13. Nila is now x years old. Three years ago, her brother Ricky was twice as old as she. Write Ricky’s age ten years from now in terms of x. 14. Together, Pearl and Harvey are going to visit their aunt on Sunday. If Pearl visits their aunt every 6 days, while Harvey every 8 days, in what day will the visit their aunt together again? 15. What should be added to (x-3)(x+2) in order to get (x-4)^2 16. What is the largest prime factor of 2013? 17. In a triangle, one angle is twice the second, and the third angle is 20° less than the second. What is the measure of the largest angle? 18. It costs (x+3) pesos per square foot to paint a wall. If the wall stands (x+3) ft high and (7×-2) ft long, how much does it costs to paint the wall?

19. A polynomial has quotient (x^2-3x) and remainder (x^2-1) when divided by (x^3-1). What is the polynomial? 20. Aldo cut a long piece of bamboo into four pieces. The second piece was onethird of the first piece, the third piece was one-third of the second, and finally the fourth piece was one-third of the third. If the smallest piece was 2 dm, how long was the bamboo before it was cut?

1. In teacher Ella’s class, a student receives a final grade of A if the student garners an average of at least 92% in the five long tests. After four long tests, Jonathan got an average of 91%. At least how much should he get in the last long test to get a final grade of A? 2. A class of 47 students took examinations in algebra and in Geometry. If 20 passed Algebra, 26 passed Geometry and four failed in both subjects, how many passed both subjects? 3. A runner started a course at a steady rate of 8 kph. Five minutes later, a second runner started the same course at 10 kph. How long did it take for the second runner to overtake the first? 4. A rectangle has sides (2x+3) cm and (4x+5) cm. how many squares of side x cm can be cut from it? 5. Let ABCDE is a regular Pentagon. What is the measure of \angle{CAD}? 6. The average of five numbers is 20. If the sum of two numbers is 23, what is the average of other 3 numbers? 7. A long steel bar is to be cut in the ratio of 2:3:5. If the middle piece is 7 , how long is the steel bar? 8. Marvin is 10% taller than Homer and homer is 10% taller than August. How much (in percent) is Marvin taller than August? 9. Which is the largest? a=2^{48}, b=3^{28}, c=5^{24} 10. When 3n is divided by 7 the remainder is 4. What is the remainder when 2n is divided by 7? 11. Which is smaller? A=(2015)(2014)(2013)(2012)(2011) or B=2013^5 ?

12. If \displaystyle\frac{-12}{5}\leq x\leq\frac{-1}{2} and 3\leq y\le\displaystyle \frac{9}{2}, what is the largest possible value of \displaystyle\frac{x-y}{x+y} 13. If x^2-3x+1=0, find the value of x^2+\displaystyle\frac{1}{x^2} 14. If (x+3)(x-3)(x+1)=(x+2)Q(x)+(x+3)(x-2), what is Q(x)? 15. All faces of a 4-inch cube have been painted. If the cube is cut into 1-inch smaller cubes, how many of them have no paint on all their faces? 16. If x=-1 find the value of 2013x^{2013}+2012x^{2012}+2011x^{2011}+\ldots+2x^2+x? 17. The sum of two numbers is 20 and their product is 15. Find the sum of their cubes? 18. How many positive factors does 62(63^3+63^2+63+1)+1 have? 19. If the sides of the cube are tripled, what percent of the original volume is the new volume? 20. If the number 100 is expressed as a sum of 100 consecutive positive odd integers, what is the largest among all numbers?