g7.Mtap Elim 2013

Metrobank – MTAP – DepEd Math Challenge 2013 Grade 7, Category B Instruction: Give all fractions in lowest terms and all expressions in expanded form.

1. Write

in scientific notation.

2. Simplify: (4 – ) – (3 – ) + (2 – ). 3. Let A = {a, b, c, d, e}, B = {a, e, i, o, u}, C = {e, f, g, h, i}. Find A – (B

C).

4. Simplify: (1 – )² – (1 + )². 5. Nonoy left Butuan City to drive to Cagayan de Oro City at 6:15 PM and arrived 9:15 PM. If he averaged 80 kph and stopped 30 minutes for dinner, approximately how far is Cagayan de Oro from Butuan? 6. What is the product of two consecutive odd numbers if the larger number is (x² – 2x + 3)? 7. Let the universal set 17, 18, 19, 20}, find (S

be {1, 2, 3, … , 20}. If S = {2, 4, 6, 8, 10, 12}, E = {3, 6, 9, 12, 15, 18}, and T = {15, 16, E

T)’?

8. Two angles are supplementary. One angle is 24 less than thrice the older. What is the supplement of the complement of the smaller angle? 9. Simplify: 10. Kristine receives a basic monthly salary of Php 18000 plus commission of 12% on her total sales. In her recent monthly payday, she received Php 21000. How much was her total sales last month? 11. Simplify: (x + 1)(x + 2) – (x+2)(x – 3) + (x + 3)(x – 4) – (x + 4) (x – 5). 12. Let the universal set

be the set of all prime numbers less than 20, A = {x|x is a prime factor of 210}, B

= {x|x is a prime number greater than 10}, and C ={3, 19}. Find A’

(B

C)’.

13. Two years ago, Nila was 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. How many two – digit prime numbers are there whose units digit is less than its tens digit? 15. Together, Pearl and Harvey are going to visit their aunt on Sunday. If Pearl visits their aunt every 12 days, while Harvey every 15 days, on what day will they visit their aunt together again?

16. In the Math Department of a school, 10 teachers have Yahoo! accounts, 13 have Gmail accounts, and 6 have both accounts. How many teachers in the department have Yahoo! or Gmail accounts? 17. Simplify: 18. What should be added to x(x – 2)(x – 10) in order to get (x – 4)³? 19. In a class of 40 students, 27 like Math and 25 like Filipino. At most how many students do not like at least one of these subjects? 20. In a triangle, one angle is twice the second, and the third angle is 20 less than the second. What is the measure of largest angle? 21. It costs (x + 3) pesos per square foot to paint a wall. If the wall stands (4x + 3) ft high and (7x – 2) ft long, how much does it cost to paint the wall? 22. Manuel can walk from his house to his school at the rate of 5.4 kph, and back at the rate of 3.6 kph. What is his average speed for the entire walk in meters per second? 23. How many four – digit numbers are multiples of 9? 24. Triangle ABC is isosceles with AB = AC. Let D be the foot of the altitude from A on BC, and let E be the point of side AC such that DE bisects ADC. If DEC = 67°, what is the measure of the vertex angle? 25. A polynomial has quotient (x² – 3x) and remainder (x² – 1) when divided by (x³ – 1). What is the polynomial? 26. A runner started of 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? 27. What is the largest prime factor of 2013? 28. 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? 29. A class of 47 students took examinations in Algebra and in Geometry. If 29 passed Algebra, 26 passed Geometry, and 4 failed in both subjects, how many passed both subjects? 30. Let ABCDE be a regular pentagon. What is the measure of CAD?

31. The average of five numbers is 20. If the sum of two of the numbers is 28, what is the average of the other three numbers? 32. A long straight steel bar is to be cut in the ratio 2 : 3 : 5. If the middle piece is 7 m, how long is the steel bar? 33. Marvin is 10% taller than Homer, and Homer is 10% taller than August. How much (in percent) is Marvin taller than August? 34. A rectangle has sides (7x + 2) cm and (4x + 5) cm. How many squares of sides x cm can be cut from it? 35. If 2ax⁴ – bx³ + 4cx² – dx + 3e = (2x – 3)(x + 1)(x – 2)(3x + 1), what is ab + cd +e? 36. Which is the largest, a = 2⁴⁸, b = 3³⁶, or c = 5²⁴? 37. If the sides of a cube are tripled, what percent of the original volume is the new volume? 38. What is the least value of x that satisfies the inequality 4(x + 3) – 7(2 – x) ≥ 2(2x – 7)? 39. When 3n is divided by 7, the remainder is 4. What is the remainder when 2n is divided by 7? 40. Which is larger, A = (2015) (2014) (2013) (2012) (2011) or B 2013⁵? 41. 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? 42. If

≤x ≤

and

≤ y ≤ , what is the largest possible value of

?

43. If x = –1, find the value of 2013x²°¹³ + 2012x²°¹² + 2011x²°¹¹ + 2010x²°¹° + … + 2x² + x. 44. If (x + 3)(x – 2)(x + 1) = (x + 2)Q(x) + (x + 3) (x – 2), what is Q(x)? 45. How many positive integers n satisfy ≤

≤ ?

46. How many positive factors does 62 x (63³ + 63² + 63 + 1) + 1 have? 47. If the number 42000 is expressed as the sum of 200 consecutive odd positive integer, what is the largest among the odd integers? 48. If x² – 5x +1 = 0, find the value of x² + 49. The sum of two numbers is 20 and their product is 15. Find the sum of their cubes. 50. What is the least number of square pieces into which a cardboard, 13 feet long and 8 feet wide, can be cut?