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Upcat math 2014

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Mark Garrido
Mark Garrido

This document contains 54 multiple choice questions testing various math and problem solving skills. The questions cover topics like arithmetic, algebra, geometry, ratios, functions and more. They range in difficulty from basic calculations to more complex word problems requiring multiple steps to solve. The full set of questions and possible answer choices are provided for review.

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1. What is the value of 44 + 4 4 4? a. 16 b. 28 c. 76 d. 268 e. 1036 2. Which of the following is/are true? a. Given the sequence 5,10,20,40,80is an arithmetic sequence. b. In the sequence 3,5,8,13,21,.. the next term is 34. c. Given the sequence 6,10,14,18,22the common difference is 4. d. In the sequence 2.0.4,0.08,0.016,0.0032the common ratio is 0.02 a. I only b. II only c. II and III only d. I, III and IV only 3. Two rectangles measuring 6 cm 7 cm and 8 cm 9 cm overlap as shown. The region shaded black has an area of 62 cm2. What is the area of the grey region? a. 12 cm2 b. 22 cm2 c. 32 cm2 d. 42 cm2 e. 52 cm2 4. If the height of a triangle is divided by 4 and the base is multiplied by 4, what is the ratio of the area of the new triangle to the area of the original triangle? a. 1:1 b. 1:2 c. 1:4 d. 2:1 e. 4:1
5. The base of a pyramid has edges. In terms of n, what is the difference between the number of edges of the pyramid and the number of its faces? a. 2 1 b. 1 c. 2 d. 2 + 1 e. 2 6. Paul is 32 years old. In 10 years' time, Paul's age will be the sum of the ages of his three sons. What do the ages of each of Paul's three sons add up to at present? a. 20 b. 18 c. 16 d. 12 e. 10 7. The diagram shows a grid of 16 identical equilateral triangles. How many different rhombuses are there made up of two adjacent small triangles? a. 6 b. 12 c. 18 d. 24 e. 30 8. Consider the set of numbers {1, 2, 2, . . . , 5, 5, 5, 5, 5}, where the number n appears n- times for 1 10. What is the absolute value of the difference between the mode and the median of the set? a. 1 b. 2 c. 3 d. 4 e. 5 9. In triangle ABC, <CAB=84; D is a point on AB such that<CDB = 3 <ACD and DC = DB. What is the size of <BCD? a. 126o b. 54o c. 48o d. 42o e. 27o
10. If two printers can print five pages in four minutes, how many printers are needed to print 20 pages on 16 minutes? a. 1 b. 2 c. 3 d. 4 e. 5 11. A square is cut into two rectangles, as shown, so that the sum of the lengths of the perimeters of these two rectangles is 30 cm. What is the length of a side of the square? a. 4cm b. 5cm c. 6cm d. 7cm e. 8cm 12. An athletics club has junior (i.e. boy or girl) members and adult members. The ratio of girls to boys to adults is 3 : 4 : 9 and there are 16 more adult members than junior members. In total, how many members does the club have? 13. What is the integer x so that 9 lies between 71 7 and 113 11 ? 14. What is the value of 3102 2013? 15. Simplify 5+3 23 . 16. What percentage of 村 is 1/5? 17. Calculate the value of x in the diagram shown.
18. Divide 53 14 + 3 by 2. What is the remainder? a. 2 b. 5 c. 7 d. 10 e. 15 19. Not all characters in the Woodentops series tell the truth. When Mr Plod asked them, How many people are there in the Woodentops family?, four of them replied as follows: Jenny: An even number. Willie: An odd number. Sam: A prime number. Mrs Scrubitt: A number which is the product of two integers greater than one. How many of these four were telling the truth? 20. If = 2 , then a=? 21. Find a quadratic function whose roots are the square of the roots of x2 - 6x + 9 = 0 a. f(x) = x2 18 x 81 b. f(x) = x2 18 x + 81 c. f(x) = x2 +18 x 81 d. f(x) = x2 +18x + 81 e. NOTA 22. Compute for sin 7/12 a. (2 6)/4 b. (6 2)/4 c. (2 + 6)/4 d. (2 6)/4 e. NOTA
23. Factor: ( 42 2 ) (9 )2 a. ( 2 + 3 ) ( 2 + 3 + ) b. ( 2 + 9 + ) ( 2 + 9 ) c. ( 2 + 3 ) ( 2 + 3 + ) d. ( 2 + 9 )( 2 9 + ) e. NOTA 24. Find the equation of the tangent line to the circle 2 + 2 = 289 (8,15). a.) 15x8y= 0 c.) 15x+8y-240= 0 e.) NOTA b.) 8x15y+161= 0 d.) 8x+15y-289= 0 25. Which of the following graphs does not represent a function? a. b. c.
d. 26. In a certain school, 50 students in a certain class were enrolled as follows: 30 enrolled in Mathematics 25 enrolled in Physics 25 enrolled in Chemistry 14 enrolled in Chemistry and Mathematics 12 enrolled in Chemistry and Physics 11 enrolled in Mathematics and Physics 5 enrolled in three subjects How many students did not enroll in any of the three subjects? a. 1 b. 2 c. 3 d. 4 e. 5 27. A rectangle has area 20 cm2 . Reducing the length by 2 遜 cm and increasing the width by 3 cm changes the rectangle into a square. What is the side length of the square?
28. The distance between the points 1(4,2) 2(3,1) a. 10 b. 15 c. 22 d. 30 e. 58 29. Which of the following is divisible by 6? a. one million minus one b. one million minus two c. one million minus three d. one million minus four e. one million minus five 30. How many quadrilaterals are there is this diagram, which is constructed using 6 straight lines? a. 4 b. 5 c. 7 d. 8 e. 9
Upcat math 2014
31. Which of the following has the least value? a. 10 01 b. 21 12 c. 32 23 d. 43 34 e. 54 45 32. Jane has 20 identical cards in the shape of an isosceles right-angled triangle. She uses the cards to make the five shapes below. Which of the shapes has the shortest perimeter? a. b. c. d. e. 33. For which of the following numbers is the sum of all its factors not equal to a square number? a. 3 b. 22
c. 66 d. 70 e. 40 34. The sum one + four = seventy becomes correct if we replace each word by the number of letters in it to give 3+ 4 =7. Using the same convention, which of these words could be substituted for x to make the sum three + five = x true? a. eight b. nine c. twelve d. seventeen e. eighteen 35. Which of the expressions below is equivalent to ( 歎 ( 歎 )) 歎 (( 歎 ) 歎 ) a. a2 b. b2 c. 1 d. 1 e. c2 36. The diagrams show squares placed inside two identical semicircles In the lower diagram the two squares are identical. What is the ratio of the areas of the two shaded regions? a. 1: 2 b. 2 : 3 c. 3 : 4 d. 4 : 5 e. 5 : 6
37. Which is the smallest positive integer for which all these are true? (i) It is odd. (ii) It is not prime. (iii) The next largest odd integer is not prime. a. 9 b. 15 c. 21 d. 25 e. 33 38. An equilateral triangle is placed inside a larger equilateral triangle so that the diagram has three lines of symmetry. What is the value of x? a. 110 b. 120 c. 130 d. 140 e. 150 39. The numbers x and y satisfy the equations x(y + 2) = 100 and y(x + 2) = 60. What is the value of x y? a. 60 b. 50 c. 40 d. 30 e. 20
40. Zac halves a certain number and then adds 8 to the result. He finds that he obtains the same answer if he doubles his original number and then subtracts 8 from the result. What is Zacs original number? a. 8 2 3 b. 9 1 3 c. 9 2 3 d. 10 1 3 e. 10 2 3 41. The diagram shows a circle with centre O and a triangleOPQ. Side PQ is a tangent to the circle. The area of the circle is equal to the area of the triangle. What is the ratio of the length of PQ to the circumference of the circle? a. 1 : 1 b. 2 : 3 c. 2 : d. 3 : 2 e. : 2 42. A machine cracks open 180 000 eggs per hour. How many eggs is that per second? a. 5 b. 50 c. 500 d. 5000 e. 50 000 43. How many weeks are there in 8 7 6 5 4 3 2 1 minutes? a. 1 b. 2 c. 3 d. 4 e. 5
44. Tuwing bakasyon, ginagamit ni Leah ang 50% ng kanyang oras sa pagbabasa ng mga nobela. Sa kabuuan, kay a niy ang matapos ang isang nobela ng pitong oras. Kung si a ay natutulog ng walong oras araw-araw, ilang nobela ang kay a niy ang tapusin sa loob ng dalawang linggo? a. 14 b. 16 c. 18 d. 20 45. Using the table below, fin d the value of 92.7 30.1 = 1.116 30.2 = 1.246 30.3 = 1.390 30.4 = 1.552 30.5 = 1.732 30.6 = 1.933 30.7 = 2.158 30.8 = 2.408 30.9 = 2.688
a. 377.098 b. 277.098 c. 377.136 d. 277.136 46. The numbers 2, 3, 12, 14, 15, 20, 21 may be divided into two sets so that the product of the numbers in each set is the same. What is this product? a. 420 b. 1260 c. 2520 d. 6720 e. 6 350 400 47. Which of these is the largest number? a. 2 + 0 + 1 + 3 b. 2 0 + 1 + 3 c. 2 + 0 1 + 3 d. 2 + 0 + 1 3 e. 2 0 1 3 48. What is the value of 1 23 4 56 7 89 ? a. -10 b. 10 c. -11 d. 11 e. NOTA 49. What is the value of 11 + 22 + 33 + 44 - (14 + 23 + 32 + 41)? 266 50. Mike drank 60% of his glass of milk. Afterwards, 80 ml of milk remained in the glass. What volume of milk was initially in the glass? 200m 51. The numbers x and y satisfy the equations x(y + 2) = 100 and y(x + 2) = 60. What is the value of x y?
a. 60 b. 50 c. 40 d. 30 e. 20 52. If E is the midpoint of AC and BD and 2AB = 2CD = AC = BD, what is the mAED? a. 60属 b. 120属 c. 150属 d. Cannot be determined e. NOTA 53. If (ab) (cb) = 28, what is the value of (ac) (bc) ? a. 29 c.) 28 e.) NOTA b. 30 d.) 27 54. If x + 1 is a factor of f(x) = 2x3 7x2 5x + k , find the value of K. a.) 3 c.) -2 e.) NOTA b.) 4 d.) 5 E D C A B

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Upcat math 2014

  • 1. 1. What is the value of 44 + 4 4 4? a. 16 b. 28 c. 76 d. 268 e. 1036 2. Which of the following is/are true? a. Given the sequence 5,10,20,40,80is an arithmetic sequence. b. In the sequence 3,5,8,13,21,.. the next term is 34. c. Given the sequence 6,10,14,18,22the common difference is 4. d. In the sequence 2.0.4,0.08,0.016,0.0032the common ratio is 0.02 a. I only b. II only c. II and III only d. I, III and IV only 3. Two rectangles measuring 6 cm 7 cm and 8 cm 9 cm overlap as shown. The region shaded black has an area of 62 cm2. What is the area of the grey region? a. 12 cm2 b. 22 cm2 c. 32 cm2 d. 42 cm2 e. 52 cm2 4. If the height of a triangle is divided by 4 and the base is multiplied by 4, what is the ratio of the area of the new triangle to the area of the original triangle? a. 1:1 b. 1:2 c. 1:4 d. 2:1 e. 4:1
  • 2. 5. The base of a pyramid has edges. In terms of n, what is the difference between the number of edges of the pyramid and the number of its faces? a. 2 1 b. 1 c. 2 d. 2 + 1 e. 2 6. Paul is 32 years old. In 10 years' time, Paul's age will be the sum of the ages of his three sons. What do the ages of each of Paul's three sons add up to at present? a. 20 b. 18 c. 16 d. 12 e. 10 7. The diagram shows a grid of 16 identical equilateral triangles. How many different rhombuses are there made up of two adjacent small triangles? a. 6 b. 12 c. 18 d. 24 e. 30 8. Consider the set of numbers {1, 2, 2, . . . , 5, 5, 5, 5, 5}, where the number n appears n- times for 1 10. What is the absolute value of the difference between the mode and the median of the set? a. 1 b. 2 c. 3 d. 4 e. 5 9. In triangle ABC, <CAB=84; D is a point on AB such that<CDB = 3 <ACD and DC = DB. What is the size of <BCD? a. 126o b. 54o c. 48o d. 42o e. 27o
  • 3. 10. If two printers can print five pages in four minutes, how many printers are needed to print 20 pages on 16 minutes? a. 1 b. 2 c. 3 d. 4 e. 5 11. A square is cut into two rectangles, as shown, so that the sum of the lengths of the perimeters of these two rectangles is 30 cm. What is the length of a side of the square? a. 4cm b. 5cm c. 6cm d. 7cm e. 8cm 12. An athletics club has junior (i.e. boy or girl) members and adult members. The ratio of girls to boys to adults is 3 : 4 : 9 and there are 16 more adult members than junior members. In total, how many members does the club have? 13. What is the integer x so that 9 lies between 71 7 and 113 11 ? 14. What is the value of 3102 2013? 15. Simplify 5+3 23 . 16. What percentage of 村 is 1/5? 17. Calculate the value of x in the diagram shown.
  • 4. 18. Divide 53 14 + 3 by 2. What is the remainder? a. 2 b. 5 c. 7 d. 10 e. 15 19. Not all characters in the Woodentops series tell the truth. When Mr Plod asked them, How many people are there in the Woodentops family?, four of them replied as follows: Jenny: An even number. Willie: An odd number. Sam: A prime number. Mrs Scrubitt: A number which is the product of two integers greater than one. How many of these four were telling the truth? 20. If = 2 , then a=? 21. Find a quadratic function whose roots are the square of the roots of x2 - 6x + 9 = 0 a. f(x) = x2 18 x 81 b. f(x) = x2 18 x + 81 c. f(x) = x2 +18 x 81 d. f(x) = x2 +18x + 81 e. NOTA 22. Compute for sin 7/12 a. (2 6)/4 b. (6 2)/4 c. (2 + 6)/4 d. (2 6)/4 e. NOTA
  • 5. 23. Factor: ( 42 2 ) (9 )2 a. ( 2 + 3 ) ( 2 + 3 + ) b. ( 2 + 9 + ) ( 2 + 9 ) c. ( 2 + 3 ) ( 2 + 3 + ) d. ( 2 + 9 )( 2 9 + ) e. NOTA 24. Find the equation of the tangent line to the circle 2 + 2 = 289 (8,15). a.) 15x8y= 0 c.) 15x+8y-240= 0 e.) NOTA b.) 8x15y+161= 0 d.) 8x+15y-289= 0 25. Which of the following graphs does not represent a function? a. b. c.
  • 6. d. 26. In a certain school, 50 students in a certain class were enrolled as follows: 30 enrolled in Mathematics 25 enrolled in Physics 25 enrolled in Chemistry 14 enrolled in Chemistry and Mathematics 12 enrolled in Chemistry and Physics 11 enrolled in Mathematics and Physics 5 enrolled in three subjects How many students did not enroll in any of the three subjects? a. 1 b. 2 c. 3 d. 4 e. 5 27. A rectangle has area 20 cm2 . Reducing the length by 2 遜 cm and increasing the width by 3 cm changes the rectangle into a square. What is the side length of the square?
  • 7. 28. The distance between the points 1(4,2) 2(3,1) a. 10 b. 15 c. 22 d. 30 e. 58 29. Which of the following is divisible by 6? a. one million minus one b. one million minus two c. one million minus three d. one million minus four e. one million minus five 30. How many quadrilaterals are there is this diagram, which is constructed using 6 straight lines? a. 4 b. 5 c. 7 d. 8 e. 9
  • 9. 31. Which of the following has the least value? a. 10 01 b. 21 12 c. 32 23 d. 43 34 e. 54 45 32. Jane has 20 identical cards in the shape of an isosceles right-angled triangle. She uses the cards to make the five shapes below. Which of the shapes has the shortest perimeter? a. b. c. d. e. 33. For which of the following numbers is the sum of all its factors not equal to a square number? a. 3 b. 22
  • 10. c. 66 d. 70 e. 40 34. The sum one + four = seventy becomes correct if we replace each word by the number of letters in it to give 3+ 4 =7. Using the same convention, which of these words could be substituted for x to make the sum three + five = x true? a. eight b. nine c. twelve d. seventeen e. eighteen 35. Which of the expressions below is equivalent to ( 歎 ( 歎 )) 歎 (( 歎 ) 歎 ) a. a2 b. b2 c. 1 d. 1 e. c2 36. The diagrams show squares placed inside two identical semicircles In the lower diagram the two squares are identical. What is the ratio of the areas of the two shaded regions? a. 1: 2 b. 2 : 3 c. 3 : 4 d. 4 : 5 e. 5 : 6
  • 11. 37. Which is the smallest positive integer for which all these are true? (i) It is odd. (ii) It is not prime. (iii) The next largest odd integer is not prime. a. 9 b. 15 c. 21 d. 25 e. 33 38. An equilateral triangle is placed inside a larger equilateral triangle so that the diagram has three lines of symmetry. What is the value of x? a. 110 b. 120 c. 130 d. 140 e. 150 39. The numbers x and y satisfy the equations x(y + 2) = 100 and y(x + 2) = 60. What is the value of x y? a. 60 b. 50 c. 40 d. 30 e. 20
  • 12. 40. Zac halves a certain number and then adds 8 to the result. He finds that he obtains the same answer if he doubles his original number and then subtracts 8 from the result. What is Zacs original number? a. 8 2 3 b. 9 1 3 c. 9 2 3 d. 10 1 3 e. 10 2 3 41. The diagram shows a circle with centre O and a triangleOPQ. Side PQ is a tangent to the circle. The area of the circle is equal to the area of the triangle. What is the ratio of the length of PQ to the circumference of the circle? a. 1 : 1 b. 2 : 3 c. 2 : d. 3 : 2 e. : 2 42. A machine cracks open 180 000 eggs per hour. How many eggs is that per second? a. 5 b. 50 c. 500 d. 5000 e. 50 000 43. How many weeks are there in 8 7 6 5 4 3 2 1 minutes? a. 1 b. 2 c. 3 d. 4 e. 5
  • 13. 44. Tuwing bakasyon, ginagamit ni Leah ang 50% ng kanyang oras sa pagbabasa ng mga nobela. Sa kabuuan, kay a niy ang matapos ang isang nobela ng pitong oras. Kung si a ay natutulog ng walong oras araw-araw, ilang nobela ang kay a niy ang tapusin sa loob ng dalawang linggo? a. 14 b. 16 c. 18 d. 20 45. Using the table below, fin d the value of 92.7 30.1 = 1.116 30.2 = 1.246 30.3 = 1.390 30.4 = 1.552 30.5 = 1.732 30.6 = 1.933 30.7 = 2.158 30.8 = 2.408 30.9 = 2.688
  • 14. a. 377.098 b. 277.098 c. 377.136 d. 277.136 46. The numbers 2, 3, 12, 14, 15, 20, 21 may be divided into two sets so that the product of the numbers in each set is the same. What is this product? a. 420 b. 1260 c. 2520 d. 6720 e. 6 350 400 47. Which of these is the largest number? a. 2 + 0 + 1 + 3 b. 2 0 + 1 + 3 c. 2 + 0 1 + 3 d. 2 + 0 + 1 3 e. 2 0 1 3 48. What is the value of 1 23 4 56 7 89 ? a. -10 b. 10 c. -11 d. 11 e. NOTA 49. What is the value of 11 + 22 + 33 + 44 - (14 + 23 + 32 + 41)? 266 50. Mike drank 60% of his glass of milk. Afterwards, 80 ml of milk remained in the glass. What volume of milk was initially in the glass? 200m 51. The numbers x and y satisfy the equations x(y + 2) = 100 and y(x + 2) = 60. What is the value of x y?
  • 15. a. 60 b. 50 c. 40 d. 30 e. 20 52. If E is the midpoint of AC and BD and 2AB = 2CD = AC = BD, what is the mAED? a. 60属 b. 120属 c. 150属 d. Cannot be determined e. NOTA 53. If (ab) (cb) = 28, what is the value of (ac) (bc) ? a. 29 c.) 28 e.) NOTA b. 30 d.) 27 54. If x + 1 is a factor of f(x) = 2x3 7x2 5x + k , find the value of K. a.) 3 c.) -2 e.) NOTA b.) 4 d.) 5 E D C A B