- 1. 1. What is the value of 44 + 4 × 4 − 4? a. 1036 b. 76 c. 268 d. 28 e. 16 2. Which of the following is/are true? a. Given the sequence 5,10,20,40,80…is an arithmetic sequence. b. In the sequence …3,5,8,13,21,.. the next term is 34. c. Given the sequence 6,10,14,18,22…the common difference is 4. d. In the sequence 2.0.4,0.08,0.016,0.0032…the 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? 4. If the height of a triangle is divided by 4 and the base is multiplied by 4, what is the ratio of the new triangle to the original triangle? a. 1:2 b. 2:1 c. 1:1
- 2. d. 2:2 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? 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? 7. The diagram shows a grid of 16 identical equilateral triangles. How many different rhombuses are there made up of two adjacent small triangles? 8. Consider the set of numbers {1, 2, 2, . . . , 5, 5, 5, 5, 5}, where the number n appears n- times for 1 ≤ 𝑛 ≤ 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
- 3. 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? 10. If two printers can print five pages in four minutes, how many printers are needed to print 20 pages on 16 minutes? a. 2 b. 4 c. 6 d. 8 e. NOTA J/WT = J2/W2T2 (5)/(2)(4) = 20/(x)(16) 5/8 = 20/16x 80x = 160 x = 2 printers 11. A book costs £3.40 and a magazine costs £1.60. Clara spends exactly £23 on books and magazines. How many magazines does she buy?
- 4. 12. 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? 13. 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? 14. What is the integer x so that 𝑥 9 lies between 71 7 and 113 11 ? 15. What is the value of √3102− 2013? 16. Simplify 5+√3 2−√3 .
- 5. 5 + √3 2 − √3 = 5 + √3 2 − √3 × 2 + √3 2 + √3 = 13 + 7√3 4 − 3 = 13 + 7√3 17. For how many three-digit positive integers does the product of the digits equal to 20? 18. The solid shown is made by gluing together four 2cm x 2cm x 2cm cubes. What is the total surface area of the solid? 19. What percentage of ¼ is 1/5? 20. Calculate the value of x in the diagram shown.
- 6. 21. Divide 5𝑥3 − 14𝑥 + 3 by 𝑥 − 2. What is the remainder? a. 2 b. 5 c. 7 d. 10 e. 15 22. The equilateral triangle PQR has side length 1. The lines PT and PU trisect the angle RPQ, the lines RS and RT trisect the angle QRP and the lines QS and QU trisect the angle PQR. What is the side length of the equilateral triangle STU? a. cos 80° cos 20° b. 1 3 cos20° c. 𝑐𝑜𝑠2 20° d. 1 6 e. cos20° 𝑐𝑜𝑠80°
- 7. 23. The diagram shows two straight lines PR and QS crossing at O. What is the value of x? The diagram shows two straight lines PR and QS crossing at O. What is the value of x? a. 7√2 b. 2√29 c. 7(1+√3) d. 9√2 e. 14√2 24. 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? a. 0
- 8. b. 1 c. 2 d. 3 e. 4 25. If 𝑐 = 𝑎−2𝑏 𝑎𝑏 , then a=? a. −2𝑏 𝑏𝑐−1 b. 2𝑏 𝑏𝑐+1 c. −2𝑐 𝑏𝑐−1 d. 2𝑏 𝑏𝑐+1 e. 2𝑏𝑐 𝑏𝑐+1 26. Four brothers are discussing the order in which they were born. Two are lying and two are telling the truth. Which two are telling the truth? Alfred: “Bernard is the youngest.” Horatio: “Bernard is the oldest and I am the youngest.” Inigo: “I was born last.” Bernard: “I’m neither the youngest nor the oldest.” a. Bernard and Inigo b. Horatio and Bernard c. Alfred and Horatio d. Alfred and Bernard e. Inigo and Horatio 27. 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
- 9. e. NOTA (x2 - 6x + 9) = 0 (x-3)(x-3) = 0 Root = 3 Square = 9 (x-9)(x-9) f(x) x2-18x+81 28. Compute for sin 7π/12 a. (√2 − √6)/4 b. (√6 − √2)/4 c. (√ 𝟐 + √ 𝟔)/4 d. (−√2 − √6)/4 e. NOTA sin 7π/12 = sin (π/4 + π/3) = sin π/4cos π/3 + cos π/4 sin π/3 = √2 2 (1/2) + √2 2 ( √3 2 ) = + √2+√6 4 = 29. Factor: ( 4𝑥2 𝑦2 ) − (9𝑎 − 𝑏)2 a. ( 2𝑥 𝑦 + 3𝑥 − 𝑏) ( 2𝑥 𝑦 + 3𝑥 + 𝑏) b. ( 2𝑥 𝑦 + 9𝑥 + 𝑏) ( 2𝑥 𝑦 + 9𝑥 − 𝑏) c. ( 2𝑥 𝑦 + 3𝑏 − 𝑎) ( 2𝑥 𝑦 + 3𝑏 + 𝑎) d. ( 2𝑥 𝑦 + 9𝑎 − 𝑏)( 2𝑥 𝑦 − 9𝑎 + 𝑏) e. NOTA 30. Find the equation of the tangent line to the circle 𝑥2 + 𝑦2 = 289 𝑎𝑡 (8,15). a.) 15x–8y= 0 c.) 15x+8y-240= 0 e.) NOTA b.) 8x–15y+161= 0 d.) 8x+15y-289= 0 Equation of radius: P(0,0) and (8,15) m= 𝑦2 −𝑦1 𝑥2−𝑥1 = 15−0 8−0 = 15 8 M tangent line= −8 15 , P (8,15)
- 10. 𝑦 − 𝑦1= 𝑚𝑥 + 𝑏 𝑦 − 15 = −8 15 (𝑥 − 8) 15𝑦 − 225 = −8𝑥 + 64 8𝑥 + 15𝑦 − 289 = 0 31. Which of the following graphs does not represent a function? a. b. c.
- 11. d. 32. 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 Algebra 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 33. A rectangle has area 20 cm2 . Reducing the ‘length’ by 2 ½ cm and increasing the width’ by 3 cm changes the rectangle into a square. What is the side length of the square?
- 12. 34. The distance between the points 𝑃1(−4,2) 𝑎𝑛𝑑 𝑃2(3,−1) a. √10 b. √15 c. √22 d. √30 e. √58 35. 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 36. 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
- 13. 37. Which of the following has the least value? a. 10 − 01 b. 21 − 12 c. 32 − 23 d. 43 − 34 e. 54 − 45 38. 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. 39. For which of the following numbers is the sum of all its factors not equal to a square number? a. 3 b. 22
- 14. c. 66 d. 70 e. 40 40. 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 41. Which of the expressions below is equivalent to (𝑎 ÷ ( 𝑏 ÷ 𝑐)) ÷ (( 𝑎 ÷ 𝑏) ÷ 𝑐) a. a2 b. b2 c. 1 𝑎𝑏𝑐 d. 1 e. c2 42. 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
- 15. 43. 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 44. 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 45. 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
- 16. 46. 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 Zac’s original number? a. 8 2 3 b. 9 1 3 c. 9 2 3 d. 10 1 3 e. 10 2 3 47. 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 : π d. 3 : 2 e. π : 2 48. 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 49. 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
- 17. 50. 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 51. 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
- 18. a. 377.098 b. 277.098 c. 377.136 d. 277.136 52. 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 53. 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 54. What is the value of 1 2−3 − 4 5−6 − 7 8−9 ? a. -10 b. 10 c. -11 d. 11 e. NOTA 55. What is the value of 11 + 22 + 33 + 44 - (14 + 23 + 32 + 41)? 266 56. 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 57. The numbers x and y satisfy the equations x(y + 2) = 100 and y(x + 2) = 60. What is the value of x − y?
- 19. a. 60 b. 50 c. 40 d. 30 e. 20 58. If E is the midpoint of AC and BD and 2AB = 2CD = AC = BD, what is the m∠AED? a. 60° b. 120° c. 150° d. Cannot be determined e. NOTA 59. If (a−b) (c−b) = −28, what is the value of (a−c) (b−c) ? a. 29 c.) 28 e.) NOTA b. 30 d.) 27 60. 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