EST I - Math - December 2021.pdf

EST I – Math Student’s Name _____________________________________ National ID _____________________________________ Test Center _____________________________________ Duration: 90 minutes Test sections: I- Calculator is not required, II...

EST I – Math Student’s Name _____________________________________ National ID _____________________________________ Test Center _____________________________________ Duration: 90 minutes Test sections: I- Calculator is not required, II – Calculator is required 45 Multiple Choice Questions and 13 Short Constructive Response Questions Instructions: - Place your answer on the answer sheet. Mark only one answer for each of the multiple choice questions. - Write your final result only on the answer sheet for the constructive response questions. - Avoid guessing. Your answers should reflect your overall understanding of the subject matter. - Calculator is allowed. When a calculator is used, be aware of switching between radian mode and median mode. - Formula sheet is available at the end of the booklet for your reference. Reference:  Section I Calculator is not required (30 minutes)  1. The difference between twice a 4. How many gallons of gas can number and two is three times the Ibrahim’s tank hold? number. Which of the following A. 20 represents the equation that can be B. 8 used to solve the number? C. 12 A. 2x 2 3 x 2 D. 11.95 B. 2 2x 3 5. What does 20 represent in the C. 2x 2 3x equation above? D. 2x 3x 3 x A. Ibrahim’s tank can hold 20 2. If 50% of 𝑎 is 𝑏, then 𝑎 gallons of gas. A. 50𝑏 B. Ibrahim’s car can travel 20 B. kilometers on 12 gallons of gas. C. 2𝑏 C. Ibrahim uses 20 gallons of gas D. 0.50𝑏 per kilometer. 3. Ibrahim needs enough fencing to D. Ibrahim’s car can travel 20 enclose a rectangular garden with a kilometers to the gallon. perimeter of 200 meters. If the 6. In June 2021, Peter wants to length of his garden is to be 60 manage his time carefully to know meters, which of the following the number of interviews, T, he can equations can be used to solve the take. For each interview that he width of the garden? takes, he expects to spend 3.5 hours A. 2𝑥 120 200 working on the candidate’s B. 𝑥 60 200 application. In addition to this, he C. 2𝑥 200 120 expects to spend an additional 5 D. 2𝑥 60 200 hours to schedule interviews for all candidate. If Peter has 80 hours Questions 4 and 5 refer to the same available in June, how many information interviews can he take? 𝑚 𝑔 12 A. 21 20 B. 24 Ibrahim fills up the gas tank of his car C. 9 before going on a trip. The equation above D. 23 models the amount of gas 𝑔, in gallons, remaining in Ibrahim’s car after he has driven 𝑚 kilometers. 4 May 2021  10. For what values of 𝑎 and 𝑏 will the equation 𝑥 𝑎𝑥 𝑏 have the solutions 1 and 1? A. 𝑎 1; 𝑏 1 B. 𝑎 0; 𝑏 1 C. 𝑎 0; 𝑏 1 D. 𝑎 1; 𝑏 0 11. The graphs of 𝑓 𝑥 |𝑥| 2 and 𝑔 𝑥 1 in the same system will have: A. 0 points of intersection B. 1 point of intersection 7. Which of the inequalities below C. 2 points of intersection represents the solution of the D. 4 points of intersection shaded region in the figure above? 12. What is the coefficient of 𝑥 when A. 𝑦 0.5𝑥 3 𝑥 2𝑥 3 is multiplied by B. 𝑦 0.5𝑥 3 C. 𝑦 0.5𝑥 3 5𝑥 ? D. 𝑦 0.5𝑥 3 A. 10 8. Which of the following is the B. simplest form of the expression C. ? D. A. B. 2𝑥 3 3 𝑥 3 2𝑥 6 C. 13. Which of the following is D. equivalent to the expression above, 9. A factor of the polynomial 7𝑥 given that 𝑥 3? 14𝑥 21 is: A. A. 7𝑥 7 B. 7𝑥 7 B. C. 𝑥 3 C. D. 7𝑥 3 D. 5 May 2021 14. The graph of an exponential function 𝐾 in the xy-plane, where 𝑦 𝐾 𝑥 has a y-intercept of ℎ, where ℎ is a negative constant number. Which of the following could be function 𝐾? A. 𝐾 𝑥 ℎ 𝑥 B. 𝐾 𝑥 2 ℎ C. 𝐾 𝑥 ℎ 4 D. 𝐾 𝑥 √3ℎ𝑥 15. If C is a circle of center (2,0) and radius = 2, then which of the following points is inside the 18. In the figure above, ABCD is a circle? square and points A, B and O lie on A. 1,3 the parabola of equation 𝑦 𝑥 , B. 2,-2 where 𝑘 is a constant number. If the C. 3,-1 area of ABCD is 16 𝑐𝑚 , what is D. 4,0 the value of 𝑘? (The figure is not drawn to scale). (Grid in) x y -4 -9 0 -1 2 3 p 9 16. In the figure above, d and d are 19. If the values in the table above parallel lines, ∠2 103° , represent a linear relationship ∠3 107° and ∠4 97°. What between x and y, what is the value is the measure of ∠1? (The figure of p? (Grid in) is not drawn to scale) (Grid in) 20. How many asymptotes does the curve of the function 𝑓 defined by 3𝑥 1 3𝑘 𝑥 𝑓 𝑥 admit? (Grid in) 17. If 𝑘 0 and 𝑥 2 in the equation above, what is the value of 𝑘? (Grid in) 6 May 2021  Section II Calculator is required (60 minutes) 1. If 𝑥 is a positive number less than 1, 4. Street food tickets at the park cost 10 then which of the following is true? EGP for children and 15 EGP for I. 𝑥 𝑥 adults. On a certain day, 1,500 tickets II. 𝑥 𝑥 were bought for a total of 19,750 III. 𝑥 1 1 EGP. What is the amount of money made A. III only from the tickets for adults only on that B. I and II day? C. II and III D. I and III A. 5,490 EGP B. 7,500 EGP 2. In a school competition, students C. 12,000 EGP have to prepare sketches of length 𝑥 D. 14,250 EGP minutes. The minimum length is 2 minutes and the maximum length is 3 𝑥 1 2 minutes. 2 2𝑥 3 4 5 Which inequality represents the given 5. What is the solution to the equation situation? above? A. |𝑥 2| 3 A. 𝑥 B. |𝑥 3| 2 C. |𝑥 2.5| 0.5 B. 𝑥 D. |𝑥 0.5| 2.5 C. 𝑥 (d): 𝑥 2𝑦 2 0 D. 𝑥 3. Which of the equations below could 6. If the straight line (d) of equation not be a line perpendicular to line (d) 𝑘𝑥 3𝑦 1 0 passes through the given above? point 0.5, 1 , what is the slope of A. 4𝑥 2𝑦 2 0 (d)? B. 2𝑥 𝑦 3 0 A. 4 C. 2𝑥 𝑦 1 0 B. D. 6𝑥 3𝑦 0 C. D. 8 May 2021  10. The price of the COVID-19 vaccine in the black market was first increased by 15% and then increased by 10% after two weeks. What is the percent increase in the price of the vaccine? A. 126.5% B. 26.5% C. 25% D. 1.265% 7. The graph above shows the amount of money earned by Dana who works at a restaurant based on the number of hours she works every day. What is the unit rate of Dana’s working hour? A. $8/h B. $1/h C. 1 h/$ D. $4/h 8. If 𝑎𝑥 𝑏𝑦 𝑎 𝑏 and 𝑏𝑥 𝑎𝑦 𝑎 𝑏 then: A. 𝑥 𝑦 1 11. Alice surveyed all the students in the B. 𝑥 𝑦 1 secondary department at her school to C. 𝑥 1 and 𝑦 1 see their most important concern D. 𝑥 1 and 𝑦 1 through the pandemic situation of corona virus. The results are shown in 9. On a math test of 30 questions, Mona the figure above. If the ratio of got 75% of the 12 geometry questions students who answered correct, 60% of the 10 algebra “Vaccinations” to those who questions correct and 25% of the 8 answered “Economic crisis” was 3:2, trigonometry questions wrong. What what percentage of the students percentage of all the questions did answered “Vaccinations”? Mona get correct? A. 8% A. 56.6% B. 12% B. 160% C. 18% C. 70% D. 10% D. 210% 9 May 2021 Questions 12, 13, 14 and 15 refer to the 15. Which appliances are used on same information. weekends for an average of at least three hours per day more than on weekdays? Home Electricity Use Per A. lights and washer Appliance B. TV, computer and washer 30 C. TV and heater D. Others Average Hours Used Per Day 25 20 16. In a bag there are 14 identical tokens 15 10 numbered from 0 to 13. A token is 5 drawn at random. What is the 0 probability to obtain an odd multiple of 3? A. Weekday Weekend B. C. 12. What information does the graph above provide? D. A. Average kilowatts used by each 17. How much money would you need to appliance in a day deposit today at 8% annual interest B. Total electricity per day compounded monthly to have C. Hours appliance used per day $10,000 in the account after 5 years? D. Average hours used in a day by A. $6,500.5 each appliance B. $6,680.13 13. Which appliance has more usage on C. $6,712.10 weekdays than on weekends? D. $5,989.3 A. TV 18. A box contains 7 identical balls, three B. Lights red, two green and two blue. Three C. Computer balls are drawn randomly and D. Fridge successively one after the other without replacing the ball in the box. 14. How many hours a day, on average, is What is the probability to get exactly the washer used on weekdays? one ball of each color? A. 5 B. 6 A. C. 7 B. D. 12 C. D. 10 May 2021 19. Consider 𝑘 points on the plane where no three points are collinear. How many straight lines can be drawn using these points? A. B. C. 𝑘 𝑘 1 D. ! 21. The polygon line above represents the grades distribution of a class on a history exam. What is the mode of the above distribution? A. 20 B. 40 C. 50 D. 60 22. If 3. √3 9 , then 𝑥 A. 4 B. C. D. 20. Mrs. Mary made the scatterplot above to show the relationship between the number of absences and a student’s final exam score without drawing the line of best fit. Which of the following scores could a student approximately get on the final exam with 6 absences? A. 70 B. 65 C. 87 D. 76 11 May 2021  23. The math teacher asked four of her students to draw the function 𝑓 𝑥 in the xy-plane and to write only one piece of information from their obtained curves. The table below shows the results. Maya The curve admits a center of symmetry of coordinates (1,0). Tarek The curve admits two vertices. Mirna The curve admits an asymptote of equation 𝑦 1. Albert The range of the function is ℝ. Which student could be right? A. Maya 26. The curve above represents the curve B. Tarek of function 𝑓 defined over ℝ. C. Mirna What is the solution of 0 𝑓 𝑥 D. Albert 2? 24. If 𝐴 and 𝑥 A. , 0.5 ∪ 2, ∞ 0, 𝑦 0 then 𝐴 B. 2, 1 ∪ 0, ∞ C. 2.5, 0.5 A. D. , 0.5 ∪ 2, ∞ B. 27. Which of the following represents C. 3 81 in logarithmic form? D. A. log 4 81 25. If 𝑓 𝑥 𝑥 3 and B. log 81 3 ℎ 𝑥 𝑥. 𝑓 𝑥 3𝑥, what is C. log 81 4 ℎ 1 ? D. log 3 4 A. 1 B. -7 C. -5 D. -4 12 May 2021  30. In the figure above, D1 and D2 are two parallel lines. 28. What is the area of the cross section Which of the following is always perpendicular to the base of the right true? cone with a diameter of 6? (The figure is not drawn to scale) A. 𝑧 𝑥 B. 𝑧 𝑥 𝑦 A. 36√2 C. 𝑥 𝑦 𝑧 B. 6√2 D. 𝑥 𝑧 𝑦 180 C. 18√2 31. If |2𝑥 3| 4 , what is the greatest D. 18 possible value of |3𝑥 2|? (Grid in) 32. A father decides to give his son 10 EGP for every math question solved correctly as to encourage him to study mathematics more, but takes back 5 EGP if the solution is wrong. After 30 questions, each has given and received the same amount of money. How many correct questions did the son solve? (Grid in) 33. What is 17% of 36% of 2500? (Grid in) 29. In the xy-plane above, if the coordinates of point B are √3, √3 , what is the measure, in radians, of angle AOB? A. B. C. D. 13 May 2021  Push‐ups 70 60 60 55 50 40 30 30 20 20 20 15 10 10 0 38. In the triangle above, 𝐴𝐷 ⊥ 𝐵𝐶 and 34. The graph above shows the number of 𝐶𝐸 ⊥ 𝐵𝐴 such that 𝐵𝐷 5, 𝐵𝐸 6 push-ups Bob did last week. and 𝐴𝐷 8. What is the length of 𝐶𝐸 What was the average number of ? (The figure is not drawn to scale) push-ups? (Grid in) 35. On Mother’s Day, a big store put a freezer and a refrigerator on sale. The owner of the store suggests that: The probability that a person buys a refrigerator is. The probability that a person buys a freezer if he buys a refrigerator is. The probability that a person buys a freezer if he doesn’t buy the refrigerator is 5%. What is the probability that the person buys the freezer? (Grid in) 36. In a class of 25 students, the average of the grades of the boys, girls and the class is 12, 14 and 13.2 respectively. How many girls are in this class? (Grid in) 37. How many solutions, in ℝ, does the equation 𝑒 3𝑥 3 0 admit? (Grid in) 14 May 2021