EST I – Math w/o Calculator Past Paper May 2023 PDF

EST I – Math w/o Calculator Date: Test Center: Room Number: Student’s Name: National ID: EST ID: Duration: 30 minutes 20 Multiple Choice Questions Instructions: - Place your answer on the answer sheet. Mark only one answer for each of the multiple ch...

EST I – Math w/o Calculator Date: Test Center: Room Number: Student’s Name: National ID: EST ID: Duration: 30 minutes 20 Multiple Choice Questions Instructions: - Place your answer on the answer sheet. Mark only one answer for each of the multiple choice questions. - Avoid guessing. Your answers should reflect your overall understanding of the subject matter. - Formula sheet is available on the following page of the booklet for your reference. Reference: 1. What are the solutions of the 5𝑥 5𝑥+24 5𝑥 4. If + + = 𝑥, what is the 3 3 3 equation 12𝑥 2 + 6𝑥 − 24 = 0? value of 1 − 𝑥? A. 𝑥 = −1 ± √33 A. −2 √33 1 B. 𝑥 = −1 ± B. − 4 3 19 1 √33 C. 7 C. 𝑥 = − ± D. 3 4 4 1 √33 3 2 D. 𝑥 = ± 5. If = , then what is the 4 4 2𝑥 2𝑥−1 value of 2𝑥? 1 A. 2 3 B. 2 C. 3 D. 6 𝑎𝑥 − 𝑦 = −3 { −6𝑥 + 3𝑦 = 𝑏 6. The system of equations above has 2. In the figure above, lines m, n, and infinitely many solutions. What are k are parallel. The measures of some the values of 𝑎 and 𝑏? angles are shown. Which of the A. 𝑎 = 2, 𝑏 = −9 following must be true? (Figure not B. 𝑎 = −2, 𝑏 = 9 drawn to scale) C. 𝑎 = −2, 𝑏 = −9 I. 𝑥 = 𝑎 D. 𝑎 = 2, 𝑏 = 9 II. 𝑦 + 𝑤 + 𝑏 = 𝑢 + 2𝑥 4𝑟 6𝑥 2 − 𝑟𝑥 + 3 III. 𝑥 + 𝑤 = 𝑦 + 𝑢 3𝑥 + 𝑟 + = 2𝑥 − 1 2𝑥 − 1 A. II only B. I and II 7. The equation above is true for all 1 C. II and III values of 𝑥 ≠ where 𝑟 is a 2 D. I, II, and III constant. What is the value of 𝑟? 3. A parabola with equation A. 1 𝑦 = 3(𝑥 − 𝑚)(𝑥 − 2) has a vertex 2 with 𝑥-coordinate equal to 7. What B. 1 is the 𝑦-coordinate of the vertex of C. 2 this parabola? D. 3 A. −75 8. If √12𝑦 = 𝑦√6 and 𝑦 > 0, what is B. 7 the value of 𝑦? C. 12 1 A. D. 75 3 B. 1 C. 2 D. 6 3 May 2023 9. The sum of two numbers is 6 less 4𝑥 − 2𝑦 = 14 than double the greater number. If 4𝑦 + 5𝑥 = 11 the sum of the two numbers is 40, what is the smaller number? 12. Which of the following values of 𝑦 satisfies the equations given above? A. 17 B. 20 A. −1 C. 21 B. −3 D. 37 C. 1 D. 3 10. Two curves with respective equations 𝑦 = |𝑥| − 2 and 13. ABC is a right angled triangle at B 𝑦 = 10 − |𝑥| intersect at the points such that 𝐴𝐵 = 3𝐵𝐶. What is the A and B. What is the length of value of cos 2 (𝐴) rounded to the segment AB? nearest hundredth? A. 3 A. 0.1 B. 6 B. 0.3 C. 8 C. 0.5 D. 12 D. 0.9 14. In triangle ABC, 𝑚∠𝐴 = 32°. 𝑉(𝑇) = 402𝑇 + 100 In triangle MNP, 𝑚∠𝑁 = 68°. 11. The function above describes the If 𝐴𝐵 = 3𝑀𝑁, 𝐵𝐶 = 3𝑁𝑃, and relationship between the volume 𝑉 𝐴𝐶 = 3𝑀𝑃, what is 𝑚∠𝐵 + 𝑚∠𝑃? of rain water gathered in a certain container measured in cubic meters A. 80 for a certain city and the time 𝑇 B. 100 starting the first day of January C. 112 measured in days. Based on this D. 148 information, which of the following 15. A company has 3 classes of must be true? employees: class A employees work I. From January 20 to January 23, for 6 hours a day, class B employees the volume of water in the work for 8 hours a day, and class C employees work for 12 hours a day. container increased by 1206 The number of class A employees cubic meters. is 𝑚. There are twice as many class II. There was originally only 100 B employees as there are class A cubic meters of water in the employees, and there are 𝑛 more container on January 1. class C employees than class A III. The volume of water in the employees. The total number of container increases by 402 hours worked by everyone in the cubic meters every day. company is 380 hours. Which of the A. I and II following equations best represents B. I and III this situation? C. II and III A. 34𝑚 + 12𝑛 = 380 D. I, II, and III B. 30𝑚 + 12𝑛 = 380 C. 34𝑚 + 𝑛 = 380 D. 22𝑚 + 12𝑛 = 380 4 May 2023 16. If 2𝑦 = 𝑎, which of the following is 𝑥 1 2 8 10 −4 equivalent to 4𝑦 + 6𝑦? 𝑓(𝑥) 0 1 0 −3 0 A. 10 20. The table above gives the values of 𝑎 a polynomial 𝑓(𝑥) at different B. 2 values of 𝑥. Which of the following C. 5𝑎 cannot be a factor of 𝑓(𝑥)? D. 10𝑎 A. 2𝑥 − 2 3 4 5 2 17. If 𝑥 = 𝑏 and 𝑦 = 𝑐 , which of B. 4𝑥 − 8 the following is equal to (𝑥𝑦)15 ? C. 𝑥−8 D. 5𝑥 + 20 A. 𝑏 20 𝑐 6 B. 𝑏 60 𝑐 30 C. 𝑏 45 𝑐 75 D. 𝑏15 𝑐15 18. A line drawn in a coordinate plane has equation 𝑦 = 𝑝𝑥 + 𝑐 and passes through the point A with coordinates (𝑐, 2𝑐). What is the slope of this line? A. 𝑐 B. 1 C. 2𝑐 D. 3 19. In Egypt, a tourist can travel a distance of 5 𝑘𝑚 with just 15.57 EGP. Pedro needed to go to “San Pola” hospital in Cairo. He took a taxi from “Al Marazeek” bridge, which is approximately 35 𝑘𝑚 away from the hospital. How much will Pedro pay for the driver, knowing that he gave him 10 extra EGP as tips? A. 554.95 EGP B. 477.1 EGP C. 118.99 EGP D. 109.09 EGP 5 May 2023