Gen Math Review PDF

1. Which of the following scenarios can be represented by a function? a. The number of siblings for each student in a class b. A person's weight over time c. The shoe sizes of different people d. The relationship between distance traveled and time spent driving 2. Sarah is practicing math problems....

1. Which of the following scenarios can be represented by a function? a. The number of siblings for each student in a class b. A person's weight over time c. The shoe sizes of different people d. The relationship between distance traveled and time spent driving 2. Sarah is practicing math problems. She encounters a question asking to evaluate f(3) given the function f(x) = 2x - 5. What would be Sarah's answer? a. -1 b. 1 c. 3 d. 7 3. Alex's math teacher gave him a problem to solve as homework. The problem states: given f(x) = 3x + 2 and g(x) = x^2 - 1, find f ∘ g(x). What should Alex's answer be? a. 3x^2 + 1 b. 3x^2 + 5 c. 3x^2 - 1 d. 3x^2 – 3 4. A small business owner found that N(x) = x represents the number of products sold per day, and the selling price per product is given by p(x) = 200 - x, for 0 ≤ x ≤ 15. What is (N · p)(x) per day and what does it represent? a. (N · p)(x) = 200x - x^2, 0 ≤ x ≤ 15, and (N · p)(x) represents the daily revenue. b. (N · p)(x) = 200x - x^2, 0 ≤ x ≤ 15, and (N · p)(x) represents the daily profit. c. (N · p)(x) = 200x - x^2, 0 ≤ x ≤ 15, and (N · p)(x) represents the daily cost. d. (N · p)(x) = 200x - x^2, 0 ≤ x ≤ 15, and (N · p)(x) represents the daily loss. 5. The percentage y (in decimal form) of fuel remaining in a car x hours after starting a journey is y = -0.1x + 1. After how many hours will the fuel level be at 60%? a. 3 hours b. 3.5 hours c. 4 hours d. 4.5 hours 6. A scientist records the number of bacteria in a petri dish at specific times listed in the table below. Time of Observation | Number of Bacteria Hour 0 | 1,000 Hour 6 | 2,000 Hour 12 | 4,000 Hour 18 | 8,000 If the bacteria continue to multiply at this rate, how many will there be at Hour 30? a. 32,000 b. 64,000 c. 128,000 d. 256,000 7. Emily wants to buy a 4,800-peso smartphone. She has no savings but can deposit 200 pesos into a savings account each week. However, before Emily can buy the phone, she must repay her friend 400 pesos. For how many weeks will Emily need to deposit money into her savings account before she can repay her friend and buy the phone? a. 25 weeks b. 26 weeks c. 27 weeks d. 28 weeks 8. Three friends go to a cafe and split a special dessert and three large coffees. The dessert costs 180 pesos. After using a 60-peso coupon, they spend a total of 330 pesos. Which equation models this situation, and what is the cost of each coffee? a. 3c + 180 - 60 = 330 and the cost of each coffee is 70 pesos. b. 3c + 180 + 60 = 330 and the cost of each coffee is 70 pesos. c. 3c + 60 - 180 = 330 and the cost of each coffee is 70 pesos. d. 3c - 60 + 180 = 330 and the cost of each coffee is 70 pesos. 9. What is the value of x in the rational algebraic expression, x^2 = 4/9? a. 2/3 b. 4/3 c. 1/3 d. 3/2 10. What are the domain and range of f(x) = 1/(x-2)? a. D = {x ∈ ℝ | x ≠ 2}, R = {y ∈ ℝ | y ≠ 0} b. D = {x ∈ ℝ | x ≠ 2}, R = {y ∈ ℝ | y ≠ 1} c. D = {x ∈ ℝ | x ≠ 0}, R = {y ∈ ℝ | y ≠ 2} d. D = {x ∈ ℝ | x ≠ 1}, R = {y ∈ ℝ | y ≠ 2} 11-12. A company has a budget of 150,000 pesos to be divided equally among its various departments. The CEO's office receives three times the amount of money than the other departments. 11. Given x as the number of departments in the company, which of the following shows the function f(x) which would give the amount of money each of the non-CEO departments would receive? a. f(x) = 150,000/x b. f(x) = 150,000/(x+1) c. f(x) = 150,000/(x+2) d. f(x) = 150,000/(x+3)  12. The HR manager counted the number of departments and found out that there were nine departments. How much would the CEO's office receive? a. 37,500 pesos b. 45,000 pesos c. 40,000 pesos d. 50,000 pesos 13. A hardware store ordered several kilograms of nails from a supplier, but the supplier only had 6 kilograms in stock. The supplier bought the remaining amount from a wholesaler for 3,000 pesos. He then sold those nails to the hardware store along with the original 6 kilograms for a total of 4,200 pesos. If the wholesaler's price per kilogram is 60 pesos, how many additional kilograms of nails did the supplier purchase? a. 48 kilograms b. 49 kilograms c. 50 kilograms d. 51 kilograms 14. Maria has 8 liters of an orange juice blend that is 40% pure orange juice. How many liters of pure orange juice does she need to add to make a juice blend that is 60% orange juice? a. 3 liters b. 4 liters c. 5 liters d. 6 liters 15. Lisa invests part of 15,000 pesos in a bond that pays 4% annually and the rest in a stock that pays 7% annually. If Lisa earns 825 pesos in interest after one year, how much did she invest in each? a. Lisa invested 9,000 pesos in the bond and 6,000 pesos in the stock. b. Lisa invested 7,500 pesos in the bond and 7,500 pesos in the stock. c. Lisa invested 10,500 pesos in the bond and 4,500 pesos in the stock. d. Lisa invested 12,000 pesos in the bond and 3,000 pesos in the stock. 16. The sum of the ages of a mother and her daughter is 50 years. Six years ago, the mother was three times as old as her daughter. How old are they now? a. The mother is 36 years old, and the daughter is 14 years old. b. The mother is 37 years old, and the daughter is 13 years old. c. The mother is 38 years old, and the daughter is 12 years old. d. The mother is 39 years old, and the daughter is 11 years old. 17. Two trains start from the same station and travel in opposite directions. Train A travels at 80 km/h and Train B travels at 100 km/h. After 2 hours, how far apart are the trains? a. 340 km apart. b. 360 km apart. c. 350 km apart. d. 370 km apart. 18. A group of painters can complete a project in 12 days. If 2 additional painters join the group, the project can be completed in 9 days. How many painters were originally in the group? a. 4 painters b. 5 painters c. 6 painters d. 7 painters 19. A chemist has a solution of 20% salt and a solution of 60% salt. How many liters of each solution should be mixed together to get 15 liters of a 35% salt solution? a. 9 liters of the 20% solution and 5 liters of the 60% solution. b. 9 liters of the 20% solution and 6 liters of the 60% solution. c. 10 liters of the 20% solution and 5 liters of the 60% solution. d. 10 liters of the 20% solution and 6 liters of the 60% solution. 20. Two numbers differ by 7. The sum of their squares is 365. What are the numbers? a. ±8 and ±15 b. ±9 and ±16 c. ±10 and ±17 d. ±11 and ±18 21-23. A ball is thrown upward from the ground. The height H reached by the ball after t seconds is given by the function, H(t) = 80t - 16t^2. 21. How high did the ball reach? a. 98 ft b. 100 ft c. 102 ft d. 104 ft 22. How long did it take to reach the maximum height? a. 2 seconds b. 2.5 seconds c. 3 seconds d. 3.5 seconds 23. Where is the ball after 6 seconds? a. 64 ft above the ground b. 72 ft above the ground c. 80 ft above the ground d. 88 ft above the ground 24. What is the domain and range of the function f(x) = 2x - 3, and what is its inverse, if it exists? a. Domain: ℝ, Range: ℝ, f^(-1)(x) = (x+3)/2 b. Domain: {x ∈ ℝ | x > 3}, Range: {y ∈ ℝ | y > 2}, f^(-1)(x) = (x+2)/3 c. Domain: {x ∈ ℝ | x ≠ 3}, Range: ℝ, f^(-1)(x) = (x-3)/2 d. Domain: {x ∈ ℝ | x > 2}, Range: {y ∈ ℝ | y ≠ -3}, f^(-1)(x) = (x-2)/3  25. The function h(x) = 1/x, has an inverse function of h^(-1)(x) = 1/x when x ≠ 0. What is the domain and range of h^(-1)(x)? a. Domain: {x ∈ ℝ}, Range: {x ∈ ℝ} b. Domain: {x ∈ ℝ | x ≠ 0}, Range: {y ∈ ℝ} c. Domain: {x ∈ ℝ | x ≠ 0}, Range: {y ∈ ℝ | y ≠ 0} d. Domain: {x ∈ ℝ | x ≠ 1}, Range: {y ∈ ℝ | y ≠ 0} 26. The temperature C in Celsius is related to the temperature K in Kelvin by the formula K = C + 273.15. What is the temperature in Kelvin if it is 25° Celsius? a. 296.15 K b. 297.15 K c. 298.15 K d. 299.15 K 27. A radioactive substance has a half-life of 5 years. If A(t) represents the amount of the substance at time t, and initially there are 80 grams, what is A(t) after 15 years? a. 10 grams b. 12 grams c. 14 grams d. 16 grams 28. Given that F · d = k and the force F exerted by a spring is inversely proportional to its displacement d. If F = 200 N when d = 0.05 m, what is d when F = 100 N? a. 0.075 m b. 0.1 m c. 0.125 m d. 0.15 m 29. Given that I · R = k, the current I in an electrical circuit is inversely proportional to the resistance R. If I = 5 Amperes when R = 10 Ohms, what is R when I = 2 Amperes? a. 22.5 Ohms b. 25 Ohms c. 27.5 Ohms d. 30 Ohms 30. Given that P · V = k, the pressure P of a gas is inversely proportional to its volume V, assuming constant temperature and amount of gas. If P = 2 atm when V = 5 L, what is V when P = 4 atm? a. 2.25 L b. 2.5 L c. 2.75 L d. 3 L 31. Sarah wants to visit her grandparents who live 300 kilometers away. If she travels at a constant speed of 75 kilometers per hour, how far is she from her grandparents' house after 3 hours? a. 65 km b. 70 km c. 75 km d. 80 km 32. David and Emma went hiking in the mountains. In the morning, they checked the temperature and found it was 20 degrees Celsius. Emma wanted to know what this temperature is in degrees Fahrenheit. If you were David, how would you convert 20 degrees Celsius to degrees Fahrenheit using the formula F° = (9/5)C° + 32? a. 65°F b. 68°F c. 70°F d. 72°F  33. What is the value of 2^(8x) when 16^x = 3? a. 9 b. 16 c. 27 d. 81 34. If 3^x = 27 and 2^y = 8, what is the value of xy? a. 6 b. 8 c. 9 d. 12 35. If 2^(3x) = 2^(x+6), what is the value of x? a. 2 b. 3 c. 4 d. 5 36. What is the value of x in the equation 4^(x+1) = 16^(x-1)? a. 2 b. 3 c. 4 d. 5 37. Given the exponential function f(x) = 3^x, which of the following describes the domain and range of the function? a. Domain: {x ∈ ℝ}, Range: {y ∈ ℝ | y > 0} b. Domain: {x ∈ ℝ | x > 3}, Range: {y ∈ ℝ} c. Domain: {x ∈ ℝ | x > 0}, Range: {y ∈ ℝ | y > 0} d. Domain: {x ∈ ℝ | 1 < x < -1}, Range: {y ∈ ℝ | 1 < y < -1} 38. Consider the function h(x) = 2^x - 1. What is its domain and range? a. D = {x ∈ ℝ | x ≠ 1}, R = ℝ b. D = {x ∈ ℝ | x ≠ 2}, R = ℝ c. D = ℝ, R = {y ∈ ℝ | y > -1} d. D = {x ∈ ℝ | x ≠ -1}, R = {y ∈ ℝ | y > -1} 39. A town's population grows exponentially at an annual rate of 3%. If the current population is 50,000, what will the population be in 4 years? a. 56,344 b. 57,455 c. 58,588 d. 59,745 40. A colony of 20 bacteria in a petri dish triples every hour. How many bacteria will there be after 4 hours? a. 480 b. 540 c. 1,620 d. 1,800 41. Sophia deposits 5,000 pesos in a bank that pays 4% compound interest annually. How much money will she have after 3 years? a. Php5,612.16 b. Php5,624.32 c. Php5,618.24 d. Php5,630.40 42. Suppose a culture of 100 algae cells are put in a tank and the culture triples every day. How many algae cells will there be after 4 days? a. 2,700 b. 5,400 c. 8,100 d. 10,800 43. How do you express log_2(9x^3) as a sum of simpler logarithms? a. log_2(9) + 3log_2(x) b. 3log_2(9) + 3log_2(x) c. log_2(9) + log_2(x) d. 3log_2(9) + log_2(x) 44. How do you evaluate log_3(81) - log_2(8) + log_5(25)? a. 3 b. 4 c. 5 d. 6 45. How do you express 2log(x) + 3log(y) as a single logarithm? a. log(x^2y^3) b. log(x^2 + y^3) c. log(x^3y^2) d. log(x^3 + y^2) 46. If log_3(log_2(512)) = x, what is the value of x? a. 2 b. 3 c. 4 d. 5 47. If log_2(x-1)^2 = log_2(x^2 - 5), what is the value of x? a. 2 b. 3 c. 4 d. 5 48. What is the domain and range of y = log_4(x – 3)? a. D = {x ∈ ℝ | x ≠ 1}, R = ℝ b. D = {x ∈ ℝ | x > 3}, R = ℝ c. D = ℝ, R = {y ∈ ℝ | y > 3} d. D = {x ∈ ℝ | x ≠ 3}, R = ℝ 49. Suppose that the number of cells in a certain culture triples every two days. How many times would it have tripled in two weeks? a. 5 times b. 6 times c. 7 times d. 8 times 50. The half-life of a radioactive substance is 12 days and there are 16 grams initially. Determine the amount of substance left after 36 days. a. 1.5 grams b. 2 grams c. 2.5 grams d. 3 grams