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PCAT Practice: Quantitative Reasoning
2024 Exam Prep Test
What is the range of the function below? f(x) = 3x2- 5 A. (-โ, โ) B. (0, โ) C. (-5, โ) D. (5, โ) - Answer>>Answer : C Explanation : The range of a function is the list of possible outputs of the function. It is impossible for this function to generate any number less than -5, and there is no upper limit to the output of this function. The range is (-5, โ). Which is equivalent to 3i2 + 2i4? A. - B. 1 C. 5 D. 3 + 2i - Answer>>Answer : A Explanation : This question asks you to manipulate complex numbers. The key to solving this problem is that i2 = -1. Substitute this into the expression: 3i2+2i4=3i2+2(i2)(i2)=3(โ1)+2(โ1)(โ1)=โ3+2=โ If f(x)=x+25 , then what is f-1(x)? A. xโ2/ B. 5x- 2 C. 5/x+ D. 2โx/5 - Answer>>Answer : B Explanation : If the function is y=f(x)=x+2/5. To find the inverse function, switch x and y and then solve for y:
x = y+2/ 5x = y+ y = 5x- What is the sum of the two vectors (3 + 2i) and (-2 + i)? A. 2 + 2i B. - C. -6 + 2i D. 1 + 3i - Answer>>Answer : D Explanation : To add vectors, group the real parts together and the imaginary parts together, and then add: (3 + 2i) + (-2 + i) = (3 + -2) + (2i + i) = 1 + 3i Which of the following is equivalent to (-2 + i)(3 + 2i)? A. -8 -i B. 1 + 3i C. -6 + 2i D. 5 + 3i - Answer>>Answer : A Explanation : To multiply two complex numbers, first distribute the parenthesis: (-2 + i)(3 + 2i) = -6 + 3i- 4i + 2i2 = -6 - i + 2i2. Then use the fact that i2 = -1: -6 - i + 2 i2 =-6 - i + 2(-1) = -8 - i. A candy store has 75 pounds of candy in stock at the beginning of the day. If x is the percentage of the stock sold when 24 one- quarter pound blocks of fudge, 51 one-third pound bags of gummies, and 84 one-twelfth pound bags of marshmallows are sold, what is x? A. 24 B. 30 C. 35
logic, here is a different solution. In the form of an algebraic equation: (18%)(18) = 6%(x). When both sides of the equation are divided by 6%, we will have the expression: (18%)(18)/6%= x. Solving for x : x= 54. For f(x) = 2e^-3x, what is fโณ(x)? A. 18e^x B. -6e^-3x C. 9e^ D. 18e^-3x - Answer>>Answer : D Explanation : The question asks you to find the second derivative of the function f(x) - 2e^-3x. Find the first derivative: f'(x) = (-3)2e^-3x = -6e^-3x Remember that when you take the derivative of an exponential function, the exponent does not change. You only bring down the derivative of the exponent. Now find the second derivative: f"(x) = (-3) - 6e^-3x = 18e^-3x If xโ 0, which of the following is equal to (x/3+3/x+x/3+3/x)/(x^2+9)/x? A. 2/ B. 3/ C. 2x/ D. 2/3x - Answer>>Answer : A Explanation : Choice A is the correct answer. In this question, we are asked to determine a value for the expression x/3+3/x+x/3+3/x)/(x^2+9)/x. There are complex fractions in both the numerator and denominator, so we need to get rid of them. The common denominator for the fractions in the numerator is 3x, multiply these fractions with a denominator of 3 by x/x (This expression equals 1, so the value of the denominator will not change). We can also multiply the fractions with a denominator of x by 3/3, which also equals 1. Now all these fractions have the
denominator 3x; therefore, the numerator of the original complex fraction is now: x23x+93x+x23x+93x, which can be simplified to 2(x2+9)3x. The denominator of the original complex fraction has the expression (x2+9)x, which cannot be simplified. The new expression reads 2(x2+9)3x/(x2+9)x/. Now you can multiply the numerator by the reciprocal of the denominator, giving you 2(x2+9)3xรxx2+9. You can cancel x2+ 9 from each fraction, leaving you with 2x3x , or. 23 What is โซ(4x + e^x)dx? A. 4 + ex + C B. 2x^2 + e^1 + C C. 2x^2 + e^x + C D. x^2 + e^x + C - Answer>>Answer : C Explanation : To find the integral, calculate the integral of each term separately. Remember, the integral of ex is ex. โซ(4x+ex)dx=โซ4xdx+โซexdx+C=4x22+ex+C=2x2+ex+C Elaine had an average (arithmetic mean) score of 76 on the first three exams she took and a score of 84 on her fourth exam. What was her average (arithmetic mean) score on all four exams? A. 77 B. 78 C. 79 D. 80 - Answer>>Answer : D Explanation : You need to know the average formula: Average = Sum of terms/Number of terms. In this question, it is also important to be familiar with the average formula in the rearranged form Sum of terms = Average Number of terms. Elaine's average score on all 4 exams was sum of the four scores/4. So the sum of all 4 scores must first be found. We can obtain the sum of all 4 scores. Elaine's average on the first 3 exams was 76, so the sum of her scores on the first 3 exams was
B. 396
C. 400
D. 440 - Answer>>Answer : C Explanation :Choice C is the correct answer. In a question like this, it is important to identify the "whole" so you can calculate the correct percentage. We are told that the price of a stereo at store xis 90% of the price of the same stereo at store y. Based on this information, it can be concluded that the stereo costs less at store x. Therefore, the whole will be the price of the stereo at store y and the part will be the price at store x. Since part equals percent times whole, we can set up an equation: $360 = 90%y. Solving for the stereo's price at store y: y = $360/0.9., which is $400. Suppose h(x)= 4 sin x - 2 cos x. Then hโฒ(x) = A. 4 sin x - 2 sin x B. 4 cos x + 2 sin x C. 4 cos x + 2 cosx D. -4 cos x - 2 cos x - Answer>>Answer : B A group of seven friends decide to play a board game together. In the game, one of them will act as the game master and the rest will work in pairs. How many different pairs of people can be selected from a group of 7 people? A. 14 B. 21 C. 28 D. 35 - Answer>>Answer : B Explanation : There are 7 different people that can be chosen first. For each of these 7 people chosen first, there are 6 people that can be chosen second. So there is a total of 7 ร 6, or 42 ordered pairs of people that can be chosen. However, the order in which two people are chosen does not matter. Thus, choosing A first and then B is the same as choosing B first and then A. So to
find the number of different pairs of people that can be chosen, the number of ordered pairs, 42, must be divided by 2. So the number of different pairs of people that can be chosen is 42/2, or 21, and choice B is correct. At a fast food restaurant there are a group of a friends. When seven of them leave, only one is left behind. At the only other table that had people, the b individuals at that table each order three cheeseburgers, for a total of fifteen cheeseburgers at that table. What is a + b? A. 9 B. 11 C. 12 D. 13 - Answer>>Answer : D Explanation : Choice D is the correct answer. In this question, we are given two equations, one in terms of a and the other in terms of b. We are asked to determine a value for a + b. The simplest approach would most likely be to solve each equation for a and b, then add the two quantities. In the first equation, a- 7 = 1; therefore, a = 8. In the second equation, 3b = 15; hence, b = 5. Therefore, a + b = 8 + 5 = 13. If log49(x) = 1/2, then x = A. 7 B. 24. C. 98 D. 2401 - Answer>>Answer : A Explanation : The key to answer ing questions like this one on logarithms is to translate it into an equivalent equation involving powers. The equation given, log49(x) = 1/2, can be rewritten as: 49^1/2 = x. Using the law of exponents, 49(1/2)=โ49=7,which is the value of x.
The temperatures in city X on Monday through Sunday of last week were 26, 14, 18, 31, 33, 29, and 31, respectively. What was the median temperature in city X for these 7 days? A. 17 B. 19 C. 26 D. 29 - Answer>>Answer : D Explanation : Arrange the temperatures in increasing order. The temperatures are 14, 18, 26, 29, 31, 31, and 33. There is an odd number of terms, so the median is the middle value, 29. A group of twelve students participate in a fundraiser where they sell frozen pizzas. The twelve students sell 3, 3, 4, 7, 7, 7, 10, 10, 14, 18, 21, and 24 pizzas, respectively. What is the mode number of pizzas sold? A. 3 B. 4 C. 7 D. 9 - Answer>>Answer : C Explanation : The number 7 occurs 3 times, and no other number occurs more than twice. Which of the following sets of numbers has the smallest standard deviation? A. {12, 14, 18} B. {31, 7, 43} C. {150, 175, 200} D. {325, 326, 327} - Answer>>Answer : D Explanation : The set with the numbers closest together will have the smallest standard deviation. Answer choice (D) consists of consecutive integers. They are only one number apart.
Three partners divided a profit of $14,000 so that one partner received $1,400 and one partner received $2,800. What is the range, in dollars, of the amounts the three partners received? A. 1, B. 4, C. 5, D. 8,400 - Answer>>Answer : D Explanation : To find the range, we must first find the amount that the third partner received. The amount that the third partner received was 14,000 - (1,400 + 2,800) which equals 14,000 - 4,200 or 9,800. The range is 9,800 - 1,400 or 8,400. Choice (D) is correct. Thank you for your purchase! Need academic assistance? Look no further! ๐ From assignments to exams, essays to study guides, I've got you covered. Specializing in top-notch writing services, including essay writing, report drafting, and research & citation assistance. Whether you need help with assignments, online classes, exams, or academic writing tasks, I'm here to support you every step of the way. I also offer test banks, study guides, and exams for any subject at a favorable price. Access study materials from Stuvia, Docsity, Docmerit, and Course Hero. Feel free to DM me for more information. If you're satisfied with my service, I'd greatly appreciate a positive review! Your feedback helps me improve and assist more students like you. For compliments and complaints, please DM me. Additionally, I'm open to discussing any document or topic you need help with. Let's achieve academic success together! ๐๐
