PSAT/NMSQT Practice Test 2 PDF

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1 4............................................................................................................................................................................................................................................................................................................... x + 45 = 48 A contract for a certain service requires a onetime activation cost of $35 and a monthly cost of $23. What is the positive solution to the given equation? Which equation represents this situation, where c is A) 3 the total cost, in dollars, of this service contract for B) 48 t months? C) 93 t A) c = + 35 D) 96 23 t B) c = + 23 35 C) c = 23t + 35 D) c = 35t + 23 2 x=4 y = 5−x The solution to the given system of equations is (x, y). What is the value of y ? A) 1 5 B) 4 C) 5 The function f is defined by f (x) = 3x − 8. What is D) 9 the value of f (7) ? A) 29 B) 13 C) −5 D) −29 3 A mixture consisting of only vitamin D and calcium has a total mass of 150 grams. The mass of vitamin D in the mixture is 50 grams. What is the mass, in grams, of calcium in the mixture? A) 200 B) 150 C) 100 D) 50 Unauthorized copying or reuse of any part of this page is illegal. 32 CO NTI N U E  6 8............................................................................................................................................................................................................................................................................................................... A geologist needs to collect at least 67 samples of lava from a volcano. If the geologist has already collected 63 samples from the volcano, what is the minimum number of additional samples the geologist needs to collect? A) 130 B) 63 C) 4 D) 0 The y-intercept of the graph shown is (x, y). What is the value of y ? 9 Each of 157 gemstones can be classified as one of three classifications, as shown in the frequency table. Classification Frequency color X 119 color Y 3 7 color Z 35 8x − 7x + 130 = 260 What value of x is the solution to the given If one of the gemstones is selected at random, what is equation? the probability of selecting a gemstone of color Y? 3 A) 157 35 B) 157 119 C) 157 154 D) 157 Unauthorized copying or reuse of any part of this page is illegal. 33 CO NTI N U E  10 12............................................................................................................................................................................................................................................................................................................... P(t ) = 24.8(1.036)t The function P gives the predicted population, in millions, of a certain country for the period from 1984 to 2018, where t is the number of years after 1984. According to the model, what is the best interpretation of the statement “P(8) is approximately equal to 32.91”? A) In 1984, the predicted population of this country was approximately 8 million. B) In 1984, the predicted population of this country was approximately 32.91 million. C) 8 years after 1984, the predicted population of The shaded region shown represents the solutions to this country was approximately 32.91 million. which inequality? D) 32.91 years after 1984, the predicted population 2 of this country was approximately 8 million. A) y ≥ x − 6 3 2 B) y ≥ x+6 3 2 C) y ≥ x−9 3 2 13 D) y ≥ x+9 3 A right circular cylinder has a volume of 377 cubic centimeters. The area of the base of the cylinder is 13 square centimeters. What is the height, in centimeters, of the cylinder? 11 In triangle ABC , AB = 4,680 millimeters (mm) and BC = 4,680 mm. Which statement is sufficient to prove that triangle ABC is equilateral? 14 The list gives the mass, in grams, of 5 alpine A) AC = 4,680 mm marmots. B) AC = 468 mm 4,010; 4,010; 3,030; 4,050; 3,050 C) AC = 46.8 mm What is the mean mass, in grams, of these 5 alpine D) AC = 4.68 mm marmots? Unauthorized copying or reuse of any part of this page is illegal. 34 CO NTI N U E  15 17............................................................................................................................................................................................................................................................................................................... x=3 A circle has a radius of 43 meters. What is the area, in y = (15 − x)2 square meters, of the circle? 43π A solution to the given system of equations is (x, y). A) What is the value of xy ? 2 A) 432 B) 43π B) 54 C) 45 C) 86π D) 18 D) 1,849π 16 18 An object has a mass of 168 grams and a volume of 24 cubic centimeters. What is the density, in grams per cubic centimeter, of the object? A) 7 B) 144 C) 192 D) 4,032 What is the value of cos A in the triangle shown? 42 A) 41 41 B) 42 1 C) 42 1 D) 41 Unauthorized copying or reuse of any part of this page is illegal. 35 CO NTI N U E  19 21............................................................................................................................................................................................................................................................................................................... A company has a newsletter. In January 2018, there were 1,300 customers subscribed to the newsletter. For the next 24 months after January 2018, the total number of customers subscribed to the newsletter each month was 7% greater than the total number subscribed the previous month. Which equation gives the total number of customers, c, subscribed to the company’s newsletter m months after January 2018, where m ≤ 24 ? A) c = 1,300(0.07)m B) c = 1,300(1.07)m In the figure, RT = TU , the measure of angle VST C) c = 1,300(1.7)m is 29° , and the measure of angle RVS is 41°. What is D) c = 1,300(7)m the value of x ? 20 22 −12x + 14y = 36 −6x + 7y = −18 How many solutions does the given system of equations have? A) Exactly one B) Exactly two C) Infinitely many D) Zero The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown. For how many of the 11 data points does the line of best fit predict a greater y-value than the actual y-value? Unauthorized copying or reuse of any part of this page is illegal. 36 CO NTI N U E  23 25............................................................................................................................................................................................................................................................................................................... The expression 0.35x represents the result of decreasing a positive quantity x by what percent? A) 3.5% B) 35% C) 6.5% D) 65% 24 The graph shows a linear relationship between x and y. Which equation represents this relationship, Objects R and S each travel at a constant speed. where R is a positive constant? The speed of object R is half the speed of object S. Object R travels a distance of 4x inches in y seconds. A) Rx + 18y = 36 Which expression represents the time, in seconds, it B) Rx − 18y = −36 takes object S to travel a distance of 24x inches? C) 18x + Ry = 36 A) 12y D) 18x − Ry = −36 B) 3y C) 16y D) 6y Unauthorized copying or reuse of any part of this page is illegal. 37 CO NTI N U E  26 27............................................................................................................................................................................................................................................... A sample of a certain alloy has a total mass The product of two positive integers is 462. If the of 50.0 grams and is 50.0% silicon by mass. The first integer is 5 greater than twice the second integer, sample was created by combining two pieces of what is the smaller of the two integers? different alloys. The first piece was 30.0% silicon by mass and the second piece was 80.0% silicon by mass. What was the mass, in grams, of the silicon in the second piece? A) 9.0 B) 16.0 C) 20.0 D) 30.0 STOP If you finish before time is called, you may check your work on this module only. Do not turn to any other module in the test. Unauthorized copying or reuse of any part of this page is illegal. 38 No Test Material On This Page  Module 2 Math 27 QUESTIONS DIRECTIONS The questions in this section address a number of important math skills. Use of a calculator is permitted for all questions. ,a-nH NOTES Unless otherwise indicated: All variables and expressions represent real numbers. Figures provided are drawn to scale. All figures lie in a plane. The domain of a given function f is the set of all real numbers x for which f(x) is a real number. li04ii1Ut31 REFERENCE G £ CJw b~ ~x 0 '~ 45° b a x--../3 s A =nr 2 A= Rw A =_!bh c2 = a2 + b2 Special Right Triangles 2 C=2nr 62h £ V= Rwh E} V= nr 2 h @ V = i,.r3 4 V=½nr 2 h £ 1 V = 3 £wh 3 The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2n. The sum of the measures in degrees of the angles of a triangle is 180. Unauthorized copying or reuse of any part of this page is illegal. 40 CO NTI N U E  Module 2 For multiple-choice questions, solve each problem, choose the correct answer from the choices provided, and then circle your answer in this book. Circle only one answer for each question. If you change your mind, completely erase the circle. You will not get credit for questions with more than one answer circled, or for questions with no answers circled. For student-produced response questions, solve each problem and write your answer next to or under the question in the test book as described below. Once you've written your answer, circle it clearly. You will not receive credit for anything written outside the circle, or for any questions with more than one circled answer. If you find more than one correct answer, write and circle only one answer. Your answer can be up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer, but no more. If your answer is a fraction that is too long (over 5 characters for positive, 6 characters for negative), write the decimal equivalent. If your answer is a decimal that is too long (over 5 characters for positive, 6 characters for negative), truncate it or round at the fourth digit. If your answer is a mixed number (such as 3.!. ), write it as an improper fraction (7/2) or its decimal equivalent (3.5). 2 Don't include symbols such as a percent sign, comma, or dollar sign in your circled answer. Unauthorized copying or reuse of any part of this page is illegal. 41 CO NTI N U E  1 2............................................................................................................................................................................................................................................................................................................... The bar graph shows the distribution of the number of walnuts per container for 20 containers at a grocery store. The line graph shows the probability of snow, as a How many of these containers of walnuts contain percent, at a certain location for each day during a exactly 78 walnuts? four-day period. According to the line graph, for which day during this four-day period is the A) 2 probability of snow 30%? B) 7 A) Tuesday C) 20 B) Wednesday D) 78 C) Thursday D) Friday Unauthorized copying or reuse of any part of this page is illegal. 42 CO NTI N U E  3 4............................................................................................................................................................................................................................................................................................................... In the figure, two lines intersect at a point. If w = 136 , what is the value of z ? A) 36 B) 44 The graph of a system of a linear equation and a C) 68 nonlinear equation is shown. What is the solution D) 136 (x , y ) to this system? A) (6, 0) B) (−2, 6) C) (0, −2) D) (0, 0) 5 Which expression is equivalent to 19(x 2 − 7) ? A) 19x 2 − 133 B) 19x 2 − 26 C) 19x 2 − 7 D) 19x 2 + 12 Unauthorized copying or reuse of any part of this page is illegal. 43 CO NTI N U E  6 8............................................................................................................................................................................................................................................................................................................... The scatterplot shows the relationship between two variables, x and y. The parabola shown intersects the y-axis at the point (x , y). What is the value of y ? Which equation is the most appropriate linear model for this relationship? A) y = −0.9x − 2.2 B) y = −0.9x + 2.2 C) y = −0.9x 7 D) y = 0.9x + 2.2 If 2x + 3 = 9, what is the value of 6x − 1 ? 9 x d = 16 − 30 The equation shown gives the estimated amount of diesel d, in gallons, that remains in the gas tank of a truck after being driven x miles, where 0 ≤ x ≤ 480. What is the estimated amount of diesel, in gallons, that remains in the gas tank of the truck when x = 300 ? A) 0 B) 6 C) 14 D) 16 Unauthorized copying or reuse of any part of this page is illegal. 44 CO NTI N U E  10 12............................................................................................................................................................................................................................................................................................................... g (x) = 11x + 4 The function f is defined by f (x ) = 4x −1. What is For the given linear function g, which table shows the value of f (21) ? three values of x and their corresponding values of g (x) ? A) −84 A) x g(x) 1 B) –1 7 84 0 11 4 1 15 C) 21 B) x g (x) 21 D) –1 –4 4 0 0 1 4 C) x g (x) –1 –7 0 4 1 15 13 D) x g (x) The area of a rectangle is 57 square inches. The –1 –11 length of the longest side of the rectangle is 0 0 19 inches. What is the length, in inches, of the 1 11 shortest side of this rectangle? 11 14 The pressure exerted on a scuba diver at sea level is How many yards are equivalent to 77 rods? 14.70 pounds per square inch (psi). For each foot the (5.5 yards = 1 rod) scuba diver descends below sea level, the pressure exerted on the scuba diver increases by 0.44 psi. What is the total pressure, in psi, exerted on the scuba diver at 105 feet below sea level? A) 60.90 B) 31.50 C) 14.70 D) 0.44 Unauthorized copying or reuse of any part of this page is illegal. 45 CO NTI N U E  15 17............................................................................................................................................................................................................................................................................................................... x 2 − 12x + 27 = 0 How many distinct real solutions does the given equation have? A) Exactly two B) Exactly one C) Zero D) Infinitely many The graph gives the estimated population y, in thousands, of a town x years since 2003, where 16 0 ≤ x ≤ 5. Which of the following best describes the For the linear function g, the graph of y = g (x) in increase in the estimated population from x = 0 the xy-plane has a slope of 2 and passes through the to x = 1 ? point (1, 14). Which equation defines g ? A) The estimated population at x = 1 is 0.5 times the estimated population at x = 0. A) g (x) = 2x B) The estimated population at x = 1 is 1.5 times B) g (x) = 2x + 2 the estimated population at x = 0. C) g (x) = 2x + 12 C) The estimated population at x = 1 is 2.5 times D) g (x) = 2x + 14 the estimated population at x = 0. D) The estimated population at x = 1 is 3.5 times the estimated population at x = 0. Unauthorized copying or reuse of any part of this page is illegal. 46 CO NTI N U E  18