DIGITAL SAT FREE FULL MATH PRACTICE TEST 4 DIGITAL SAT MATH PRACTICE -TEST 4 Tackle a series of math questions designed to assess your quantitative skills.Navigate through a 70-minute timed challenge, testing your ability to solve math problems efficiently.Answer 44 questions divided into two modules (22 each).Receive immediate feedback with the display of your raw total math score right after completing the test.Your converted full math score will be promptly emailed to you for comprehensive review. 1. C = 60 + 0.25d4. The equation above represents the monthly cost of a cell phone thatincludes up to 1 gigabyte of data after which there is a charge for dgigabytes of any additional data. Which of the following must be true?I. The cost of each additional megabyte of data is \$60.25.II. The y-intercept of the graph of the cost equation represents thecharge for each additional megabyte of data used.III. If between 5 and 6 megabytes of data are used in a month, themonthly charge is \$61.25. II only III only I and II only I and III only None 2. If n is a positive integer and \(m=2^{n+2}+2^{n}\), what is \(2^{n+3}\) in terms of m? 3m² $$\frac{2m}{5}$$ m $$\frac{8m}{5}$$ None 3. A gardener is planting two types of trees. One type is seven feet talland grows at a rate of 8 inches per year. The other type is four feet talland its rate of growth is 50% greater than the rate of the other tree. Inhow many years will the two trees grow to the same height?Write your answer 4. 3x² = 4x + cIn the equation above, c is a constant. If x = −1 is a solution of this equation, what other value of x satisfies the equation? 1/7 7 4/3 7/3 None 5. An information technology company estimates the cost of a project, in dollars, using the expression 240 1 3nt, where n is the number of computer servers working on the project and t is the total time, in hours, the project will take using n servers. Which of the following is the best interpretation of the number 3 in the expression? A minimum of 3 servers will work on the project. The price of the project increases by $3 every hour Each server can work 3 hours per day Each server costs the company $3 per hour to run. None 6. A pizza parlor has a fixed initial cost of \$180,000, and a variable costof \$4 for each pizza sold. If the pizza parlor charges \$10 for eachpizza, how many pizzas will it have to sell before it makes a profit? 42,000 38,000 24,000 30,000 None 7. George spent 25% of the money he had on lunch and 60% of theremaining money on dinner. If he then had \$9.00 left, how muchmoney did he spend on lunch and dinner? 21 20 27 19 None 8. If the expression 1/2 (x + c)(x − c), where c is a positive constant,can be rewritten as 1/2 x² − 5, what is the value of c? √5 √10 10 5 None 9. For how many values of x between 0 and 2π does \(\sin 3x=\frac{1}{2}\)? Six Four Two Three None 10. The figure above shows the graphs of functions f and g in the xy-plane. Which of the following equations could express the relationship between f and g ? f(x) = g(x) + 2 f(x) = g(x - 2) f(x) = g(x + 2) f(x) = g(x) - 2 None 11. With the exception of the shaded squares in the first row and first column, every square in the table above is to be filled in with a number equal to the sum of the number directly above it and the number directly to its left. For instance, the number 7 in the second row is the sum of 3 in the square above it and 4 in the square directly to its left. What is the value of x ? 112 84 96 16 None 12. Which of the four graphs above best shows the relationship between xand y if x represents a student score on a test and y represents thenumber of incorrect answers a student received on the same test? Graph (1) Graph (3) Graph (4) Graph (2) None 13. In the xy-plane above, line p is perpendicular to line q. What is thevalue of k? 32/3 28/3 28/5 32/5 None 14. Katie hikes 5 miles north, 7 miles east, and then 3 miles north again.What number of miles, measured in a straight line, is Katie from herstarting point? √113 82 √11 115 None 15. If m³=√√n , where n > 0, what is the value of m in terms of n ? $$n^{\frac{1}{12}}$$ $$n^{\frac{1}{7}}$$ $$n^{\frac{3}{4}}$$ $$n^{\frac{7}{12}}$$ None 16. A psychology student randomly selected 300 people from agroup of people who indicated that they preferred to workalone. Those 300 people were given a task to work onindividually and then asked whether they were happy orunhappy while doing the task. Of those surveyed, 5% stated theywere unhappy while doing the task. Which of the followinginferences can appropriately be drawn from this survey result? Less than 5% of people will be happy doing this task if they do not work alone Few people who do not prefer working alone will be happy doing this task. Less than 5% of people will be unhappy doing this task if they work alone. Few people who prefer working alone will be unhappy doing this task None 17. The function f is a quadratic function with zeros at x = 1 and x = 5. The graph of y = f(x) in the xy-plane is a parabola with a vertex at (3, -2). What is the y-intercept of this graph? 5/3 5/2 5/8 5/6 None 18. A homeowners’ association limits the dimensions of the poolsthat it will allow in a particular subdivision. The bylaws statethat permits will only be granted for pools shaped likerectangular prisms, for which the sum of the length of the pooland the perimeter of the vertical side containing the laddercannot exceed 200 meters. The perimeter of the ladder side isdetermined using the width and the depth of the pool. If a poolhas a length of 75 meters and its width is 1.5 times its depth,which of the following shows the allowable depth a, in meters,of the pool? 0 < a ≤ 62 0 < a ≤ 31 0 < a ≤ 50 0 < a ≤ 25 None 19. The coordinates of the vertex of a parabola in the xy-plane are (−4, k).If the y-intercept of the parabola is 12 and the parabola passes throughthe point (−3, 7), what is the value of k? 16/5 20/3 12/5 14/3 None 20. When graphed in the xy-plane, the line y = mx - 4 intersects the x-axis at an angle of q. If m > 0, 0° < q < 90°, and of cos θ = \(\frac{3}{\sqrt{58}} \),What is the value of m? 7/3 1/3 6/3 2/3 None 21. Perfectioner’s Chocolate Company makes two varieties of truffles: dark chocolate and milk chocolate. Each dark chocolate truffle requires 0.65 ounces of cocoa powder, and each milk chocolate truffle requires 0.45 ounces of cocoa powder. If cocoa powder costs c dollars per pound, and Perfectioner’s Chocolate Company has budgeted \$200 per week for cocoa powder, which of the following inequalities indicates the restrictions on the number of dark chocolate truffles, d, and the number of milk chocolate truffles, m, the company can make in one week? (1 pound = 16 ounces) $$\frac{200}{16c}\geq 0.65d +0.45m$$ $$3,200c\geq \frac{0.65}{d}+\frac{0.45}{m}$$ $$\frac{200}{c}\geq 0.65d +0.45m$$ $$\frac{3,200}{c}\geq 0.65d +0.45m$$ None 22. In the figure above, the measures of the angles are as marked. What is the value of a + b? 155 123 132 145 None 23. In the figure above, if the edge length of the cube is 4, what is the shortest distance from A to D? 4√2 4√2 +4 8 4√3 None 24. When a baseball is hit by a batter, the height of the ball, h(t), at time t,is determined by the equation h(t) = −16t² + 64t + 4 where t ≥ 0. Forwhich interval of time, in seconds, is the height of the ball at least 52feet above the playing field? 1.0 ≤ t ≤ 3.0 1.5 ≤ t ≤ 3.5 0.5 ≤ t ≤ 2.5 2.0 ≤ t ≤ 4.0 None 25. A: 2, 7, 12, 17, 22, . . . B: 5, 15, 25, 35, 45, . . . Two sequences, A and B, follow the patterns shown above. If the nth term of sequence A is 72, what is the nth term of sequence B? 145 125 135 155 None 26. xa³ + ya² + za = 012. In the equation above, x, y, and z are constants. If the equationhas roots −6, 0, and 4, which of the following is a factor of xa³ +ya²+ za? a + 6 a + 4 a − 2 a − 6 None 27. In the xy-plane, the graph of the line \(y=\frac{15}{4}\)intersects the graph of the equation y = x² + x at two points. What is the distance between these two points? 15/4 4 5/2 3/2 None 28. \(\sqrt{m^{2}-13}-x=0\)If m<0 and x = 6 in the equation above, what is the value of m ? -7 -13 -3 -10 None 29. Which of the following could be the x-intercept and y-intercept of a line that is perpendicular to the line 3x + 6y = 0 ? (-6, 0) and (0, 3) (3, 0) and (0, 6) (6, 0) and (0, 3) (3, 0) and (0, -6) None 30. The bottom of a ski slope is 6,500 feet above sea level, the top of theslope is 11,000 feet above sea level, and the slope drops 5 feetvertically for every 11 feet traveled in the horizontal direction. Fromthe top of the slope, Kayla skis down at an average speed of 30 milesper hour. Which of the following functions gives the best estimate forthe distance above sea level, d, Kayla is t seconds after she begins herski run where 6,500 < d < 11,000? [Note: 5,280 feet = 1 mile] d(t) = 11,000 −202t d(t) = 11,000 −2.2t d(t) = 11,000 −20t d(t) = 4,500 −1,200t None 31. h(t) = −4.9t² + 88.2tWhen a projectile is launched from ground level, the equation above gives the number of meters in its height, h, after t seconds have elapsed.How many seconds after the projectile is launched will it hit theWrite your answer ground? 32. Maggie’s farm stand sold a total of 165 pounds of apples and peaches.She sold apples for \$1.75 per pound and peaches for \$2.50 per pound.If she made \$337.50, how many pounds of peaches did she sell? 65 11 100 18 None 33. The function f is defined by the equation f(x) = x - x². Which of the following represents a quadratic with no real zeros? $$f(x)-\frac{1}{2}$$ $$f(x)+\frac{1}{2}$$ $$f\left ( x-\frac{1}{2} \right )$$ $$f\left ( \frac{x}{2} \right )$$ None 34. During a 40-minute session at a 220 volt charging station, the charge on an electric car battery increases from an initial charge of 50 power units to a final charge of 106 power units. If this charge increases linearly with time, which of the following best describes the charge, q, in power units, on this same battery after charging for t hours from an initial charge of 20 power units? (1 hour = 60 minutes) q = 84t + 20 q = 55t + 50 q = 84t + 50 q = 55t + 20 None 35. The functions f, g, and h are defined by the equations$$f(x)=x^{2}, g(x)=x ,h(x)=\sqrt{x}$$ Which of the following must be true?$$A.h\left ( \frac{1}{2} \right )<f\left ( \frac{1}{2} \right )<g\left ( \frac{1}{2} \right )$$$$B.h\left ( \frac{1}{2} \right )<g\left ( \frac{1}{2} \right )<f\left ( \frac{1}{2} \right )$$$$C.g\left ( \frac{1}{2} \right )<h\left ( \frac{1}{2} \right )<f\left ( \frac{1}{2} \right )$$$$D.f\left ( \frac{1}{2} \right )<g\left ( \frac{1}{2} \right )<h\left ( \frac{1}{2} \right )$$ B D C A None 36. A troy ounce is a unit of mass used for precious metals such as gold.There are 12 troy ounces in a troy pound and a troy pound is equivalentto 373.2 grams. If the density of gold is 19.3 grams per cubiccentimeter, which of the following is closest to the number of cubiccentimeters in the volume of a block of gold with a mass of 5 troyounces? [Note: density is mass divided by volume] 9 8 7 10 None 37. A researcher is conducting a survey for which she currently has a 93%confidence level. What would be two actions that she could take thatwould be most likely to increase the confidence level in her surveyresults? Increase the sample size and modify the design of the survey to decrease the standard deviation. Increase the sample size and modify the design of the survey to increase the standard deviation. Decrease the sample size and increase the randomness of the survey sample. Modify the design of the survey to increase the standard deviation and decrease the randomness of the survey sample. None 38. If three times 1 less than a number n is the same as two times thenumber increased by 14, what is the value of n? 15 21 19 17 None 39. In the figure above, AB = BC. If AB has a slope of m and BC has a slope of n, what is the value of mn ? 1/9 -9 -1/9 9 None 40. The breakdown of a 500-milligram sample of a chemical compound inthe bloodstream is represented by the function p(n) = 500(0.8)^n, wherep(n) represents the number of milligrams of the compound thatremains at the end of n hours. Which of the following is true?I. The amount of the compound present is decreasing by a constantamount.II. Each hour the compound gets reduced by 20% of the amountpresent at the beginning of that hour.III. Each hour the compound gets reduced by 80% of 500. II and III only II only I only I and III only None 41. (ax + 7)(bx − 1) = 12x² + kx + (b − 13) If the equation above is true for all values of x where a, b, and k arenon-zero constants, what is the value of k? 17 8 40 25 None 42. An animal boarding facility houses 3 dogs for every 2 cats. If thecombined total of dogs and cats at the boarding facility is 250, howmany cats are housed? 120 80 100 150 None 43. If g(x + 1) = x2 + 2x + 4 for all values of x, which of the following is equal to g(x) ? x²+3 (x-1)²+4 (x-1)²+3 x²+4 None 44. The equation of a parabola in the xy-plane is y = 2x²− 12x + 7. What isthe distance between the vertex of the parabola and the point (3, 4)? 11 15 6 8 None 1 out of 44 Please Share This Share this content Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Leave a Reply Cancel replyCommentEnter your name or username to commentEnter your email address to commentEnter your website URL (optional) Save my name, email, and website in this browser for the next time I comment.