SAT Practice Test 8

A bus is traveling at a constant speed along a straight portion of road. The equation \(d = 30t\) gives the distance \(d\), in feet from a road marker, that the bus will be \(t\) seconds after passing the marker. How many feet from the marker will the bus be 2 seconds after passing the marker?

For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?

[Graph shows a line passing through approximately (-6, 0) and (0, 6) with positive slope] What is the y-intercept of the graph shown?

Which expression is equivalent to \((2x^2 + x - 9) + (x^2 + 6x + 1)\)?

An analyst collected data on the price of a carton of grape tomatoes at 30 locations selected at random in Utah. The mean price of a carton of grape tomatoes in Utah was estimated to be \$4.23, with an associated margin of error of \$0.08. Which of the following is a plausible statement about the mean price of a carton of grape tomatoes for all locations that sell this product in Utah?

\(2.6 + x = 2.8\) What value of \(x\) is the solution to the given equation?

Out of 300 seeds that were planted, 80% sprouted. How many of these seeds sprouted?

\(f(x) = 4x + b\) For the linear function \(f\), \(b\) is a constant and \(f(7) = 28\). What is the value of \(b\)?

Right triangles \(L M N\) and \(P Q R\) are similar, where \(L\) and \(M\) correspond to \(P\) and \(Q\), respectively. Angle \(M\) has a measure of \(53^{\circ}\). What is the measure of angle \(Q\)?

What is the equation of the line that passes through the point \((0, 5)\) and is parallel to the graph of \(y = 7x + 4\) in the xy-plane?

[Scatterplot showing data points with negative correlation, y values from about 1 to 10, x values from 1 to 10] Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

A model predicts that the population of Bergen was 15,000 in 2005. The model also predicts that each year for the next 5 years, the population \(p\) increased by 4% of the previous year's population. Which equation best represents this model, where \(x\) is the number of years after 2005, for \(x \leq 5\)?

\(2a + 8b = 198\) \(2a + 4b = 98\) The solution to the given system of equations is \((a, b)\). What is the value of \(b\)?

The expression \(90y^5 - 54y^4\) is equivalent to \(r y^4(15y - 9)\), where \(r\) is a constant. What is the value of \(r\)?

[Graph shows a cubic function with y-intercept around -12, crossing x-axis at three points] The graph of \(y = f(x)\) is shown, where the function \(f\) is defined by \(f(x) = a x^3 + b x^2 + c x + d\) and \(a\), \(b\), \(c\), and \(d\) are constants. For how many values of \(x\) does \(f(x) = 0\)?

The area \(A\), in square centimeters, of a rectangular cutting board can be represented by the expression \(w(w + 9)\), where \(w\) is the width, in centimeters, of the cutting board. Which expression represents the length, in centimeters, of the cutting board?

\(p = \dfrac{k}{4j + 9}\) The given equation relates the distinct positive numbers \(p\), \(k\), and \(j\). Which equation correctly expresses \(4j + 9\) in terms of \(p\) and \(k\)?

Circle \(A\) has a radius of \(3n\) and circle \(B\) has a radius of \(129n\), where \(n\) is a positive constant. The area of circle \(B\) is how many times the area of circle \(A\)?

The measure of angle \(R\) is \(\dfrac{2 \pi}{3}\) radians. The measure of angle \(T\) is \(\dfrac{5 \pi}{12}\) radians greater than the measure of angle \(R\). What is the measure of angle \(T\), in degrees?

\(y = x^2 - 14x + 22\) The given equation relates the variables \(x\) and \(y\). For what value of \(x\) does the value of \(y\) reach its minimum?

A small business owner budgets \$2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays \$4.90 per candle to purchase small candles and \$11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

\(y \leq x + 7\) \(y \geq -2x - 1\) Which point \((x, y)\) is a solution to the given system of inequalities in the xy-plane?

Weight (pounds)	Frequency
13	12
14	8
15	5
16	7
17	9
18	10
19	13
20	7

The frequency table summarizes a data set of the weights, rounded to the nearest pound, of 71 tortoises. A weight of 39 pounds is added to the original data set, creating a new data set of the weights, rounded to the nearest pound, of 72 tortoises. Which statement best compares the mean and median of the new data set to the mean and median of the original data set?

\(x - 29 = (x - a)(x - 29)\) Which of the following are solutions to the given equation, where \(a\) is a constant and \(a > 30\)? I. \(a\) II. \(a + 1\) III. 29

In the xy-plane, the graph of the equation \(y = -x^2 + 9x - 100\) intersects the line \(y = c\) at exactly one point. What is the value of \(c\)?

The functions \(f\) and \(g\) are defined by the given equations, where \(x \geq 0\). Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where \(x \geq 0\)? I. \(f(x) = 18(1.25)^x + 41\) II. \(g(x) = 9(0.73)^x\)

The perimeter of an equilateral triangle is 852 centimeters. The three vertices of the triangle lie on a circle. The radius of the circle is \(w \sqrt{3}\) centimeters. What is the value of \(w\)?

[Graph shows a line with positive slope passing through approximately (-10, 0) and (0, 5)] What is the y-intercept of the line graphed?

Average number of employees by type of store

Type of store	Average number of employees
Warehouse store	365
Department store	213
Supermarket	130

For a certain region, the table shows the average number of store employees in 2016 by type of store. Based on the table, how much greater was the average number of store employees in warehouse stores than in supermarkets?

[Figure shows two parallel lines m and n cut by transversal t, with angle of \(33^{\circ}\) marked and angle \(x^{\circ}\) marked] In the figure, line \(m\) is parallel to line \(n\), and line \(t\) intersects both lines. What is the value of \(x\)?

Sean rents a tent at a cost of \$11 per day plus a onetime insurance fee of \$10. Which equation represents the total cost \(c\), in dollars, to rent the tent with insurance for \(d\) days?

[Figure shows a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\)] For the right triangle shown, \(a = 4\) and \(b = 5\). Which expression represents the value of \(c\)?

The function \(g\) is defined by \(g(x) = 6x\). For what value of \(x\) is \(g(x) = 54\)?

The function \(f\) is defined by \(f(x) = 8x^3 + 4\). What is the value of \(f(2)\)?

The function \(f\) is defined by \(f(x) = \dfrac{1}{10}x - 2\). What is the y-intercept of the graph of \(y = f(x)\) in the xy-plane?

A producer is creating a video with a length of 70 minutes. The video will consist of segments that are 1 minute long and segments that are 3 minutes long. Which equation represents this situation, where \(x\) represents the number of 1-minute segments and \(y\) represents the number of 3-minute segments?

The function \(f\) is defined by \(f(x) = 7x^3\). In the xy-plane, the graph of \(y = g(x)\) is the result of shifting the graph of \(y = f(x)\) down 2 units. Which equation defines function \(g\)?

\(y = -3x\) \(4x + y = 15\) The solution to the given system of equations is \((x, y)\). What is the value of \(x\)?

[Figure shows right triangle with angle A, leg BC = 35, hypotenuse AB = 171] In the right triangle shown, what is the value of \(\sin A\)?

What is the area, in square centimeters, of a rectangle with a length of 34 centimeters (cm) and a width of 29 cm?

If \(\dfrac{x}{y} = 4\) and \(\dfrac{24x}{n y} = 4\), what is the value of \(n\)?

A bowl contains 20 ounces of water. When the bowl is uncovered, the amount of water in the bowl decreases by 1 ounce every 4 days. If 9 ounces of water remain in this bowl, for how many days has it been uncovered?

If \(9(4 - 3x) + 2 = 8(4 - 3x) + 18\), what is the value of \(4 - 3x\)?

A certain township consists of a 5-hectare industrial park and a 24-hectare neighborhood. The total number of trees in the township is 4,529. The equation \(5x + 24y = 4529\) represents this situation. Which of the following is the best interpretation of \(x\) in this context?

Which expression is equivalent to \(a^{\dfrac{11}{12}}\), where \(a > 0\)?

[Two dot plots shown for Data Set A and Data Set B, each with values from 10 to 16] The dot plots represent the distributions of values in data sets A and B. Which of the following statements must be true? I. The median of data set A is equal to the median of data set B. II. The standard deviation of data set A is equal to the standard deviation of data set B.

A circle has center \(O\), and points \(R\) and \(S\) lie on the circle. In triangle \(O R S\), the measure of \(\angle R O S\) is \(88^{\circ}\). What is the measure of \(\angle R S O\), in degrees? (Disregard the degree symbol when entering your answer.)

The regular price of a shirt at a store is \$11.70. The sale price of the shirt is 80% less than the regular price, and the sale price is 30% greater than the store's cost for the shirt. What was the store's cost, in dollars, for the shirt? (Disregard the \$ sign when entering your answer. For example, if your answer is \$4.97, enter 4.97)

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

\(y = 6x + 18\) One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system?

Triangles \(P Q R\) and \(L M N\) are graphed in the xy-plane. Triangle \(P Q R\) has vertices \(P\), \(Q\), and \(R\) at \((4, 5)\), \((4, 7)\), and \((6, 5)\), respectively. Triangle \(L M N\) has vertices \(L\), \(M\), and \(N\) at \((4, 5)\), \((4, 7 + k)\), and \((6 + k, 5)\), respectively, where \(k\) is a positive constant. If the measure of \(\angle Q\) is \(t^{\circ}\), what is the measure of \(\angle N\)?

\(2x + 3y = 7\) \(10x + 15y = 35\) For each real number \(r\), which of the following points lies on the graph of each equation in the xy-plane for the given system?

\(\dfrac{x^2}{\sqrt{x^2 - c^2}} = \dfrac{c^2}{\sqrt{x^2 - c^2}} + 39\) In the given equation, \(c\) is a positive constant. Which of the following is one of the solutions to the given equation?

The quadratic function \(g\) models the depth, in meters, below the surface of the water of a seal \(t\) minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water?