SAT MATH(Calc Allowed) Practice Tests
You have 55 minutes to finish the task.Your response will be judged on the quality of your writing and on how well your response presentsthe key points presented in the lectures
1. The use of a calculator is permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f(x) of x is a real number.
Begin skippable figure descriptions.
The figure presents information for your reference in solving some of the problems.
Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.
A equals pi times the square of r.
C equals 2 pi r.
Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.
A equals ℓ w.
Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.
A equals one half b h.
Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.
c squared equals a squared plus b squared.
Special Right Triangles
Reference figure 5 is a right triangle with a 30 degree angle and a 60 degree angle. The side opposite the 30 degree angle is labeled x. The side opposite the 60 degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.
Reference figure 6 is a right triangle with two 45 degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.
Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.
V equals ℓ w h.
Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.
V equals pi times the square of r times h.
Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.
V equals four thirds pi times the cube of r.
Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.
V equals one third times pi times the square of r times h.
Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.
V equals one third ℓ w h.
Additional Reference Information
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2 pi.
The sum of the measures in degrees of the angles of a triangle is 180.
End skippable figure descriptions.
For student produced response questions, students will also see the following directions:
For questions 31 through 38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.
1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, grid only one answer.
5. Mixed numbers such as three and one half must be recorded as three point five or seven slash two. (If three and one half is entered into the grid as , three, one, slash, two, it will be interpreted as thirty one halves, not three and one half).
6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.
The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.
Examples 1 and 2
Beging skippable figure description.
Example 1: If your answer is a fraction such as seven twelfths, it should be recorded as follows. Enter seven in the first space, the fraction bar (a slash) in the second space, one in the third space, and two in the fourth space. All four spaces would be used in this example.
Example 2: If your answer is a decimal value such as two point five, it could be recorded as follows. Enter two in the second space, the decimal point in the third space, and five in the fourth space. Only three spaces would be used in this example.
End skippable figure description.
Beging skippable figure description.
Example 3: Acceptable ways to record two thirds are: two slash three, point six six six, and point six six seven.
End skippable figure description.
Note: You may start your answers in any column, space permitting. Columns you don’t need should be left blank.
Beging skippable figure description.
Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record two in the first space, zero in the second space, and one in the third space. Alternatively, you may record two in the second space, zero in the third space, and one in the fourth space. Spaces not needed should be left blank.
End skippable figure description.
The monthly membership fee for an online television and movie service is $9.80. The cost of viewing television shows online is included in the membership fee, but there is an additional fee of $1.50 to rent each movie online. For one month, Jill’s membership and movie rental fees were $12.80. How many movies did Jill rent online that month?
One of the requirements for becoming a court reporter is the ability to type 225 words per minute. Donald can currently type 180 words per minute, and believes that with practice he can increase his typing speed by 5 words per minute each month. Which of the following represents the number of words per minute that Donald believes he will be able to type m months from now?
A. 5 + 180m
B. 225 + 5m
C. 180 + 5m
D. 180 - 5m
If a 3-pound pizza is sliced in half and each half is sliced into thirds, what is the weight, in ounces, of each of the slices? (1 pound = 16 ounces)
Nick surveyed a random sample of the freshman class of his high school to determine whether the Fall Festival should be held in October or November. Of the 90 students surveyed, 25.6% preferred October. Based on this information, about how many students in the entire 225-person class would be expected to prefer having the Fall Festival in October?
The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters, of an object with a mass of 24 grams and a density of 3 grams per milliliter?
Last week Raul worked 11 more hours than Angelica. If they worked a combined total of 59 hours, how many hours did Angelica work last week?
Movies with Greatest Ticket Sales in 2016
The table above represents the 50 movies that had the greatest ticket sales in 2016, categorized by movie type and Motion Picture Association of America (MPAA) rating. What proportion of the movies are comedies with a PG-13 rating?
Line A in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the following must be true?
A. The slope of line A is undefined.
B. The slope of line A is zero.
C. The slope of line A is positive.
D. The slope of line A is negative.
Number of Registered Voters in the United States in 2012, in Thousands
The table above shows the number of registered voters in 2012, in thousands, in four geographic regions and five age groups. Based on the table, if a registered voter who was 18 to 44 years old in 2012 is chosen at random, which of the following is closest to the probability that the registered voter was from the Midwest region?
Questions 10 and 11 refer to the following information.
A curator at a wildlife society created the scatterplot above to examine the relationship between the gestation period and life expectancy of 10 species of animals.
What is the life expectancy, in years, of the animal that has the longest gestation period?
Of the labeled points, which represents the animal for which the ratio of life expectancy to gestation period is greatest?
In the xy-plane, the graph of function f has x-intercepts at −3, −1, and 1. Which of the following could define f ?
A. f(x) = (x − 3)( x − 1)(x + 1)
B. f(x) = (x − 3)( x − 1)2
C. f(x) = (x - 1)(x + 1)(x + 3)
D. f(x) = (x + 1)2(x + 3)
The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table.
Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?
A. increasing linear
B. decreasing linear
C. exponential growth
D. exponential decay
1,000 (1 + R/1,200) 12
The expression above gives the amount of money, in dollars, generated in a year by a $1,000 deposit in a bank account that pays an annual interest rate of r %, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3% ?
Which of the following scatterplots shows a relationship that is appropriately modeled with the equation y ax = b, where a is positive and b is negative?
Question 16 and 17 refer to the following information?
Mr. Martinson is building a concrete patio in his backyard and deciding where to buy the materials and rent the tools needed for the project. The table below shows the materials’ cost and daily rental costs for three different stores.
The total cost, y, for buying the materials and renting the tools in terms of the number of days, x, is given by y = M + (W + K)x.
For what number of days, x, will the total cost of buying the materials and renting the tools from Store B be less than or equal to the total cost of buying the materials and renting the tools from Store A ?
A. x <= 6
B. x >= 6
C. x <= 7.3
D. x >= 7.3
If the relationship between the total cost, y, of buying the materials and renting the tools at Store C and the number of days, x, for which the tools are rented is graphed in the xy-plane, what does the slope of the line represent?
A. The total cost of the project
B. The total cost of the materials
C. The total daily cost of the project
D. The total daily rental costs of the tools
Jim has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glasses that he can pour from one gallon of milk? (Note: There are 231 cubic inches in 1 gallon.)
If 3p − 2 ≥ 1, what is the least possible value of 3p + 2 ?
The mass of living organisms in a lake is defined to be the biomass of the lake. If the biomass in a lake doubles each year, which of the following graphs could model the biomass in the lake as a function of time? (Note: In each graph below, O represents (0, 0).)
Questions 21 and 22 refer to the following information.
The bar graph above shows renewable energy consumption in quadrillions of British thermal units (Btu) in the United States, by energy source, for several energy sources in the years 2000 and 2010
In a scatterplot of this data, where renewable energy consumption in the year 2000 is plotted along the x-axis and renewable energy consumption in the year 2010 is plotted along the y-axis for each of the given energy sources, how many data points would be above the line y x = ?
Of the following, which best approximates the percent decrease in consumption of wood power in the United States from 2000 to 2010 ?
The tables below give the distribution of high temperatures in degrees Fahrenheit (°F) for City A and City B over the same 21 days in March.
Which of the following is true about the data shown for these 21 days?
A. The standard deviation of temperatures in City A is larger.
B. The standard deviation of temperatures in City B is larger.
C. The standard deviation of temperatures in City A is the same as that of City B.
D. The standard deviation of temperatures in these cities cannot be calculated with the data provided.
In the circle above, segment AB is a diameter. If the length of arc qADB is 8π , what is the length of the radius of the circle?
The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible by 2x +3 ?
Let x and y be numbers such that − y < x < y. Which of the following must be true? I. x < y
II. x > 0
III. y > 0
A. I only
B. I and II only
C. I and III only
D. I,II and III
The relative housing cost for a US city is defined to be the ratio (average housing cost for the city/ national average housing cost ), expressed as a percent.
The scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005. The line of best fit is also shown and has equation y x = 0.0125 + 61. Which of the following best explains how the number 61 in the equation relates to the scatterplot?
A. In 2005, the lowest housing cost in the United States was about $61 per month.
B. In 2005, the lowest housing cost in the United States was about 61% of the highest housing cost.
C. In 2005, even in cities with low population densities, housing costs were never below 61% of the national average.
D. In 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.
f(x)=(x+6)(x-4) Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient?
A. f(x) = x2 - 24
B. f(x) = x2 + 2x - 24
C. f(x) = (x - 1)2 - 21
D. f(x) = (x + 1)2 - 25
If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m ?
A. m + 6
B. m + 7
C. 2m + 14
D. 3m + 21
The function f(x) = x3 - x2 - x - 11/4 is graphed in the xy-plane above. If k is a constant such that the equation f(x) = k has three real solutions, which of the following could be the value of k ?