**Free video explanations for SAT Practice Test #8 aka January 2017 QAS test with Megan Leinenbach from SoFlo Tutors. Every math question is broken down so that students can turn the mistakes from practice tests into learning opportunities.**

**Question 1:**

One pound of grapes costs $2. At this rate, how many dollars will c pounds of grapes cost?

A) 2c

B) 2 + c

C) 2/c

D) c/2

**The correct answer is A) 2c**

**Question 2:**

Tracy collects, sells, and trades figurines, and she tracks the number of figurines in her collection on the graph below.

On what interval did the number of figurines decrease the fastest?

A) Between 1 and 2 months

B) Between 2 and 3 months

C) Between 3 and 4 months

D) Between 4 and 5 months

**The correct answer is C) Between 3 and 4 months**

**Question 3:**

In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect?

A) 150

B) 200

C) 250

D) 300

**The correct answer is A) 150**

**Question 4:**

The scatterplot above shows data collected on the lengths and widths of Iris setosa petals. A line of best fit for the data is also shown. Based on the line of best fit, if the width of an Iris setosa petal is 19 millimeters, what is the predicted length, in millimeters, of the petal?

A) 21.10

B) 31.73

C) 52.83

D) 55.27

**The correct answer is C) 52.83**

**Question 5:**

In the figure above, lines B and m are parallel, y = 20, and z = 60. What is the value of x ?

A) 120

B) 100

C) 90

D) 80

**The correct answer is B) 100**

**Question 6:**

Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost $75 each, and tickets to sit on the lawn during the concert cost $40 each. Organizers of the concert announced that 350 tickets had been sold and that $19,250 had been raised through ticket sales alone. Which of the following systems of equations could be used to find the number of tickets for bench seats, B, and the number of tickets for lawn seats, L, that were sold for the concert?

A) (75B)(40L) = 1,950

B + L = 350

B) 40B + 75L = 19,250

B + L = 350

C) 75B + 40L = 350

B + L = 19,250

D) 75B + 40L = 19,250

B + L = 350

**The correct answer is D) 75B + 40L = 19,250B + L = 350**

**Question 7:**

In the xy-plane, the graph of which of the following equations is a line with a slope of 3?

A) y = (1/3)x

B) y = x – 3

C) y = 3x + 2

D) y = 6x + 3

**The correct answer is C) y = 3x + 2**

**Question 8:**

x + 1 = 2/(x + 1)

In the equation above, which of the following is a possible value of x + 1?

A) 1 – √2

B) √2

C) 2

D) 4

**The correct answer is B) √2**

**Questions 9-11 refer to the following information.**

**Questions 9-11 refer to the following information.**

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.

**Question 9:**

What is the value of k, in centimeters?

A) 2.52

B) 7.67

C) 7.79

D) 10.11

**The correct answer is D) 10.11**

**Question 10:**

Water pours into the glass slowly and at a constant rate. Which of the following graphs best illustrates the height of the water level in the glass as it fills?

A)

B)

C)

D)

**The correct answer is C)**

**Question 11:**

Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? (1 gallon = 128 fluid ounces)

A) 16

B) 8

C) 4

D) 3

**The correct answer is B) 8**

**Question 12:**

Roberto is an insurance agent who sells two types of policies: a $50,000 policy and a $100,000 policy. Last month, his goal was to sell at least 57 insurance policies. While he did not meet his goal, the total value of the policies he sold was over $3,000,000. Which of the following systems of inequalities describes x, the possible number of $50,000 policies, and y, the possible number of $100,000 policies, that Roberto sold last month?

A) x + y < 57

50,000x + 100,000y < 3,000,000

B) x + y > 57

50,000x + 100,000y > 3,000,000

C) x + y < 57

50,000x + 100,000y > 3,000,000

D) x + y > 57

50,000x + 100,000y < 3,000,000

**The correct answer is C) x + y < 5750,000x + 100,000y > 3,000,000**

**Question 13:**

If a^{-1/2} = x, where a > 0, what is a in terms of x?

A) √x

B) -√x

C) 1/x^{2}

D) -1/x^{2}

**The correct answer is C) 1/x ^{2}**

**Question 14:**

Which of the following is a value of x for which the expression

-3/(x^{2} + 3x – 10) is undefined?

A) -3

B) -2

C) 0

D) 2

**The correct answer is D) 2**

**Question 15:**

A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by 40 centimeters by 50 centimeters. The block has a density of 2.8 grams per cubic centimeter. What is the mass of the block, in grams? (Density is mass per unit volume.)

A) 336

B) 3,360

C) 16,800

D) 168,000

**The correct answer is D) 168,000**

**Question 16:**

Number of Adults Contracting Colds

Cold | No cold | Total | |

Vitamin C | 21 | 129 | 150 |

Sugar pill | 33 | 117 | 150 |

Total | 54 | 246 | 300 |

The table shows the results of a research study that investigated the therapeutic value of vitamin C in preventing colds. A random sample of 300 adults received either a vitamin C pill or a sugar pill each day during a 2-week period, and the adults reported whether they contracted a cold during that time period. What proportion of adults who received a sugar pill reported contracting a cold?

A) 11/18

B) 11/50

C) 9/50

D) 11/100

**The correct answer is B) 11/50**

**Question 17:**

Ages of 20 Students Enrolled in a College Class

Age | Total |

18 | 6 |

19 | 5 |

20 | 4 |

21 | 2 |

22 | 1 |

23 | 1 |

30 | 1 |

The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages?

A) mode < median < mean

B) mode < mean < median

C) median < mode < mean

D) mean < mode < median

**The correct answer is A) mode < median < mean**

**Question 18:**

The figure below shows the relationship between the percent of leaf litter mass remaining after decomposing for 3 years and the mean annual temperature, in degrees Celsius (°C), in 18 forests in Canada. A line of best fit is also shown.

A particular forest in Canada, whose data is not included in the figure, had a mean annual temperature of −2°C. Based on the line of best fit, which of the following is closest to the predicted percent of leaf litter mass remaining in this particular forest after decomposing for 3 years?

A) 50%

B) 63%

C) 70%

D) 82%

**The correct answer is C) 70%**

**Question 19:**

The range of the polynomial function f is the set of real numbers less than or equal to 4. If the zeros of f are −3 and 1, which of the following could be the graph of y = f (x) in the xy-plane?

A)

B)

C)

D)

**The correct answer is A)**

**Question 20:**

The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

A) 25,000 > (4,334 − 2,712)t

B) 25,000 < (4,334 − 2,712)t

C) 25,000 − 4,334 > 2,712t

D) 25,000 > (4,332/2,712)t

**The correct answer is B) 25,000 < (4,334 − 2,712)t**

**Questions 21 and 22 refer to the following information.**

Between 1985 and 2003, data were collected every three years on the amount of plastic produced annually in the United States, in billions of pounds. The graph below shows the data and a line of best fit. The equation of the line of best fit is y = 3.39x + 46.89, where x is the number of years since 1985 and y is the amount of plastic produced annually, in billions of pounds.

**Question 21:**

Which of the following is the best interpretation of the number 3.39 in the context of the problem?

A) The amount of plastic, in billions of pounds, produced in the United States during the year 1985

B) The number of years it took the United States to produce 1 billion pounds of plastic

C) The average annual plastic production, in billions of pounds, in the United States from 1985 to 2003

D) The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003

**The correct answer is D) The average annual increase, in billions of pounds, of plastic produced per year in the United States from 1985 to 2003**

**Question 22:**

Which of the following is closest to the percent increase in the billions of pounds of plastic produced in the United States from 2000 to 2003?

A) 10%

B) 44%

C) 77%

D) 110%

**The correct answer is A) 10%**

**Question 23:**

M = 1,800(1.02)^{t}

The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens?

A) M = 1,800(1.02)^{q/4}

B) M = 1,800(1.02)^{4q}

C) M = 1,800(1.005)^{4q}

D) M = 1,800(1.082)^{q}

**The correct answer is A) M = 1,800(1.02) ^{q/4}**

**Question 24:**

For the finale of a TV show, viewers could use either social media or a text message to vote for their favorite of two contestants. The contestant receiving more than 50% of the vote won. An estimated 10% of the viewers voted, and 30% of the votes were cast on social media. Contestant 2 earned 70% of the votes cast using social media and 40% of the votes cast using a text message. Based on this information, which of the following is an accurate conclusion?

A) If all viewers had voted, Contestant 2 would have won.

B) Viewers voting by social media were likely to be younger than viewers voting by text message.

C) If all viewers who voted had voted by social media instead of by text message, Contestant 2 would have won.

D) Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.

**The correct answer is D) Viewers voting by social media were more likely to prefer Contestant 2 than were viewers voting by text message.**

**Question 25:**

Population of Greenleaf, Idaho

Year | Population |

2000 | 862 |

2010 | 846 |

The table above shows the population of Greenleaf, Idaho, for the years 2000 and 2010. If the relationship between population and year is linear, which of the following functions P models the population of Greenleaf t years after 2000?

A) P(t ) = 862 − 1.6t

B) P(t ) = 862 − 16t

C) P(t ) = 862 + 16(t − 2,000)

D) P(t ) = 862 − 1.6(t − 2,000)

**The correct answer is A) P(t ) = 862 − 1.6t**

**Question 26:**

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

A) The mean number of children per household in the community is 2.4.

B) A determination about the mean number of children per household in the community should not be made because the sample size is too small.

C) The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

D) The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

**The correct answer is C) The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.**

**Question 27:**

In the xy-plane, the point (p, r ) lies on the line with equation y = x + b , where b is a constant. The point with coordinates (2p, 5r ) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of r/p?

A) 2/5

B) 3/4

C) 4/3

D) 5/2

**The correct answer is B) 3/4**

**Question 28:**

The 22 students in a health class conducted an experiment in which they each recorded their pulse rates, in beats per minute, before and after completing a light exercise routine. The dot plots below display the results.

Let s_{1} and r_{1} be the standard deviation and range, respectively, of the data before exercise, and let s_{2} and r_{2} be the standard deviation and range, respectively, of the data after exercise. Which of the following is true?

A) s_{1} = s_{2} and r_{1} = r_{2}

B) s_{1} < s_{2} and r_{1} < r_{2}

C) s_{1} > s_{2} and r_{1} > r_{2}

D) s_{1} ≠ s_{2} and r_{1} = r_{2}

**The correct answer is D) s _{1} ≠ s_{2} and r_{1} = r_{2}**

**Question 29:**

A photocopy machine is initially loaded with 5,000 sheets of paper. The machine starts a large job and copies at a constant rate. After 20 minutes, it has used 30% of the paper. Which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing?

A) p = 5,000 − 20m

B) p = 5,000 − 75m

C) p = 5,000(0.3)^{m/20}

D) p = 5,000(0.7)^{m/20}

**The correct answer is B) p = 5,000 − 75m**

**Question 30:**

The complete graph of the function f and a table of values for the function g are shown above. The maximum value of f is k. What is the value of g (k) ?

A) 7

B) 6

C) 3

D) 0

**The correct answer is B) 6**

**Question 31:**

There are two atoms of hydrogen and one atom of oxygen in one molecule of water. How many atoms of hydrogen are there in 51 molecules of water?

**The correct answer is 102**

**Question 32:**

x – (1/2)a = 0

If x = 1 in the equation above, what is the value of a?

**The correct answer is 2**

**Question 33:**

In the xy-plane, the equations x + 2y = 10 and 3x + 6y = c represent the same line for some constant c. What is the value of c?

**The correct answer is 30**

**Question 34:**

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

**The correct answer is 25.4 or 127/5**

**Question 35:**

The graph of the function f, defined by f (x) = −(1/2)(x − 4)^{2} + 10, is shown in the xy-plane above. If the function g (not shown) is defined by g (x) = − x + 10, what is one possible value of a such that f (a) = g (a)?

**The correct answer is 2 or 8**

**Question 36:**

In triangle RST above, point W (not shown) lies on RT . What is the value of cos(∠RSW ) − sin(∠WST )?

**The correct answer is 0**

**Questions 37 and 38 refer to the following information:**

When a patient receives a penicillin injection, the kidneys begin removing the penicillin from the body. The table and graph above show the penicillin concentration in a patient’s bloodstream at 5-minute intervals for the 20 minutes immediately following a one-time penicillin injection.

**Question 37:**

According to the table, how many more micrograms of penicillin are present in 10 milliliters of blood drawn from the patient 5 minutes after the injection than are present in 8 milliliters of blood drawn 10 minutes after the injection?

**The correct answer is 576**

**Question 38:**

The penicillin concentration, in micrograms per milliliter, in the patient’s bloodstream t minutes after the penicillin injection is modeled by the function P defined by P(t) = 200b^{t/5}. If P approximates the values in the table to within 10 micrograms per milliliter, what is the value of b, rounded to the nearest tenth?

**The correct answer is 0.8 or 4/5**

Authors Note: The January 2017 QAS test is the same test as the SAT Practice Test #8

### About the Author: Megan Leinenbach

Megan comes from Princeton University where she studies Ecology and Evolutionary Biology on a Pre-Med track. She scored a 36 on the ACT, 790 on SAT Reading, and a 740 on SAT Math. Originally from Alaska but residing in Florida, Megan loves being outdoors and hiking. In addition to being an SAT master, Megan is also an expert at doing a handstand.