## SAT Test 1 Explanations

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### Test 1 Section 3

You may not use a calculator.

Question 1

If (x-1) / 3 = k and k = 3, what is the value of x ?

Question 2

For i = √-1, what is the sum (7 + 3i) + (-8 + 9i) ?

Question 3

On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which if the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?

Question 4

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 - 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

Question 5

Which of the following is equivalent to the expression above?

Question 6

A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy's age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy's height each year?

Question 7

The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N ?

Question 8

If a/b = 2, what is the value of 4b/a ?

Question 9

What is the solution (x, y) to the system of equations above?

Question 10

For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4) ?

Question 11

In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?

Question 12

A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?

Question 13

If x > 3, which of the following is equivalent to

Question 14

If 3x - y = 12, what is the value of 8^x / 2^y ?

Question 15

If (ax + 2)(bx + 7) = 15x² + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ?

Question 16

If t > 0 and t² - 4 = 0, what is the value of t ?

Question 17

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?

Question 18

According to the system of equations above, what is the value of x ?

Question 19

In a right triangle, one angle measures x°, where sin x° = 4/5. What is cos(90° - x°) ?

Question 20

If a = 5√2 and 2a = √2x, what is the value of x ?

### Test 1 Section 4

You may use a calculator.

Question 1

John runs at different speeds as part of his training program. The graph shows his target heart rate at different times during his workout. On which interval is the target heart rate strictly increasing then strictly decreasing?

Question 2

If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?

Question 3

In the figure above, lines l and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°, what is the measure of ∠2 ?

Question 4

If 16 + 4x is 10 more than 14, what is the value of 8x ?

Question 5

Which of the following graphs best shows a strong negative association between d and t ?

Question 6

A hospital stores one type of medicine in 2-decagram containers. Based on the information given in the box above, how many 1-milligram doses are there in one 2-decagram container?

Question 7

The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?

Question 8

For what value of n is | n - 1 | + 1 equal to 0 ?

Question 9

Which of the following expresses the air temperature in terms of the speed of a sound wave?

Question 10

At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?

Question 11

Which of the following numbers is NOT a solution of the inequality 3x - 5 ≥ 4x - 3 ?

Question 12

Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?

Question 13

A group of tenth-grade students responded to a survey that asked which math course they were currently enrolled in. The survey date were broken down as shown in the table above. Which of the following categories accounts for approximately 19 percent of all the survey respondents?

Question 14

The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?

Question 15

What does the C-intercept represent in the graph?

Question 16

Which of the following represents the relationship between h and C ?

Question 17

The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its minimum?

Question 18

In the xy-plane, if (0,0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?

Question 19

A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck's revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?

Question 20

Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?

Question 21

The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y ?

Question 22

Which of the following best approximates the average rate of change in the annual budget for agriculture/natural resources in Kansas from 2008 to 2010 ?

Question 23

Of the following, which program's ratio of its 2007 budget to its 2010 budget is closest to the human resources program's ratio of its 2007 budget to its 2010 budget?

Question 24

Which of the following is an equation of a circle in the xy-plane with center (0, 4) and a radius with endpoint (4/3, 5) ?

Question 25

The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?

Question 26

Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina's observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?

Question 27

Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters beneath the ground's surface in the entire field?

Question 28

If the system of inequalities y ≥ 2x + 1 and y > (1/2)x - 1 is graphed in the xy-plane above, which quadrant contains no solutions to the system?

Question 29

For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p(x) ?

Question 30

Which of the following is an equivalent form of the equation of the graph shown in the xy-plane above, from which the coordinates of vertex A can be identified as constants in the equation?

Question 31

Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?

Question 32

The posted weight limit for a covered wooden bridge in Pennsylvania is 6000 pounds. A delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. If the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridge's posted weight limit?

Question 33

According the line graph above, the number of portable media players sold in 2008 is what fraction of the number sold in 2011 ?

Question 34

A local television station sells time slots for programs in 30-minute intervals. If the station operates 24 hours per day, every day of the week, what is the total number of 30-minute time slots the station can sell for Tuesday and Wednesday?

Question 35

A dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. If the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards?

Question 36

For what value of x is the function h above undefined?

Question 37

What is the value of x in the expression?

Question 38

Jessica's friend Tyshaun found an account that earns 2.5 percent interest compounded annually. Tyshaun made an initial deposit of $100 into this account at the same time Jessica made a deposit of $100 into her account. After 10 years, how much more money will Tyshaun's initial deposit have earned than Jessica's intial deposit? (Round your answer to the nearest cent and ignore the dollar sign when gridding your response.)