SAT Math Prep Calculator 16 Questions Part 1

SAT Math Prep Calculator 16 Questions Part 1

Math Test - Calculator

1) Remember you have 55 minutes to answer 38 questions.

2) The first 30 are multiple choice. The last 8 are gridded response.

3) We will begin on page 1237 in your SAT Prep Book.

4) You may use a calculator but may not need it for every question.

5) Answer to the best of your ability and we will go over each question after it has been answered.

Multiple Choice

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?

• Between 0 and 30 minutes

• Between 40 and 60 minutes

• Between 50 and 65 minutes

• Between 70 and 90 minutes

Answer Explanation

A section of a graph with a positive slope (up from left to right) means it is increasing. A section of a graph with negative slope (down from left to right) means it is decreasing, and a horizontal section of a graph means the y-axis is staying contant (not changing) in the section. The only section that increases and then decreases immediately with no constant sections is between 40 and 60 minutes.

Multiple Choice

2.)

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

• 6

• 15

• 20

• 23

Answer Explanation

First, it says y = 24 and x = 6, so plugging that into y = kx, we see

24 = k(6). Therefore, k must be 4 because 4(6) = 24. Then, we plug

k = 4 and x = 5 into y = kx, and we get y = (4)(5) so y = 20.

Multiple Choice

3.) 

In the figure above, lines l and m are parallel and lines s and t are parallel. If the measure of <1 is $35\degree$ , what is the measure of <2? 

•  $35\degree$  

•  $55\degree$  

•  $70\degree$  

•  $145\degree$  

Answer Explanation

When you look at <2, it is wider than a right angle which means it is great than 90 degrees and is an obtuse angle.  Also, if <1 is 35 degrees, the angle directly attached to <2 to the right is also 35 degrees.  These 2 angles form a straight angle so 

180 degrees - 35 degrees = 145 degrees. 

Multiple Choice

4.)

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

• 2

• 6

• 16

• 80

Answer Explanation

Rather than just giving what 16 + 4x is equal to, they decide to use words. 10 more than 14 is 24 so the equation you are solving is

16 + 4x = 24. Subtracting 16 and dividing by 4 to both sides we see

x = 2. Then plugging 2 in for x into the second expression, 8(2) = 16.

Multiple Choice

5.)

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

Answer Explanation

It is important that you read the problem carefully, because it needs to not only be a negative association but a STRONG, NEGATIVE association. A negative association is very simliar to a negative slope (goes down from left to right). Graphs A and D both have negative associations but in order for an association to be strong, the points need to be grouped tightly together.

Multiple Choice

6.)

1 decagram = 10 grams

1,000 milligrams = 1 gram

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?

• 0.002

• 200

• 2,000

• 20,000

Answer Explanation

If a medicine is put in 2 decagram containers, that means that if there's 10 grams in a decagram, 2 x 10 = 20 grams. Then if there's 1,000 milligrams in a gram, 20 x 1,000 = 20,000 milligrams, so there are 20,000 1-milligram doses in a 2 decagram container.

Multiple Choice

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?

• Number of installations (in tens)

• Number of installations (in hundreds)

• Number of installations (in thousands)

• Number of installations (in tens of thousands)

Answer Explanation

Looking at the bar graph, A reaches to 9, B to 5, C to 6, D to 4 and E to 3.5. It says all 5 cities have 27,500 solar panel installations so each number on the bar graph needs to be multiplied by 10, 100, 1,000 or 10,000 and be added together to equal 27,500.

90+50+60+40+35 = 275

900+500+600+400+350 = 2750

9,000+5,000+6,000+4,000+3,500 = 27,500

so the number of installations needs to be in thousands on the vertical axis.

Multiple Choice

8.) 

For what value of n is $\left|n-1\right|+1$ equal to 0? 

• 0

• 1

• 2

• There is no such value of n

Answer Explanation

The absolute value of any number is always positive. Because n-1 is in absolute value bars, it will be positive. Therefore, a positive number +1 will always be positive and higher than 0 so there is not a vlaue of n that will make the equation true.

Multiple Choice

9.)

a = 1,052 + 1.08t
The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit  $\left(\degree F\right)$ .

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

•  $t=\frac{a-1,052}{1.08}$  

•  $t=\frac{a+1,052}{1.08}$  

•  $t=\frac{1,052-a}{1.08}$  

•  $t=\frac{1.08}{a+1,052}$  

Answer Explanation

In this equation, because they want you to solve in terms of the air temperature, they want you to solve for t in this equation.
a = 1,052 + 1.08t (Subtract 1,052 to both sides)
a - 1,052 = 1.08t (Divide both sides by 1.08)

 $\frac{a-1,052}{1.08}=t$  

Multiple Choice

10.)
a = 1,052 + 1.08t
The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit  $\left(\degree F\right)$ 
At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?

•  $-46\degree F$  
  

•  $-48\degree F$  
  

•  $-49\degree F$  

•  $-50\degree F$  

Answer Explanation

Since a represents the speed of sound in feet per second, plug 1,000 in for a in the equation a = 1,052 + 1.08t.

1,000 = 1,052 + 1.08t (SUbtract 1,052 to both sides)

-52 = 1.08t (Divide both sides by 1.08)

t = -48.148148... so -48 degrees Fahrenheit

Multiple Choice

11.) 

Which of the following numbers is NOT a solution of the inequality

 $3x-5\ge4x-3\ ?$  

• -1

• -2

• -3

• -5

Answer Explanation

You solve an inequality with variables on both sides the same way you solve an equation with variables on both sides.

 $3x-5\ge4x-3$  (Subtract 3x to both sides)

 $-5\ge x-3$  (Add 3 to both sides)
 $-2\ge x\ or\ x\le-2$  
Be careful with negatives! -2, -3, and -5 are all less than or equal to -2

Multiple Choice

12.)

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

• 4

• 5

• 6

• 7

Answer Explanation

The first thing you must do is see how many seeds (on the x-axis) there were in all the apples by multiplying how many seeds were in each apple by how many apples (on the y-axis) had that amount of seeds. So for example:

3 seeds x 2 apples = 6 seeds
5 seeds x 4 apples = 20 seeds
6 seeds x 1 apple = 6 seeds
7 seeds x 2 apples = 14 seeds
9 seeds x 3 apples = 27 seeds
6+20+6+14+27 = 73 total seeds
Average =  $73\div12\ =\ 6.08333...\ so\ 6\ apples.$  

Multiple Choice

13.)

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

• Females taking Geometry

• Females taking Algebra II

• Males taking Geometry

• Males taking Algebra I

Answer Explanation

Remember a percent is part of a whole. So 19% is

 $\frac{19}{100}$ .  A proportion could be set up to solve this problem.   The total number of students which represents the whole is 310.  We could solve  $\frac{19}{100}=\frac{x}{310}so\ x=\frac{19\cdot310}{100}=\frac{5890}{100}=58.9\ or\ 59\ students$  59 students were in the category of Males taking Geometry.  

Multiple Choice

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?

• Mean

• Median

• Range

• They will all change by the same amount.

Answer Explanation

Mean is finding the average. 
 $\frac{8+9+9...+24}{21}=\frac{262}{21}=12.5\ and\ \ \frac{8+9+9...+16}{20}=\frac{238}{20}=11.9$  
Median is the middle number. If an odd number in the data set, there is one number in the middle and if 2 numbers are in the middle, take the average of the 2 numbers in the middle. The median stays 12 whether the 24 is present or not.  
Range is the biggest number in the data set minus the smallest number so 24 - 8 = 16 and 16 - 8 = 8 so there is a difference of 8 which is the largest difference.  

Multiple Choice

The graph above displays the total cost C, in dollars, of renting a boat for h hours.

15.)

What does the C-intercept represent in the graph?

• The initial cost of renting the boat

• The total number of boats rented

• The total number of hours the boat is rented

• The increase in cost to rent the boat for each additional hour

Answer Explanation

The C-intercept is the same thing as the y-intercept which is where the line touches or crosses the y-axis and represents the problem's "Initial/starting" amount. The line is starting at 5 on the y-axis so it represents the cost for renting the boat before any hours had been accumulated.

Multiple Choice

The graph above displays the total cost C, in dollars, of renting a boat for h hours.

16.

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

• C = 5h

• $C=\frac{3}{4}h+5$

• C = 3h + 5

• h = 3C

Answer Explanation

To find the equation of the line you need to use the slope-intercept form, y = mx + b, where m represents the slope of the line and b represents the y-intercept. In the last problem, we saw the line crosses the y-axis at 5 so the y-intercept is 5.

You need to be careful when finding the slope because each line is not increasing by 1 on the x-axis. The rise from one point to the next is 3 but the run is only 1 because each line is increasing by 0.25. Therefore, the slope of the line is 3 and the equation is C = 3h + 5.