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# Cracking The SAT

## Educators ### Problem 33

As used in line $31,$ "doors" most nearly means
A) openings.
B) operations.
C) entrances.
D) lights. Brenda S.

### Math Test - Calculator - Problem 1

Rebecca and Natalie begin bicycling from their homes at the same time to a destination that is 2,400 yards from Natalie’s house. The graph shows the distance that Rebecca and Natalie are from Natalie’s house along the route. Natalie and Rebecca each bicycle at a constant rate and Rebecca’s house is on the way from Natalie’s house to the destination. Natalie reached the destination in 8 minutes and Rebecca reached the destination in 12 minutes. According to the graph,
Rebecca’s trip is how many yards shorter than Natalie’s?
A) 2,400
B) 900
C) 600
D) 300 Brenda S.

### Math Test - Calculator - Problem 2

Alejandro began driving to work and then stopped in a store for some time.
Once he began again, he continued to work at a slower speed. Which of the following graphs could model the total distance traveled by Alejandro versus time?
A)
B)
C)
D) Brenda S.

### Math Test - Calculator - Problem 3

Which expression is equivalent to $\left(4 y^{2}-5\right)-\left(-6 y^{2}+3 y-11\right) ?$
$$\begin{array}{l}{\text { A) }-2 y^{2}+3 y-16} \\ {\text { B) }-2 y^{2}-3 y-16} \\ {\text { C) } 10 y^{2}+3 y-6} \\ {\text { D) } 10 y^{2}-3 y+6}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 4

$$12 a+9 b<36$$
Which of the following inequalities is equal to the inequality shown above?
$$\begin{array}{l}{\text { A) } a+b<3} \\ {\text { B) } 3 a+4 b<12} \\ {\text { C) } 4 a+3 b<12} \\ {\text { D) } 4 a+3 b<3}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 5

What Is the Most Important Issue in the Election? The table above shows a summary of 1,800 responses to a survey question. Based on the information in the table, how many of those surveyed believe that the most important issue in the election is the economy or crime?
A) 1,242
B) 1,296
C) 1,328
D) 1,384 Brenda S.

### Math Test - Calculator - Problem 6

A cable company charges customers a one-time installation fee of $\$ 150$plus$x$dollars for each month. If a customer paid$\$960$ for the first 18 months, including the installation fee, what is the value of $x ?$
A) 45
B) 55
C) 65
D) 75 Brenda S.

### Math Test - Calculator - Problem 7

The table above shows the coffee selections of the people at an office. Of
people who select milk, what fraction also select sugar?
$$\begin{array}{l}{\text { A) } \frac{6}{11}} \\ {\text { B) } \frac{5}{11}} \\ {\text { C) } \frac{6}{31}} \\ {\text { D) } \frac{5}{31}}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 8

The administrative staff of a high school wanted to gauge the preference of its entire student body for increasing funding to the athletic department. The staff surveyed 200 students who play a sport. The survey showed that the majority of those surveyed were in favor of increasing funding to the athletic department. Which of the following is true about the administrative staff’s survey?
A) The survey should have included more students who play a sport.
B) The survey sample is biased because it is not representative of the entire student body.
C) It shows that a majority of students favored increased funding to the athletic department.
D) The survey sample should have only included students who did not play a sport. Brenda S.

### Math Test - Calculator - Problem 9

Between 1839 and 1860, the United Kingdom and China engaged in the
two wars known as the Opium Wars. The length of the First Opium War
was 218 days shorter than the Second, and the two wars together lasted a total of 2,738 days. How many days did the First Opium War last?
A) $1,140$
B) $1,180$
C) $1,260$
D) 1.480 Brenda S.

### Math Test - Calculator - Problem 10

Over which time period is the average growth of a fetus the greatest?
A) Week 0 to Week 12
B) Week 12 to Week 24
C) Week 30 to Week 39
D) Week 39 to Week 42

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### Math Test - Calculator - Problem 11

In 2011 , Toronto had a population of 2.615 million people, which was an
increase of 0.134 million people from the population in 2001 . In 2001 ,
there were 43 hospitals located within Toronto. Which of the following is
the approximate number of residents served per hospital in Toronto in 2001
A) 320
B) $3,100$
C) $57,700$
D) $60,800$ Brenda S.

### Math Test - Calculator - Problem 12

The growth rate of a fetus from Week 33 to Week 39 is nearly constant. On this interval, which of the following best models the weight, w, in ounces, of a fetus $t$ weeks after conception?
A) $w=2.5 t-220$
B) $w=5.8 t-180$
C) $w=8.1 t-200$
D) $w=12.4 t-150$ Brenda S.

### Math Test - Calculator - Problem 13

The function $w$ , defined by $w(t)=c t+d,$ where $c$ and $d$ are constants, models the weight, in ounces, of a fetus after $t$ weeks of growth during a time period in which the growth is approximately linear. What does $c$ represent?
A) The predicted total increase in weight, in ounces, of a fetus during the period
B) The predicted number of ounces of growth per week during the period
C) The predicted weight, in ounces, of a fetus at the beginning of the period
D) The predicted weight, in ounces, of a fetus at the end of the period Brenda S.

### Math Test - Calculator - Problem 14

$$\begin{array}{l}{6 x+5 y=9} \\ {5 x-5 y=2}\end{array}$$
For the solution $(x, y)$ to the system of equations above, what is the value of $x-y ?$
$$\begin{array}{l}{\text { A) }-\frac{8}{5}} \\ {\text { B) } \frac{1}{5}} \\ {\text { C) } \frac{2}{5}} \\ {\text { D) } \frac{8}{5}}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 15

Triangles $P Q R$ and $X Y Z$ are shown above. Which of the following is equal to the ratio $\frac{P Q}{P R} ?$
A) $\frac{Y Z}{X Y}$
B) $\frac{X Y}{X Z}$
C) $\frac{X Z}{Y Z}$
D) $\frac{Y Z}{X Z}$ Brenda S.

### Math Test - Calculator - Problem 16

$$\begin{array}{|c|c|}\hline x & {y} \\ \hline 1 & {\frac{31}{4}} \\ \hline 2 & {\frac{49}{4}} \\ \hline\end{array}$$
$$\begin{array}{c|c}{3} & {\frac{67}{4}} \\ {4} & {\frac{85}{4}} \\ {5} & {\frac{103}{4}}\end{array}$$
Which of the following equations relates $y$ to $x$ for the values in the table above?
$$\begin{array}{l}{\text { A) } y=\frac{1}{2} \cdot\left(\frac{7}{2}\right)^{x}} \\ {\text { B) } y=\frac{47}{4} x-4} \\ {\text { C) } y=\frac{9}{2} x+\frac{13}{4}} \\ {\text { D) } y=2 \cdot\left(\frac{47}{4}\right)^{x}}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 17

Juliet wants to use a strategy in which she mines at least 4 ounces of gold and at least 14 ounces of silver at the beginning of each round. According to the game’s equation, which of the following inequalities represents the set of all possible amounts of gold that she can mine to meet this strategy?
$$\begin{array}{l}{\text { A) } 8 \leq g \leq 14} \\ {\text { B) } 4 \leq g \leq 8} \\ {\text { C) } g \geq 4} \\ {\text { D) } 0 \leq g \leq 4}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 18

Johnny wants to create a strategy designed to mine 6 pounds of go taking between 10 and 15 ounces per round for a game in which there is an even number of rounds. Within Johnny's strategy, which of the following must be the amount of silver, in ounces, Johnny mines? ( 16 ounces $=1$ pound)
A) 2
B) 8
C) 9.6
D) 12 Brenda S.

### Math Test - Calculator - Problem 19

Which of the following expresses the amount of gold mined each round in terms of the amount of silver mined in that round?
$$\begin{array}{l}{\text { A) } g=-\frac{1}{3}(38+s)} \\ {\text { B) } g=-\frac{1}{3}(38-s)} \\ {\text { C) } g=\frac{1}{3}(38+s)} \\ {\text { D) } g=\frac{1}{3}(38-s)}\end{array}$$ Brenda S.

### Math Test - Calculator - Problem 20

A study was conducted on the heights of fourth-graders in a particular county. A random sample of girls was taken with each girl's height measured and recorded. The sample contained 250 girls, and 20$\%$ of the girls were more than 57 inches tall. Which of the following conclusions is best supported by the sample data?
A) Approximately 20% of all fourth-grade girls in the county were taller than 57 inches.
B) Approximately 20% of all fourth-graders in the county were taller than 57 inches.
C) The average height of all fourth-graders in the county was 57 inches.
D) The majority of all fourth-graders in the county are shorter than 57 inches. Brenda S.

### Math Test - Calculator - Problem 21

What is the sum of the solutions to $(x+5)(x-0.4)=0 ?$
A) $-5.4$
B) $-4.6$
C) 4.6
D) 5.4 Brenda S.

### Math Test - Calculator - Problem 27

At a constant temperature, if the ratio of the volumes of two containers filled with equal amounts of gas is p:q, then the ratio of the pressures in the containers is q:p. In the diagram below, Container X is filled with gas and the pressure in Container X is measured. Then all the gas is pumped into Container Y. Once the pressure in Container Y is measured, the gas is finally pumped into Container Z, and the pressure in Container Z is measured. If the pressure in Container $X$ is 300 torr, what is the pressure, in torr, in Container $Z$ after the gas has been pumped into it?
.A) 100
B) 330
C) 900
D) 9.000 Brenda S.

### Math Test - Calculator - Problem 28

he mean distance, d, in micrometers, glucose travels in free solution in t seconds can be determined using the formula d = 10 . Which of the following gives the average speed of the glucose, in micrometers per second, over the first t seconds after it begins to move?
$$\begin{array}{l}{\text { A) } 10 t \sqrt{5 t}} \\ {\text { B) } \frac{10}{\sqrt{5 t}}} \\ {\text { C) } \frac{10 \sqrt{5 t}}{t}} \\ {\text { D) } \frac{100 \sqrt{5 t}}{t}}\end{array}$$ Brenda S.
$$\begin{array}{l}{\text { A) } y=-0.4339 x^{2}+5.6673 x+0.7685} \\ {\text { B) } y=0.4339 x^{2}+5.6673 x+0.7685} \\ {\text { C) } y=-0.4339 x^{2}-5.6673 x-0.7685} \\ {\text { D) } y=0.4339 x^{2}+5.6673 x-0.7685}\end{array}$$ 