_______________________
SAT Practice Test 2015.
$a=18t+15$
Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount to the account. The equation above models the amount a, in dollars, that Jane has deposited after t weekly deposits. According to the model, how many dollars was Jane’s initial deposit? (Disregard the $ sign when gridding your answer.)
Answer:
The amount Jane deposited in the fixed weekly deposits is the amount of the weekly deposit times t. This amount must be given by the term 18t in the equation.
The other term in the equation (15) should be the initial deposit.
Answer: 15
_____________________________
SAT Practice Test 2015.
In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7, 2) and (1, 0), respectively. Which of the following is an equation of the line that passes through points B and D ?
A) y = -3x - 1
B) y = -3(x - 1)
C) y = -(1/3)x + 4
D) y = -(1/3)x - 1
Answer:
The line that passes by the vertices B and D should also pass by the center of the square (E). Therefore point (1, 0) belongs to the line whose equation we're trying to find. Thus,
$y=ax+b$
$0=a(1)+b$
$a=-b$
The only choice that satisfies this condition is B:
$y = -3(x - 1)$
$y = -3x + 3$, where a=-3 and b=3
Answer: B
_____________________________
SAT Practice Test 2015.
The complete graph of the function f is shown in the xy-plane above. Which of the following are equal to 1?
I. f(−4)
II. f(3/2)
III. f(3)
A) III only
B) I and III only
C) II and III only
D) I, II, and III
Answer:
The points on the graph of f with x-coordinates −4, 3/2, and 3 are, respectively, (-4, 1), (3/2, 1), and (3, 1). Thus, all of the values of f given in I, II, and III are equal to 1.
Answer: D
_____________________________
SAT Practice Test 2015. The graph of the linear function f has intercepts at (a, 0) and (0, b) in the xy-plane. If a + b = 0 and a ≠ b, which of the following is true about the slope of the graph of f ?
A) It is positive.
B) It is negative.
C) It equals zero.
D) It is undefined.
Answer:
If $a+b=0$, then $a=-b$.
Thus, if $a>0$, then $b<0$, and the intercepts (a, 0) and (0, b) belong to a line with positive slope.
If $a<0$, then $b>0$, and again the intercepts (a, 0) and (0, b) belong to a line with positive slope.
Answer: A
_____________________________
SAT Practice Test 2015. On January 1, 2000, there were 175,000 tons of trash in a landfill that had a capacity of 325,000 tons. Each year since then, the amount of trash in the landfill increased by 7,500 tons. If y represents the time, in years, after January 1, 2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?
A) 325,000 − 7,500 ≤ y
B) 325,000 ≤ 7,500y
C) 150,000 ≥ 7,500y
D) 175,000 + 7,500 ≥ 325,000
Answer:
If the amount of trash in the landfill increases by 7,500 tons each year, after y years the amount of trash in the landfill increased by 7,500*y tons.
The total amount of trash in the landfill after y year is this amount plus 175,000 tons, that is, 7,500*y+175,000.
The landfill will be at or above capacity when this amount is greater than or equal to 325,000 tons (the landfill capacity):
7,500*y+175,000≥325,000
Answer: D
_____________________________
SAT Practice Test 2015. In a video game, each player starts the game with k points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points, what is the value of k?
A) 0
B) 150
C) 250
D) 400
Answer:
If the player fails to complete "t" tasks, he or she will lose "2t" points. Since the player starts with k points, the score after "t" fails will be "k-2t" points.
It is given that when t=100 the score is 200 points. Thus,
$200=k-2(100)$
$200=k-200$
$k=400$
Answer: D
_____________________________
SAT Practice Test 2015. When 4 times the number x is added to 12, the result is 8. What number results when 2 times x is added to 7?
A) -1
B) 5
C) 8
D) 9
Answer:
When 4 times the number x is added to 12, the result is 8. Thus,
$4x+12=8$
$4x=-4$
$x=-1$
What number results when 2 times x is added to 7?
$2x+7=y$
$2(-1)+7=y$
$-2+7=y$
$5=y$
Answer: B
_____________________________
SAT Practice Test 2015. $l=24+3.5m$
One end of a spring is attached to a ceiling. When an object of mass m kilograms is attached to the other end of the spring, the spring stretches to a length of A centimeters as shown in the equation above. What is m when A is 73?
A) 14
B) 27.7
C) 73
D) 279.5
Answer:
$l=24+3.5m$
$73=24+3.5m$
$49=3.5m$
$m=14$
Answer: A
_____________________________
SAT Practice Test 2015. If 5x+6=10, what is the value of 10x+3?
A) 4
B) 9
C) 11
D) 20
Answer:
$5x+6=10$
Multiplying both sides by 2:
$10x+12=20$
$10x+12-9=20-9$
$10x+3=11$
Answer: C
_____________________________
SAT 2015 Test.
If the system of inequalities $y\geq2x+1$ and $y>(1/2)x-1$ is graphed in the xy-plane above, which
quadrant contains no solutions to the system?
A) Quadrant II
B) Quadrant III
C) Quadrant IV
D) There are solutions in all four quadrants
Answer:
The solution to the system of inequalities is the intersection of the regions above the graphs of both lines in the following graph:
The solutions are the regions above both lines, because both inequations are of the kind $>$ or $\geq$.
Note that there is no region above the red line in quadrant IV, so there will be no intersection of the regions in this quadrant.
Answer: C
_____________________________
SAT 2015 Test.
$y<-x+a$
$y>x+b$
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?
A) a>b
B) b>a
C) |a|>|b|
D) a=-b
Answer:
If (0, 0) is a solution to the system:
$0<-0+a$, or $a>0$
$0>0+b$, or $b<0$
If a is positive, and b is negative, then $a>b$.
Answer: A
_____________________________
SAT Test 2015. Which of the following numbers is NOT a solution of the inequality $3x-5\geq4x-3$?
A) −1
B) −2
C) −3
D) −5
Answer:
$3x-5\geq4x-3$
$-5+3\geq4x-3x$
$-2\geq{x}$
$x\leq-2$
Answer: A
_____________________________
SAT Test 2015.
$a=1,052+1.08t$
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 (°F).
At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?
A) −46°F
B) −48°F
C) −49°F
D) −50°F
Answer:
$a=1,052+1.08t$
$1,000=1,052+1.08t$
$-52=1.08t$
$t=-48.1$°F
Answer: B
_____________________________
SAT Test 2015. If 16+4x is 10 more than 14, what is the value of 8x ?
A) 2
B) 6
C) 16
D) 80
Answer:
"10 more than 14" is 24. Therefore:
$16+4x=24$
$4x=24-16$
$4x=8$
$x=2$
And $8x=8(2)=16$
Answer: C
"10 more than 14" is 24. Therefore:
$16+4x=24$
$4x=24-16$
$4x=8$
$x=2$
And $8x=8(2)=16$
Answer: C
SAT Test 2015. If $y=kx$, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5?
A) 6
B) 15
C) 20
D) 23
Answer:
It is given that y = 24 when x = 6, so
$y=kx$
$24=k6$
$k=4$
Now it is possible to calculate the value of y when x = 5:
$y=kx$
$y=4x$
$y=4.5=20$
Answer: C
It is given that y = 24 when x = 6, so
$y=kx$
$24=k6$
$k=4$
Now it is possible to calculate the value of y when x = 5:
$y=kx$
$y=4x$
$y=4.5=20$
Answer: C
SAT Test 2015. 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?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
Answer:
The general equation of a line is $f(x)=y=ax+b$, where a (the slope) and b are constants. It is given that the line passes through the origin; therefore $b=0$. Therefore, the equation of the given line is: $y=(1/7)x$.
Now let's check this equation for x=0, x=1, x=7, and x=14:
$f(0)=(1/7).0=0$
$f(1)=(1/7).1=1/7$
$f(7)=(1/7).7=1$
$f(14)=(1/7).14=2$
Answer: D
The general equation of a line is $f(x)=y=ax+b$, where a (the slope) and b are constants. It is given that the line passes through the origin; therefore $b=0$. Therefore, the equation of the given line is: $y=(1/7)x$.
Now let's check this equation for x=0, x=1, x=7, and x=14:
$f(0)=(1/7).0=0$
$f(1)=(1/7).1=1/7$
$f(7)=(1/7).7=1$
$f(14)=(1/7).14=2$
Answer: D
SAT Test 2015. $h=3a+28.6$
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?
A) 3
B) 5.7
C) 9.5
D) 14.3
Answer:
At age 2, the height is: $h=3.2+28.6$
At age 3, the height is: $h=3.3+28.6$
At age 4, the height is: $h=3.4+28.6$
Therefore the height increases by 3 in each year.
Answer: A
At age 2, the height is: $h=3.2+28.6$
At age 3, the height is: $h=3.3+28.6$
At age 4, the height is: $h=3.4+28.6$
Therefore the height increases by 3 in each year.
Answer: A
SAT Test 2015. If $\frac{x-1}{3}=k$ and k = 3, what is the value of x ?
A) 2
B) 4
C) 9
D) 10
Answer:
$\frac{x-1}{3}=k$
$x-1=3k$
$x-1=3.3$
$x=9+1$
$x=10$
Answer: D
$\frac{x-1}{3}=k$
$x-1=3k$
$x-1=3.3$
$x=9+1$
$x=10$
Answer: D
SAT Practice Test. If k is a positive constant different from 1, which of the following could be the graph of $y-x=k(x+y)$, in the x y plane?
Each of the four answer choices presents a graph in the x y plane. The numbers -6 through 6 appear along both axes, and the origin is labeled O.
A.
B.
C.
D.
Answer:
Manipulating the equation to solve for y:
$y-x=k(x+y)$
$y-x=kx+ky$
$y-ky=x+kx$
$(1-k)y=(1+k)x$
$y=\frac{1+k}{1-k}.x$
It is a first degree equation. One of its solutions is (0, 0). Therefore, its graph must be a line that passes through the origin.
Answer: B
Manipulating the equation to solve for y:
$y-x=k(x+y)$
$y-x=kx+ky$
$y-ky=x+kx$
$(1-k)y=(1+k)x$
$y=\frac{1+k}{1-k}.x$
It is a first degree equation. One of its solutions is (0, 0). Therefore, its graph must be a line that passes through the origin.
Answer: B
SAT Practice Test.
The figure, titled “Count of Manatees,” presents the graph of a scatterplot with a line. The horizontal axis is labeled “Year,” and the vertical axis is labeled “Number of Manatees.” The years 1990 through 2015 are labeled on the horizontal axis, in increments of 5 years. The numbers 1,000 through 6,000 are labeled on the vertical axis, in increments of 1,000. Grid lines extend from the labeled increments of both axes.
There are 24 data points on the graph. The data points range horizontally from years 1991 to 2011 and vertically from approximately 1,300 manatees to approximately 5,100 manatees.
Year 1995: 1,800 manatees.
Year 2000: 2,600 manatees.
Year 2005: 3,300 manatees.
Year 2010: 4,100 manatees.
A. 0.75
B. 75
C. 150
D. 750
Answer:
The line of best fit is given:
Year 2000: 2,600 manatees.
Year 2010: 4,100 manatees.
The increase in the number of manatees in this 10 year period is $4100-2600=1500$.
Therefore, the yearly increase is $1500/10=150$.
Answer: C
The line of best fit is given:
Year 2000: 2,600 manatees.
Year 2010: 4,100 manatees.
The increase in the number of manatees in this 10 year period is $4100-2600=1500$.
Therefore, the yearly increase is $1500/10=150$.
Answer: C
SAT Practice Test. If $-\frac{9}{5}<-3 t+1<-\frac{7}{4}$, what is one possible value of $9t-3$?
Answer:
$-\frac{9}{5}<-3t+1<-\frac{7}{4}$
$-\frac{9}{5}<-3t+1<-\frac{7}{4}$
$\frac{9}{5}>3t-1>\frac{7}{4}$
$3.\frac{9}{5}>3(3t-1)>3.\frac{7}{4}$
$\frac{27}{5}>9t-3>\frac{21}{4}$
_____________________________$3.\frac{9}{5}>3(3t-1)>3.\frac{7}{4}$
$\frac{27}{5}>9t-3>\frac{21}{4}$
SAT Practice Test. Aaron is staying at a hotel that charges 99.95 dollars per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional one time untaxed fee of 5.00 dollars is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying x nights?
A. $(99.95+0.08.x)+5$
B. $1.08.(99.95.x)+5$
C. $1.08.(99.95.x+5)$
D. $1.08.(99.95+5).x$
Answer:
Room rate for x nights: $99.95.x$ dollars.
Tax: $0.08.(99.95.x)$ dollars.
One time untaxed fee: 5 dollars.
The total charge will be the sum of these three values:
$99.95.x+0.08.(99.95.x)+5=$
$1.08.(99.95.x)+5$
Room rate for x nights: $99.95.x$ dollars.
Tax: $0.08.(99.95.x)$ dollars.
One time untaxed fee: 5 dollars.
The total charge will be the sum of these three values:
$99.95.x+0.08.(99.95.x)+5=$
$1.08.(99.95.x)+5$
_____________________________
SAT Practice Test. The first metacarpal bone is located in the wrist. The following scatterplot shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.
The figure presents a gridded graph titled “Height of Nine People and Length of Their First Metacarpal Bone” and nine data points. The y axis is labeled “Length of first metacarpal bone,” in centimeters, and the x axis is labeled “Height,” in centimeters. The values 4, 4.5, and 5 are labeled on the x axis with a vertical grid line at every increment of 0.1. The values 155 through 185, in increments of 5, are labeled on the y axis with a horizontal grid line at every increment of one.
The approximate values of the nine data points on the scatterplot are as follows.
4.0 comma 157.
4.1 comma 163.
4.3 comma 175.
4.5 comma 171.
4.6 comma 173.
4.7 comma 173.
4.8 comma 172.
4.9 comma 183.
5.0 comma 178.
A straight line of best fit is drawn for the data points. The approximate coordinates of the line are as follows.
4.0 comma 161.5
4.1 comma 163.
4.2 comma 165.
4.3 comma 167.
4.4 comma 169.
4.5 comma 171.
4.6 comma 172.5.
4.7 comma 174.5.
4.8 comma 176.
4.9 comma 178.
5.0 comma 180.
A. 2
B. 4
C. 6
D. 9
Answer:
The following list compares the values of the nine data points on the scatterplot and the approximate coordinates of the line:
4.0: 157-161.5=-4.5cm
4.1: 163-163=0cm
4.3: 175-167=8cm
4.5: 171-171=0cm
4.6: 173-172.5=0.5cm
4.7: 173-174.5=-1.5cm
4.8: 172-176=-4cm
4.9: 183-178=5cm
5.0: 178-180=-2cm
The module of the difference is greater than 3cm in 4 points.
Answer: B
_____________________________
SAT Practice Test. This question refers to the same graph and data of the previous question:
Which of the following is the best interpretation of the slope of the line of best fit in the context of this problem?
A. The predicted height increase in centimeters for one centimeter increase in the first metacarpal bone
B. The predicted first metacarpal bone increase in centimeters for every centimeter increase in height
C. The predicted height in centimeters of a person with a first metacarpal bone length of 0 centimeters
D. The predicted first metacarpal bone length in centimeters for a person with a height of 0 centimeters
Answer:
The slope of the line is calculated by the formula:
$Slope=\frac{\Delta(height)}{\Delta(metacarpal)}$
Therefore the slopes corresponds to the predicted height increase in centimeters for one centimeter increase in the first metacarpal bone.
Answer: A
_____________________________
SAT Practice Test. This question refers to the same graph and data used in the two previous questions:
Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters?
A. 168 centimeters
B. 169 centimeters
C. 170 centimeters
D. 171 centimeters
Answer:
The approximate given coordinates of the line are as follows:
4.4: 169cm.
4.5: 171cm.
4.45 is halfway between 4.4 and 4.5. The predicted height is (169+171)/2=170cm
4.4: 169cm.
4.5: 171cm.
4.45 is halfway between 4.4 and 4.5. The predicted height is (169+171)/2=170cm
Answer: C
_____________________________
SAT Practice Test. $\frac{5(k+2)-7}{6}=\frac{13-(4-k)}{9}$
In the equation above, what is the value of $k$?
A. 9/17
B. 9/13
C. 33/17
D. 33/13
Answer:
$\frac{5(k+2)-7}{6}=\frac{13-(4-k)}{9}$
$(5(k+2)-7).9=(13-(4-k)).6$
$(5k+10-7).9=(13-4+k).6$
$(5k+3).9=(9+k).6$
$45k+27=54+6k$
$45k-6k=54-27$
$39k=27$
$13k=9$
$k=9/13$
Answer: B
_____________________________
SAT Practice Test - The mean number of students per classroom, y, at Central High School can be estimated using the equation y equals 0.8636 x plus 27.227, where x represents the number of years since 2004 and x is less than or equal to 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?
A. The estimated mean number of students per classroom in 2004.
B. The estimated mean number of students per classroom in 2014.
C. The estimated yearly decrease in the mean number of students per classroom.
D. The estimated yearly increase in the mean number of students per classroom.
Answer:
Using the formula, the mean number of students per classroom is...
in 2005 is 0.8636 times 1 plus 27.227 = 28,0906
in 2006 is 0.8636 times 1 plus 27.227 = 28,9542
in 2007 is 0.8636 times 1 plus 27.227 = 29,8178
and so on, until 2014.
We see that the number 0.8636 is how much the mean number of students per classroom increase yearly.
Answer: D
_____________________________
SAT Practice Test - The following question is based on the figure below, which presents the graph of line ℓ in the x y plane.
Begin skippable figure description.
The figure presents the graph of line ℓ in the x y plane. The x and y axes have tick marks. The fifth tick marks from the origin in the positive and negative directions on both axes are labeled 5 and negative 5, respectively.
Six points are marked on line ℓ. The following are the coordinates of the six points on line ℓ.
(-2,10) parenthesis, negative 2 comma 10, close parenthesis
(0,7) parenthesis, zero comma 7, close parenthesis
(2,4) parenthesis, 2 comma 4, close parenthesis
(4,1) parenthesis, 4 comma 1, close parenthesis
(6,-2) parenthesis, 6 comma negative 2, close parenthesis
(8,-5) parenthesis, 8 comma negative 5, close parenthesis
From left to right, line ℓ extends from quadrant 2 downward to the right through quadrant 1 and into quadrant 4. Line ℓ intersects the y axis at value 7 and intersects the x axis between values 4 and 5.
End skippable figure description.
Question 1.
If line ℓ is translated up 5 units and right 7 units, then what is the slope of the new line?
A. -2/5 negative two fifths
B. -3/2 negative three halves
C. -8/9 negative eight ninths
D. -11/14 negative eleven fourteenths
Answer:
Translating the line does not change its slope. So the slope of the new line is the same as the one presented in the graph.
The slope can be calculated using any two points on the line. Let's consider the points (-2,10) and (8,-5).
Variation in Y is -5 - 10 = -15
Variation in X is 8 - (-2) = 8 + 2 = 10
The slope is the devision of the Variations in Y by the Variation in X.
Slope = -15 / 10 = -3/2.
Answer: B
_____________________________
