SAT Prep Math Domain 1

Equations in One Variable

100

2n+6=14 

A tree had a height of 6 feet when it was planted. The equation above can be used to find how many years n it took the tree to reach a height of 14 feet. Which of the following is the best interpretation of the number 2 in this context?

A. The number of years it took the tree to double its height
B. The average number of feet that the tree grew per year
C. The height, in feet, of the tree when the tree was 1 year old
D. The average number of years it takes similar trees to grow 14 feet

B. The average number of feet that the tree grew per year 

200

a(3-x)-b=-1-2x

In the equation above, a and b are constants. If the equation has infinitely many solutions, what are the values of a and b? 

a) a=2 and b=1

b) a=2 and b=7

c) a=-2 and b=5

d) a=-2 and b=-5

a=2 and b=7

300

Meganʼs regular wage at her job is p dollars per hour for the first 8 hours of work in a day plus 1.5 times her regular hourly wage for work in excess of 8 hours that day. On a given day, Megan worked for 10 hours, and her total earnings for that day were $137.50. What is Meganʼs regular hourly wage?

A) $11.75

B) $12.50

C) $13.25

D) $13.75

$12.50

400

If (x+6)/3=(x+6)/13, the value of x+6 is between which of the following pairs of values?

A) -7 and -3                      B)-2 and 2

C) 2 and 7                        D) 8 and 13

- 2 and 2

500

The equation  9x+5= a(x+b) , where a and b are constants, has no solutions. Which of the following must be true? 

I. a=9                  II. b=5                     III. b =/ 5/9

A None                            C I and II only

B I only                           D I and III only 

 

I and III

600

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger
when 12,840 bushels of corn remain in the bin?

A) 3              B)7              C) 8                D)12

12

Equations in Two Variables

100

On a 210-mile trip, Cameron drove at an average speed of 60 miles per hour for the first x hours. He then completed the trip, driving at an average speed of 50 miles per hour for the remaining y hours. If x=1 , what is the value of y ?

60x+50y=210

If x=1, then 60(1)+50y=210

y=3

200

In the xy-plane, line k passes through the points (0,-5) and (1,-1) . Which equation defines line k?

A) y=-x+1/4

B) y=1/4x-5

C) y=-x+4

D) y=4x-5

y=4x-5

300

A line passes through the points (4,6) and (15,24) in the xy-plane. What is the slope of the line?

18/11

400

Line a in the xy-plane is perpendicular to the line with equation x=0. What is the slope of line a?

0

500

In the xy-plane, line k is defined by x+y=0. Line j is perpendicular to line k, and the y-intercept of line j is (0,3). Which of the following is an equation of line j?

A) x+y=3                            C) x-y=3

B) x+y=-3                          D) x-y=-3 

x-y=-3

600

In the xy-plane, line k intersects the y-axis at the point (0,-6) and passes through the point (2,2). If the point (20,w) lies on line k, what is the value of w?

74

Linear Functions

100

In the xy-plane, the points (-2,3) and (4,-5) lie on the graph of which of the following linear functions?

a) f(x)=x+5

b) f(x)=1/2x+4

c) f(x)=-4/3x+1/3

d) f(x)=-3/2x+1

f(x)=-4/3x+1/3

200

j(x)=mx+144 

For the linear function j, m is a constant and j(12)=18

What is the value of j(10)?

39

300

y=18-5x

The equation above represents the speed y, in feet per second, of Sheila’s bicycle x seconds after she applied the brakes at the end of a ride. If the equation is graphed in the xy-plane, which of the following is the best interpretation of the x-coordinate of the line’s x-intercept in the context of the problem?

A. The speed of Sheila’s bicycle, in feet per second, before Sheila applied the brakes

B. The number of feet per second the speed of Sheila’s bicycle decreased each second after Sheila applied the brakes

C. The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop

D. The number of feet Sheila’s bicycle traveled from the time she began applying the brakes until the bicycle

came to a complete stop

The number of seconds it took from the time Sheila began applying the brakes until the bicycle came to a complete stop

400

The function f is defined by f(x)=mx+b , where m and b are constants. If f(0)=18 and f(1)=20 , what is the value of m ?

2

500

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y , in dollars, of renting the backhoe for x days, where is a positive integer and  x < 11?

A) y=270x-135

B) y=270x+135

C) y=135x+270

D) y=135x+135

y= 135x+135

600

k= 4.2x

Linear Inequalities

100

In North America, the standard width of a parking space is at least 7.5 feet and no more than 9.0 feet. A restaurant owner recently resurfaced the restaurant’s parking lot and wants to determine the number of parking spaces, n, in the parking lot that could be placed perpendicular to a curb that is 135 feet long, based on the standard width of a parking space.

Which of the following describes all the possible values of n ?

A) 18 < n < 135

B) 7.5< n <9

C) 15< n< 135

D) 15 < n < 18

15< n< 18

200

y< -4x+4

Which point ( x, y) is a solution to the given inequality in the xy-plane?

A) (-4,0)

B) (0,5)

C) (2,1)

D) (2,-1)

(-4,0)

300

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of 6 and 12 , which inequality represents the possible lengths ,x, of the third side of the triangle?

A) x<18
B) x>18

C) 6<x<18

D) x<6 or x>18

6<x<18

400

A model estimates that whales from the genus Eschrichtius travel  72 to 77 miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated total number of miles ,x, a whale from the genus Eschrichtius could travel in 16 days of its migration?

500

Y> 2x-1

2x> 5

Which of the following consists of the y-coordinate of all the points that satisfy the systems of inequalities above?

A) y>6

B) y>4

C) y> 5/2

D) y> 3/2

y> 4

600

A number x is at most 2 less than 3 times the value of y . If the value of y is -4 , what is the greatest possible

value of  x?

-14

System of Equations

100

x+2y=6

x-2y=4

The solution to the given system of equation is (x,y). What is the value of x?

5

200

-x +y =-3.5

x+ 3y=9.5

If (x,y) satisfies the system of equations above, what is the value of y? 

3/2 or 1.5

300

5x+14y=45

10x+7y=27

The solution to the given system of equations is (x,y). What is the value of xy? 

1.8 or 9/5

400

y= 2x+1

y= ax-8

In the system of equations above, a is a constant. If the system of equations has no solution, what is the value of a? 

2

600

A group of 202 people went on an overnight camping trip, taking 60 tents with them. Some of the tents held 2 people each, and the rest held 4 people each. Assuming all the tents were filled to capacity and every person got to sleep in a tent, exactly how many of the tents were 2-person tents?

19