SAT Prep No Calculator Portion

A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painter’s fee can be calculated by the expression nKAh, where n is the number of walls, K is a constant with units of dollars per square foot, A is the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change?

• h

• l

• K

• n

If  $3r=18$  , what is the value of  $6r+3$  ?

• 6

• 27

• 36

• 39

Which of the following is equal to  $a^{\frac{2}{3}}$ , for all values of a?

•  $\sqrt{a^{\frac{1}{3}}}$  

•  $\sqrt{a^3}$  

•  $cube\ root\ \left(a^{\frac{1}{2}}\right)$  

•  $cube\ root\ \left(a^2\right)$  

4 The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?

• $30x=2$

• $2x=30$

• $\frac{x}{2}=30$

• $x+30=2$

If  $\frac{5}{x}=\frac{15}{x+20}$  , what is the value of  $\frac{x}{5}$  ?

• 10

• 5

• 2

• 1/2

 $2x-3y=-14$  
 $3x-2y=-6$  
If (x, y) is a solution to the system of equations above, what is the value of x - y?

• -20

• -8

• -4

• 8

• x - 2

• x - 3

• x - 4

• x - 5

The line  $y=kx+4$ , where k is a constant, is graphed in the xy-plane. If the line contains the point (c, d), where  $c\ne0\ and\ d\ne0$  , what is the slope of the line in terms of c and d?

•  $\frac{d-4}{c}$  

•  $\frac{c-4}{d}$  

•  $\frac{4-d}{c}$  

•  $\frac{4-c}{d}$  

 $kx-3y=4$  
 $4x-5y=7$  
In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?

•  $\frac{12}{5}$  

•  $\frac{16}{7}$  

•  $-\frac{16}{7}$  

•  $-\frac{12}{5}$  

In the xy-plane, the parabola with equation  $y=\left(x-11\right)^2$  intersects the line with equation  $y=25$  at two points, A and B. What is the length of  $\overline{AB}$  ?

• 10

• 12

• 14

• 16