PSAT Heart of Algebra Practice (non-calculator)

Line f is graphed in the x-y plane pictured.

If line f is translated up 5 units and right 7 units, then what is the slope of the new line?

•  $-\frac{2}{5}$  

•  $-\frac{3}{2}$  

•  $-\frac{8}{9}$  

•  $-\frac{11}{14}$  

The mean number of students per classroom, y, at Central High School can be estimated using the equation  $y=0.8636x+27.227$  where x represents the number of years since 2004 and  $x\le10$ . Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

• The estimated mean number of students per classroom in 2004

• The estimated mean number of students per classroom in 2014

• The estimated yearly decrease in the mean number of students per classroom

• The estimated yearly increase in the mean number of students per classroom

 $\frac{5\left(k+2\right)-7}{6}=\frac{13-\left(4-k\right)}{9}$  

In the equation above, what is the value of k?

•  $\frac{9}{17}$  

•  $\frac{9}{13}$  

•  $\frac{33}{17}$  

•  $\frac{33}{13}$  

 $\frac{1}{2}x-\frac{1}{4}y=5$  
 $ax-3y=20$  

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

•  $\frac{1}{2}$  

•  $2$  

•  $6$  

•  $12$  

If  $\frac{1}{2}x+\frac{1}{3}y=4$ , what is the value of  $3x+2y$ ?  

 $4x-y=3y+7$  
 $x+8y=4$  

Based on the system of equations above, what is the value of the product xy?

•  $-\frac{3}{2}$  

•  $\frac{1}{4}$  

•  $\frac{1}{2}$  

•  $\frac{11}{9}$  

In 2014, County X had 783 miles of paved roads. Starting in 2015, the county has been building 8 miles of newly paved roads each year. At this rate, how many miles of paved road will County X have in 2030? (Assume that no paved roads go out of service.)

In 2014, County X had 783 miles of paved roads. Starting in 2015, the county has been building 8 miles of new paved roads each year. At this rate, if n is the number of years after 2014, which of the following functions f gives the number of miles of paved road there will be in County X? (Assume that no paved roads go out of service.)

• f(n) = 8 + 783n

• f(n) = 2,014 + 783n

• f(n) = 783 + 8n

• f(n) = 2,014 + 8n

A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?

• 8 + 3x, where x is the number of hours

• 3 + 8x, where x is the number of hours

• x(8 + 2) + 3, where x is the number of children

• 3 + (8 + 2)x, where x is the number of children

 $\frac{1}{2}x-\frac{1}{4}y=10$  

 $\frac{1}{8}x-\frac{1}{8}y=19$  

Which ordered pair (x,y) satisfies the system of equations above?

• (-112, -264)

• (64, 88)

•  $\left(\frac{232}{3},\frac{224}{3}\right)$  

• (288, 536)