PSAT Advanced & Additional Math Practice (calculator)

The figure shows the graph of r(x). Which of the following cannot be a value of x for which r(x) = 0 ?

• -3

• -2

• 2

• 5

A construction company plans to build a long row of houses, each with a certain number of brown shingles on its roof. The number of brown shingles on a house’s roof, f (h), is a function of its house number, h. The first few houses are shown here. If only brown shingles are used, how many shingles will the seventh house have?

• 7

• 27

• 46

• 60

The function f(x) = (x − 4)² is shown here. Which of the following correctly depicts the transformation g(x) = (–x + 2) + 3?

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• 
• 
• 

If f (x) = –x + 5 and g(x) = x ², which of the following is not in the range of f (g(x)) ?

• -11

• 0

• 1

• 9

 $x^2+y^2=5$  
 $y=x^2-3$  
 $x-y=1$  

A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?

• one

• two

• three

• four

A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2014 was estimated to be 50 animals. If P represents the population n years after 2014, then which of the following equations represents the class’s model of the population over time?

• $P=12+50n$
  

• $P=50+12n$
  

• $P=50\left(2\right)^{12n}$

• $P=50\left(2\right)^{\frac{n}{12}}$

In the figure above,  $\Delta ABC\sim\Delta EDC$ .  

Which of the following must be true?

•  $\overline{AE}\ \parallel\overline{BD}$  

•  $\overline{AE}\ \perp\ \overline{BD}$  

•  $\overline{AB}\ \parallel\overline{DE}$  

•  $\overline{AB}\ \perp\ \overline{DE}$  

 $x^2+y^2=153$  
 $y=-4x$  

If (x,y) is a solution to the system of equations above, what is the value of  $x^2$  ?

• -51

• 3

• 9

• 144

The figure shows a metal hex nut with two regular hexagonal faces and a thickness of 1 cm. The length of each side of a hexagonal face is 2 cm. A hole with a diameter of 2 cm is drilled through the nut. The density of the metal is 7.9 grams per cubic cm. What is the mass of this nut, to the nearest gram? (Density is mass divided by volume.)

The function f is defined by  $f\left(x\right)=2x^3+3x^2+cx+8$   where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (-4,0), and  $\left(\frac{1}{2},0\right)$ . What is the value of c?

• -18

• -2

• 2

• 10