PSAT Practice 3-3

In the expression (ax + by)(cx - dy), a, b, c, and d are non-zero constants and ad = bc. If ac = 18 and bd = 50, what is the value of the coefficient of the xy term when the expression is multiplied out and the like terms are collected?

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

• -14

• -12

• -4

• 16

The equation y = 36 + 18x models the relationship between the height y, in inches, of a typical golden delicious apple tree and the number of years, x, after it was planted. If the equation is graphed in the xy-plane, what is indicated by the y-intercept of the graph?

• The age, in years, of a typical apple tree when it is planted

• The height, in inches, of a typical apple tree when it is planted

• The number of years it takes a typical apple tree to grow

• The number of inches of a typical apple tree grows each year

Giovanni wants to buy shirts that cost $19.40 each and sweaters that cost $24.80 each. An 8% sales tax will be applied to the entire purchase. If Giovanni buys 2 shirts, which equation related the number of sweaters purchased, p, and the total cost in dollars, y?

• 1.08(38.80 + 24.80p) = y

• 38.80 + 24.80p = 0.92y

• 38.80 + 24.80p = 1.08y

• 0.92(38.80 + 24.80p) = y

A line is graphed in the xy-plane. If the line has a positive slope and negative y-intercept, which of the following points cannot lie on the line?

• (-3, -3)

• (-3, 3)

• (3, -3)

• (3, 3)