PSAT - No calculator #1

Which of the following is an equivalent form of the expression 15x + 24ax ?

• 39ax²

• 39(a + 2x)

• (5 + 8a)x

• (5 + 8a)3x

Which of the following ordered pairs (x,y) satisfies both equations y = x² + 3x − 4 and x = y −4 ?

• (0,-4)

• (2,6)

• (3,14)

• (5,9)

Which of the following is a solution to the equation 2x² + 4x = 3 + 3x²?

• -1

• 0

• 3

• 6

The formula d = rt is used to calculate the distance an object travels over a period of time, t, at a constant rate, r. Based on this formula, what is the rate, r, in terms of d and t ?

• r = d/t

• r = dt

• r = t/d

• r = d - t

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 relates 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

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 a typical apple tree grows each year

A parachute design uses 18 separate pieces of rope. Each piece of rope must be at least 270 centimeters and no more than 280 centimeters long. What inequality represents all possible values of the total length of rope x, in centimeters, needed for the parachute?

• 270 ≤ x ≤ 280

• 4,860 ≤ x ≤ 4,870

• 4,860 ≤ x ≤ 5,040

• 5,030 ≤ x ≤ 5,040

In the equation below, a is a constant, for what value of a does the equation have an infinite number of solutions?

21x + 14 = 7(3x + a)

• 14

• 2

• 7

• 0

Juliene practiced her dance routine for twice as many minutes on Monday as she did on Tuesday. She practiced her routine those two days for a total of 2 hours and 15 minutes. For how many minutes did Juliene practice her dance routine on Monday?

• 60

• 45

• 120

• 90

In the equation below, a is an integer.

12x² + ax - 20

If 3x + 4 is a factor of this expression, what is the value of a?

• 1

• 4

• -1

• 0