New SAT Math Multiple Choice Practice Test 1

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1. Which of the following equations has a vertex of (3, -3) ?

  • A. y = 5(x - 3)2 - 3
  • B. y = 5(x + 3)2 - 3
  • C. y = 5(x - 3)2 + 3
  • D. y = 5(x + 3)2 + 3

2. A beverage store charges a base price of x dollars for one keg of root beer. A sales tax of a certain percentage is applied to the base price, and an untaxed deposit for the keg is added. If the total amount, in dollars, paid at the time of purchase for one keg is given by the expression 1.07x + 17, then what is the sales tax, expressed as a percentage of the base price?

  • A. 0.07%
  • B. 1.07%
  • C. 7%
  • D. 17%

3. Syed took out a cash advance of d dollars from a financing company. The company deducts a fee of of the original advanced amount along with a wire transfer fee of $30.00. Which of the following represents the final advanced amount that Syed receives after all applied fees, in dollars?

  • A. d - 30
  • B. (d - 30)
  • C. (d - 30)
  • D. d - 30

4. What is the equation of a line that contains the point (1, 6) and has a y-intercept of 4 ?

  • A. y = x + 4
  • B. y = x + 4
  • C. y = 2x + 4
  • D. y = 4x + 2

5. The number of bonus points, B(p), that a credit card holder receives is given by the function B(p) = 4p + 7, where p represents the number of purchases made. If the number of purchases is increased by 3, by how much does the number of bonus points increase?

  • A. 3
  • B. 4
  • C. 12
  • D. 19

6. Jeff tests how the total volume occupied by a fluid contained in a graduated cylinder changes when round marbles of various sizes are added. He found that the total volume occupied by the fluid, V, in cubic centimeters, can be found using the equation below, where x equals the number of identical marbles Jeff added, one at a time, to the cylinder, and r is the radius of one of the marbles.

If the volume of the graduated cylinder is 96π cubic centimeters, then, what is the maximum number of marbles with a radius of 3 centimeters that Jeff can add without the volume of the fluid exceeding that of the graduated cylinder?

  • A. 1
  • B. 2
  • C. 3
  • D. 4

7. If b is two more than one-third of c, which of the following expresses the value of c in terms of b ?

  • A. c =
  • B. c =
  • C. c = 3(b - 2)
  • D. c = 3(b - 6)

8. The rotation rate of a mixing blade, in rotations per second, slows as a liquid is being added to the mixer. The blade rotates at 1,000 rotations per second when the mixer is empty. The rate at which the blade slows is four rotations per second less than three times the square of the height of the liquid. If h is the height of liquid in the mixer, which of the following represents R(h), the rate of rotation?

  • A. 4 - 9h2
  • B. 1,000 - (4 - 3h)
  • C. 1,000 - (9h - 4)
  • D. 1,000 - (3h2 - 4)

9. A dental hygiene company is creating a new 24-ounce tube of toothpaste by combining its most popular toothpastes, Cavity Crusher and Bad Breath Obliterator. Cavity Crusher contains 0.25% of sodium fluoride as its active ingredient, and Bad Breath Obliterator contains 0.30% of triclosan as its active ingredient for a total of 0.069 ounces of active ingredients in both toothpastes. Solving which of the following systems of equations yields the number of ounces of Cavity Crusher, c, and the number of ounces of Bad Breath Obliterator, b, that are in the new toothpaste?

  • A. c + b = 0.069
    0.25c + 0.3b = 24
  • B. c + b = 24
    0.0025c + 0.003b = 0.069
  • C. c + b = 24
    0.025c + 0.03b = 0.069
  • D. c + b = 24
    0.25c + 0.3b = 0.069

10.

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

  • A. -4
  • B. 2
  • C. 4
  • D. 6

11. Which of the following is a possible equation for a circle that is tangent to both the x-axis and the line x = 4 ?

  • A. (x + 2)2 + (y + 2)2 = 4
  • B. (x + 2)2 + (y - 2)2 = 4
  • C. (x - 2)2 + (y + 4)2 = 4
  • D. (x - 6)2 + (y - 2)2 = 4

12. Reactant A is placed in a beaker, to which Reactant B will be added. Reactants A and B will not react unless B gets to a certain concentration. Once the reaction starts, both concentrations decrease until B has been consumed. Which of the following graphs, showing concentration in moles as a function of time in seconds, represents the reaction?

  • A.
  • B.
  • C.
  • D.

13. -2y ≤ 8
y - 3 ≤ x
-y + 1 ≥ x

Which of the following graphs shows the solution to the system of inequalities above?

  • A.
  • B.
  • C.
  • D.

14.

If rectangle ABCD has an area of 324 and the tangent of ∠BCA (not shown) is , then which of the following is closest to the length of BD (not shown)?

  • A. 9.8
  • B. 27
  • C. 29.5
  • D. It cannot be determined from the given information.

15. Which of the following is equivalent to ?

  • A.
  • B.
  • C.
  • D. m - 6