Free Sample SAT Math

Choice is correct. Using the property that for positive numbers x and y, with and , it follows that . By rewriting as , it is possible to simplify the square root expression as follows: .

Choice is incorrect and may be the result of .

Choice is incorrect and may be the result of incorrectly rewriting as .

Choice is incorrect and may be the result of incorrectly applying properties of exponents.

Choice Two is correct. It is given that the constants a and c are both positive; therefore, the graph of the given quadratic equation is a parabola that opens up with a vertex on the y-axis at a point below the x-axis. The graph of the second equation provided is a horizontal line that lies above the x-axis. A horizontal line above the x-axis will intersect a parabola that opens up and has a vertex below the x-axis in exactly two points.

Choices Zero, One, and More than two are incorrect and are the result of not understanding the relationships of the graphs of the two equations given. Choice Zero is incorrect because the two graphs intersect. Choice One is incorrect because in order for there to be only one intersection point, the horizontal line would have to intersect the parabola at the vertex, but the vertex is below the x-axis and the line is above the x-axis. Choice More than two is incorrect because a line cannot intersect a parabola in more than two points.

Choice 750 is correct. Adding the like terms x and yields the equation . Substituting 20 for x yields . The product is equal to 25, and the difference is equal to 30. Substituting these values in the given equation gives , and multiplying 25 by 30 results in .

Choices 250, 500, and 2,000 are incorrect and may result from conceptual or computational errors when finding the value of .

The correct answer is 1.5. The total amount, in liters, of a saline solution can be expressed as the liters of each type of saline solution multiplied by the percent concentration of the saline solution. This gives 3(0.10), x(0.25), and (x + 3)(0.15), where x is the amount, in liters, of 25% saline solution and 10%, 15%, and 25% are represented as 0.10, 0.15, and 0.25, respectively. Thus, the equation 3(0.10) + 0.25x = 0.15(x + 3) must be true. Multiplying 3 by 0.10 and distributing 0.15 to (x + 3) yields 0.30 + 0.25x = 0.15x + 0.45. Subtracting 0.15x and 0.30 from each side of the equation gives0.10x = 0.15. Dividing each side of the equation by 0.10 yields x = 1.5. Note that 1.5 and 3/2 are examples of ways to enter a correct answer.

Choice 50 is correct. The two diagonals of square ABCD divide the square into 4 congruent right triangles, where each triangle has a vertex at the origin of the graph shown. The formula for the area of a triangle is , where b is the base length of the triangle and h is the height of the triangle. Each of the 4 congruent right triangles has a height of 5 units and a base length of 5 units. Therefore, the area of each triangle is , or 12.5 square units. Since the 4 right triangles are congruent, the area of each is of the area of square ABCD. It follows that the area of the square ABCD is equal to 4 x 12.5, or 50 square units.

Choices 20 and 100 are incorrect and may result from using 5 or 25, respectively, as the area of one of the 4 congruent right triangles formed by diagonals of square ABCD. However, the area of these triangles is 12.5.

Choice 25 is incorrect and may result from using 5 as the length of one side of square ABCD. However, the length of a side of square ABCD is .

Choice 9 is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and is a central angle of the circle. From the figure, the two diameters that meet to form are perpendicular, so the measure of is 90°. Therefore, the length of minor arc AC is of the circumference of the circle. Since the circumference of the circle is 36, the length of minor arc AC is .

Choices 12, 18, and 36 are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc AC is of the circumference. However, the lengths in choices 12 and 18 are, respectively, and the circumference of the circle, and the length in choice 36 is the length of the entire circumference. None of these lengths is the circumference.

The correct answer is 4.5. According to the properties of right triangles, BD divides triangle ABC into two similar triangles, ABD and BCD. The corresponding sides of ABD and BCD are proportional, so the ratio of BD to AD is the same as the ratio of DC to BD. Expressing this information as a proportion gives . Solving the proportion for DC results in DC = 4.5. Note that 4.5 and 9/2 are examples of ways to enter a correct answer.

The correct answer is 4. Triangle PQR has given angle measures of 30° and 90°, so the third angle must be 60° because the measures of the angles of a triangle sum to 180°. For any special right triangle with angles measuring 30°, 60°, and 90° the length of the hypotenuse (the side opposite the right angle) is 2x, where x is the length of the side opposite the 30° angle. Segment PQ is opposite the 30° angle. Therefore, 2(PQ) = 8 and PQ = 4.

Choice 13t is correct. It's given that the ratio z to y is equivalent to the ratio 12 to t. This can be represented by .  Substituting 156 for x in this equation yields . This can be rewritten as 12y = 156t. Dividing both sides of this equation by 12 yields y = 13t. Therefore, when x = 156, the value of y in terms t of is 13t. 

Choice 12t is incorrect and may result from conceptual or calculation errors. 

Choice 144t is incorrect and may result from conceptual or calculation errors. 

Choice 168t is incorrect and may result from conceptual or calculation errors.

Choice 1.5 is correct. The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points (20, 34) and (30, 48) are on the line of best fit, and the slope of the line that passes through them is , or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.

Choices 2.5, 2.0, and 1.0 are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.