Free Sample PSAT Math

The correct answer is 4. The equation 60h + 10 ≤ 280, where h is the number of hours the boat has been rented, can be written to represent the situation. Subtracting 10 from both sides and then dividing by 60 yields h ≤ 4.5. Since the boat can be rented only for whole numbers of hours, the maximum number of hours for which Maria can rent the boat is 4.

Choice If 24 triangles were constructed, then 73 rectangles were constructed is correct. It's given that 364 paper straws of equal length were used to construct triangles and rectangles, where no two polygons had a common side. It's also given that the equation 3x + 4y = 364 represents this situation, where x is the number of triangles constructed and y is the number of rectangles constructed. The equation (x, y) = (24, 73) means that if x = 24, then y = 73. Substituting 24 for x and 73 for y in 3x + 4y = 364 yields 3(24) + 4(73) = 364, or 364 = 364, which is true. Therefore, in this context, the equation (x, y) = (24, 73) means that if 24 triangles were constructed, then 73 rectangles were constructed.

Choice If 24 triangles were constructed, then 73 paper straws were used is incorrect and may result from conceptual errors.

Choice If 73 triangles were constructed, then 24 rectangles were constructed is incorrect and may result from conceptual errors.

Choice If 73 triangles were constructed, then 24 paper straws were used is incorrect and may result from conceptual errors.

Choice The team will have moved all the cargo in about 4.8 hours is correct. The x-intercept of the line with equation y = 120 – 25x can be found by substituting 0 for y and finding the value of x. When y = 0, x = 4.8, so the x-intercept is at (4.8, 0). Since y represents the number of tons of cargo remaining to be moved x hours after the team started working, it follows that the x-intercept refers to the team having no cargo remaining to be moved after 4.8 hours. In other words, the team will have moved all of the cargo after about 4.8 hours.

Choice The team has been moving about 4.8 tons of cargo per hour is incorrect and may result from incorrectly interpreting the value 4.8.

Choices The team has been moving about 25 tons of cargo per hour and The team started with 120 tons of cargo to move are incorrect and may result from misunderstanding the x-intercept. These statements are accurate but not directly relevant to the x-intercept.

Choice 12 is correct. Let x represent the number of children in a whale-watching tour group. Let y represent the number of adults in this group. Because it's given that 21 people are in a group and the group consists of adults and children, it must be true that x + y = 21. Since the company's revenue is 60 dollars per child, the total revenue from a children in this group was 60x dollars. Since the company's revenue is 80 dollars per adult, the total revenue from y adults in this group was 80y dollars. Because it's given that the total revenue for this group was 1,440 dollars, it must be true that 60 + 80y = 1,440. The equations x + y = 21 and 60x + 80y = 1,440 form a linear system of equations that can be solved to find the value of x, which represents the number of children in the group, using the elimination method. Multiplying both sides of the equation x + y = 21 by 80 yields 80 + 80y= 1,680. Subtracting 60x +80y = 1,440 from 80 + 80y= 1,680 yields (80x + 80y) - (60x + 80y) = 1,680 - 1,440, which is equivalent to 80x - 60x + 80y - 80y = 240, or 20x = 240. Dividing both sides of this equation by 20 yields x = 12. Therefore, 12 people in the group were children.

Choice 3 is incorrect and may result from conceptual or calculation errors.

Choice 9 is incorrect. This is the number of adults in the group, not the number of children in the group.

Choice 18 is incorrect and may result from conceptual or calculation errors.

Choice 16 is correct. The value of f(144) is the value of f(x) wen x = 144. It's given that the function f is defined by . Substituting 144 for x in this equation yields . Since the positive square root of 144 is 12, it follows that this equation can be rewritten as , or f(144) = 16. Therefore, the value of f(144) is 16.

Choice 0 is incorrect and may result from conceptual or calculation errors.

Choice 40 is incorrect. This is the value of f(1,296), not ƒ(144).

Choice 76 is incorrect. This is the value of f(5,184), not f(144).

The correct answer is either 7, 8, or 13. Since the given equation has two integer solutions, the expression on the left-hand side of this equation can be factored as (x + c)(x + d), where c and d are also integers. The product of c and d must equal the constant term of the original quadratic expression, which is 12. Additionally, the sum of c and d must be a negative number since it's given that a > 0, but the sign preceding a in the given equation is negative. The possible pairs of values for c and d that satisfy both of these conditions are -4 and -3, -6 and -2, and -12 and -1. Since the value of -a is the sum of c and d, the possible values of -a are -4 + (-3) = -7, -6 + (-2) = -8, and 12 + (-1) = -13. It follows that the possible values of a are 7, 8, and 13. Note that 7, 8, and 13 are examples of ways to enter a correct answer.

Choice 111° is correct. The sum of the angle measures of a triangle is 180°. Adding the measures of angles B and C gives 52 + 17 = 69°. Therefore, the measure of angle A is 180 - 69 = 111°.

Choice 21° is incorrect and may result from subtracting the sum of the measures of angles B and C from 90°, instead of from 180°.

Choice 35° is incorrect and may result from subtracting the measure of angle C from the measure of angle B.

Choice 69° is incorrect and may result from adding the measures of angles B and C but not subtracting the result from 180°.

Choice is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length c and legs with lengths a and b, then . In the right triangle shown, the hypotenuse has length c and the legs have lengths a and b. It's given that a = 4 and b = 5. Substituting 4 for a and 5 for b in the Pythagorean theorem yields . Taking the square root of both sides of this equation yields . Since the length of a side of a triangle must be positive, the value of c is .

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

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

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

The correct answer is .54. It's given that the number a is 70% less than the positive number b. Therefore, , which is equivalent to a = (1 - 0.70)b, or a = 0.30b. It's also given that the number c is 80% greater than a. Therefore, , which is equivalent to c = (1 + 0.80)a, or c = 1.80a. Since a = 0.30b, substituting 0.30b for a in the equation c = 1.80a yields c = 1.80(0.30b), or c = 0.54b. Thus, c is 0.54 times b. Note that .54 and 27/50 are examples of ways to enter a correct answer.

Choice 8.2 is correct. On the line of best fit, an x-value of 25.5 corresponds to a y-value between 8 and 8.5. Therefore, at x = 25.5, 8.2 is closest to the y-value predicted by the line of best fit.

Choice 6.2 is incorrect and may result from conceptual errors.

Choice 7.3 is incorrect and may result from conceptual errors.

Choice 9.1 is incorrect and may result from conceptual errors.