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SAT Prep Help Mathematics Sample Questions Answer Explanations
1. The correct answer is (B), as the area of a rectangle can be determined by using the formula A = B * h or the formula A = l * w. This means that the area of a rectangle is equal to the length of the base of the rectangle multiplied by the height or width of the rectangle. Therefore, the area of the rectangle described in this question is equal to 7 inches * 9 inches or 63 in2. The other choices offered for this question are incorrect because they do not use the correct formula. (A) is incorrect because it simply offers the rectangle's height squared rather than using the appropriate formula. (C) is incorrect because it offers the perimeter of the rectangle rather than the area. (D) is incorrect because it offers the area of a triangle with a base of 7 inches and a height of 9 inches, and (E) is incorrect because it is simply the sum of the length and width.
2. The correct answer is (C), as the perimeter of a rectangle can be determined by using the formula P = 2 * (Side 1 + Side 2). This means that the perimeter of a rectangle can be determined by adding the length of the base of the rectangle to the height of the rectangle and multiplying by 2. Therefore, the perimeter of the rectangle described in this question is equal to 2 * (5 inches + 7 inches), or 24 inches. The other choices for this question are incorrect because they do not use the correct formula. (A) is incorrect because it simply offers the rectangle's height squared rather than using the appropriate formula. (B) is incorrect because it offers the area of the rectangle rather than the perimeter. (D) is incorrect because it offers the area of a triangle with a base of 5 inches and a height of 7 inches, and (E) is incorrect because it is simply the sum of the length and width.
3. The correct answer is (B), as a circle with a radius of 5 inches has a greater area than a circle with a diameter of 9 inches. This is because the area of a circle can be determined by using the formula A = Π * r2 and the radius of a circle is equal to half of the circle's diameter. Applying these common geometric formulas to the problem, this means that the radius of figure A is 4.5 inches and the radius of figure B, which is stated within the question, is 5 inches. Therefore, the area of figure A is equal to 3.14 * 4.52 or 63.585 and the area of figure B is equal to 3.14 * 52 or 78.5.
4. The correct answer is (B), as the volume of a rectangular box can be determined using the formula V = l * w * h. This means that the volume of a rectangular box can be determined by multiplying the length of the base of the box by the width of the box and multiplying that product by the height of the box. Therefore, the volume of the box described in this question is equal to 5 * 7 * 9, or 315 in3. (A) is incorrect because it provides the volume of a cylinder with a diameter of 9 inches and a height of 7 inches. (C) is incorrect because it provides the area of a rectangle with a base of 5 inches and a width of 9 inches. (D) is incorrect because it states the area of a rectangle with a base of 5 inches and a width of 7 inches, and (E) is incorrect because it states the sum of the length, width, and height rather than the product of length, width, and height.
5. The correct answer is (A), as the volume of a cylinder can be determined using the formula V = ? * r2 * h. This means that the volume of a cylinder is equal to Π times the radius of the cylinder squared times the height of the cylinder. The radius of a cylinder is equal to half of the cylinder's diameter, so the radius of this particular cylinder is 4.5 in. Therefore, the volume of this cylinder is equal to 3.14 * 4.52 * 7, or 445.095 in3. (B) is incorrect because it states the volume of a rectangular box with a length of 5 inches, a height of 7 inches, and a width of 9 inches. (C) is incorrect because it refers to the diameter of the cylinder times the height of the cylinder multiplied by Π. (D) is incorrect because it refers to the diameter of the cylinder multiplied by the height of the cylinder, and (E) is incorrect because it states the sum of the cylinder's diameter and height.
6. The variable x for this set of equations is equal to 3. The easiest way to determine the value of x for these equations is to isolate the x in each equation. In the first equation, this can be done by moving the 6 and 7 to the other side of the equation by adding 7 to 11 and dividing by 6. This can also be done in the second equation by moving the 4, 8, and 2 to the other side of the equation by adding 8 to 6, subtracting 2 from 6, and then dividing by 4. Therefore, the formula for determining x for the first equation would be x = (11 + 7) /6, or x = 3. The formula for determining x in the second equation would be x = (6 + 8 - 2) /4, or x = 3.
7. The variable x for this set of equations is equal to -1. This is because the first equation states that the absolute value of 4x - 3 is equal to 7, which means that 4x - 3 is equal to 7or -7. Therefore, the formula for determining x for the first equation is x = (7 + 3) / 4 or x = (-7 + 3) / 4. As a result, the x in the first equation must be equal to 2.5 or -1. The second equation states that the absolute value of 2x + 2 = 0, which means that 2x + 2 must be equal to 0 because the absolute value of 0 is 0. Therefore, the formula for determining x for the second equation is x = (0 - 2) / 2, so x must equal -1. Since both equations will work with x as -1, the correct solution to the problem is that x is equal to -1.
8. The automotive plant will have to order 125 parts in order to fill all of the orders for this scheduling period. This is because F is the number of parts required to fill the orders, x is the number of days, p is the number of parts that the plant uses on average each day, b is the number of parts that the plant has on hand for the period, and d is the number of defects that they expect. Therefore, the solution to this problem can be determined simply by plugging the numbers into the equation. The manufacturing period is five days long, so x = 5; the plant uses 15 parts per day, so p = 15; the plant has 50 parts on hand, so b = 50; and the plant expects 5 defects per day, so d = 5. Therefore, F(5) = 5 *2(15) - (50 - 5 * 5), or 125.
9. The correct answer is (D). The probability of drawing an ace on the first draw from the deck is 1/13 and the probability of drawing the ace of spades on the first draw from the deck is 1/52. The probability of drawing an ace on the first draw can be determined by dividing the number of aces in the deck by the number of cards in the deck. Since there are four aces in a deck of cards, and 52 cards in a deck, the probability of drawing an ace on the first card is 4/52, or 1/13. The probability of drawing the ace of spades, on the other hand, is 1/52 because there is only one ace of spades in each 52-card deck.
10. The correct answer is (D), or 1/221. This answer indicates the probability of drawing two aces when two cards are drawn from a deck and the first card is not replaced. It is the lack of a replacement for the first card drawn that decreases the probability of drawing a second ace from the deck. When a poker player draws two cards without replacing the first card drawn, and one of those cards is an ace, the probability of drawing a second ace from the deck is equal to the probability of drawing the first ace multiplied by the probability of drawing the second ace. The probability of drawing the first ace is 4/52, or 1/13. Since one of the aces is removed from the deck in the first draw, the probability of drawing the second ace is only 3/51, or 1/17. As a result, the probability of drawing both aces within the context of the first two cards drawn is 1/13 * 1/17, or 1/221.