Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4. c squared equals a squared plus b squared. Special Right Triangles Reference figure 5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x. Reference figure 6 is a triangle with two 45degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2. Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7. V equals ℓ w h. Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8. V equals pi times the square of r times h. Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9. V equals fourthirds pi times the cube of r. Reference figure 10 is a cone base has radius r and whose height is h. An equation is presented below reference figure 10. V equals onethird times pi times the square of r times h. Reference figure 11 is an asymmetrical pyramid base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11. V equals onethird ℓ w h. End skippable figure descriptions. Additional Reference Information The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2 pi.
John runs at different speeds as part of his training program. The graph shows his target heart rate at different times during his workout. On which interval is the target heart rate strictly increasing then strictly decreasing? A. Between 0 and 30 minutes B. Between 40 and 60 minutes C. Between 50 and 65 minutes D. Between 70 and 90 minutes Answer and explanation for . Question 2. If y equals k x where k is a constant, and y equals 24 when x equals 6, what is the value of y when x equals 5 ? A. 6 B. 15 C. 20 D. 23 Answer and explanation for . Question 3 is based on the following figure. Begin skippable figure description. The figure presents two horizontal lines ℓ and m with line ℓ above line m, and two lines s and t that are slanted upward and to the right with line s to the left of line t. Lines s and t intersect lines ℓ and m. The angle above line ℓ and to the right of line t is labeled 1, and the angle above line m and to the left of line s is labeled 2.
Questions 9 through 10 refer to the following information. a equals 1,052 plus 1.08 t The speed of a sound wave in air depends on the air temperature. The preceding formula shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit parenthesis, degrees F, close parenthesis. Question 9. of the following expresses the air temperature in terms of the speed of a sound wave? A. t equals the fraction numerator is a, minus 1,052, and whose denominator is 1.08. B. t equals the fraction whose numerator is a, plus 1,052, and whose denominator is 1.08. C. t equals the fraction whose numerator is 1,052 minus a, and whose denominator is 1.08. D. t equals the fraction numerator is 1.08, and whose denominator is a, plus 1,052. Answer and explanation for . Question 10. At of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second? A. negative 46 degrees F B. negative 48 degrees F C. negative 49 degrees F D. negative 50 degrees F
increasing. Choice D is incorrect, because the graph over the interval between 70 and 90 minutes contains horizontal line segments and no segment with a negative slope. Explanation for . Choice C is correct. Substituting 6 for x and 24 for y in y equals k x 24 equals, parenthesis, k, close parenthesis, times, parenthesis, 6, close parenthesis, which gives k equals 4. Hence, y equals 4 x. Therefore, when x equals 5 the value of y is parenthesis, 4, close parenthesis, times, parenthesis, 5, close parenthesis, equals 20. None of the other choices for y are correct because y is a function of x, and so there is only one yvalue for a given xvalue. Choice A is the result of using 6 for y and 5 for x when solving for k. Choice B results from using a value of 3 for k when solving for y. Choice D results from using y equals k plus x instead of y equals k x. Explanation for . Choice D is correct. Consider the measures of 3 and angle 4 in the following figure. Begin skippable figure description. The figure presents two horizontal lines, ℓ and m, with line ℓ above line m, and two lines, s and t, that are slanted upward and to the right, with line s to the left of line t. Lines s and t intersect lines ℓ and m. The angle above line ℓ and to the right of line t is labeled 1 and the angle above line m and to the left of line s is labeled 2. End skippable figure description. The measure of angle 3 is equal to the measure of angle 1 because they are corresponding angles for the parallel lines ℓ and m intersected by the transversal line t. Similarly, the measure of angle 3 is equal to the measure of angle 4 because they are corresponding angles for the parallel lines s and t intersected by the transversal line m. Since the measure of angle 1 is 35 degrees, the measures of angle 3 and angle 4 are
also 35 degrees. Since angle 4 and angle 2 are supplementary, the sum of the measures of these two angles is 180 degrees. Therefore, the measure of angle 2 is 180 degrees minus 35 degrees equals 145 degrees. Choice A is incorrect because 35 degrees is the measure of angle 1, and angle 1 is not congruent to angle 2. Choice B is incorrect because it is the measure of the complementary angle of angle 1, and angle 1 and angle 2 are not complementary angles. Choice C is incorrect because it is double the measure of angle 1. Explanation for . Choice C is correct. The description “ 16 plus 4 x is 10 more than 14” can be written as the equation 16 plus 4 x, equals 10 plus 14, which is equivalent to 16 plus 4 x equals 24. Subtracting 16 from each side of 16 plus 4 x equals 24 gives 4 x equals 8. Since 8 x is 2 times 4 x, multiplying both sides of 4 x equals 8 by 2 gives 8 x equals 16. Therefore, the value of 8 x is 16. Choice A is incorrect because it is the value of x, not 8 x. Choices B and D are incorrect; those choices may be a result of errors in rewriting 16 plus 4 x, equals 10 plus 14. For example, choice D could be the result of subtracting 16 from the left side of the equation and adding 16 to the right side of 16 plus 4 x, equals 10 plus 14, giving 4 x equals 40 and 8 x equals 80. Explanation for . Choice D is correct. A graph with a strong negative association between d and t would have the points on the graph closely aligned with a line that has a negative slope. The more closely the points on a graph are aligned with a line, the stronger the association between d and t, and a negative slope indicates a negative association. Of the four graphs, the points on graph D are most closely aligned with a line with a negative slope. Therefore, the graph in choice D has the strongest negative association between d and t. Choice A is incorrect because the points are more scattered than the points on choice D, indicating a weak negative association between d and t. Choice B is incorrect because the
points are aligned to either a curve or possibly a line with a small positive slope. Choice C is incorrect because the points are aligned to a line with a positive slope, indicating a positive association between d and t. Explanation for . Choice D is correct. Since there are 10 grams in 1 decagram, there are 2 times 10, equals 20 grams in 2 decagrams. Since there are 1,000 milligrams in 1 gram, there are 20 times 1,000, equals 20,000 milligrams, in 20 grams. Therefore, 20,000 1-milligram doses of the medicine can be stored in a 2decagram container. Choice A is incorrect; 0.002 is the number of in 2 milligrams. Choice B is incorrect; it could result from multiplying by 1,000 and dividing by 10 instead of multiplying by both 1,000 and 10 when converting from decagrams to milligrams. Choice C is incorrect; 2,000 is the number of milligrams in 2 grams, not the number of milligrams in 2 decagrams. Explanation for . Choice C is correct. Let x represent the number of installations that each unit on the yaxis represents. Then 9 x, 5 x, 6 x, 4 x, and 3.5 x are the number of rooftops with solar panel installations in cities A, B, C, D, and E, respectively. Since the total number of rooftops is 27,500, it follows that 9 x plus 5 x, plus 6 x plus 4 x, plus 3.5 x, equals 27,500, which simplifies to 27.5 x equals 27,500. Thus, x equals 1,000. Therefore, an appropriate label for the yaxis is “Number of installations (in thousands).” Choices A, B, and D are incorrect and may result from errors when setting up and calculating the for the yaxis. Explanation for . Choice D is correct. If the value of the absolute value of n minus 1, end absolute value, plus 1, is equal to 0, then the absolute value of n minus 1, end absolute value, plus 1, equals 0. Subtracting 1 from both sides of this equation gives the absolute value of n