SAT geometry part 2 Mastering Geometry: SAT Geometry Quiz - part 2The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experiencePlease note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.Each question is meticulously crafted to mirror the complexity and diversity of geometric problem-solving you'll encounter in the SAT.Use it as a targeted practice tool to identify and address specific areas of improvement.Track your progress and see your geometric proficiency grow. 1. If sin A = b, what is the value of the product sin A · cos A · tan A in terms of b? 1 b² 1/b b None 2. A lamp shade with a circular base is an example of a solid shape called a frustrum. In the figure above, the shaded region represents a frustrum of a right cone in which the portion of the original cone that lies 12 inches below its vertex has been cut off by a slicing plane (not shown)parallel to the base. If the height and slant height of the frustrum are 8 inches and 10 inches, respectively, what is the number of inches in the radius length, R, of the original cone? 15 9 18 12 None 3. A wedge-shaped piece is cut from a circular pizza. The radius of thepizza is 14 inches and the angle of the pointed end of the pizzameasures 0.35 radians. The number of inches in the length of therounded edge of the crust is closest to which value? 4.0 7.5 4.9 5.7 None 4. The dimensions of a rectangular box are integers greater than 1. If thearea of one side of this box is 12 and the area of another side is 15,what is the volume of the box? 40 23 60 56 None 5. What are the coordinates of the image of the point (1, 0) on theterminal side of an angle after a clockwise rotation of π/6 radians? $$\left ( \frac{1}{2},\frac{1}{2} \right )$$ $$\left ( \frac{1}{2},\frac{\sqrt{3}}{2} \right )$$ $$\left ( \frac{\sqrt{3}}{2},\frac{1}{2} \right )$$ $$\left ( -\frac{\sqrt{3}}{2},1 \right )$$ None 6. If x is a positive acute angle and cos x = a, an expression for tan x interms of a is $$\sqrt{1-a^{2}}$$ $$\frac{1}{1-a}$$ $$\frac{\sqrt{1-a^{2}}}{a}$$ $$\frac{1-a}{a}$$ None 7. The path traveled by a roller coaster is modeled by the equation y = 27sin 13x + 30 where y is measured in meters. What is the number ofmeters in the maximum altitude of the roller coaster? 30 27 57 13 None 8. Which of the following expressions is equivalent to \(\frac{\sin ^{2}x}{1+\cos x}\) 1 − sin x sin x − cos x 1 − cos x sin x + cos x None 9. If cos θ =–3/4 and tan θ is negative, the value of sin θ is $$\frac{\sqrt{7}}{4}$$ $$-\frac{\sqrt{7}}{5}$$ $$-\frac{4}{5}$$ $$\frac{4\sqrt{7}}{7}$$ None 10. What is the number of radians through which the minute hand of aclock turns in 24 minutes? 0.2π 0.8π 0.6π 0.4π None 11. The bottom of a pendulum traces an arc 3 feet in length when thependulum swings through an angle of 1/2 radian. What is the number offeet in the length of the pendulum? 1.5/π 1.5 6π 6 None 12. The height of sand in a cylinder-shaped can drops 3 inches when 1cubic foot of sand is poured out. What is the diameter, in inches, of thecylinder?2/√π 2/√π 48/√π 16/π 4/√π None 13. A planned building was going to be 100 feet long, 75 feet deep, and 30feet high. The owner decides to increase the volume of the building by10% without changing the dimensions of the depth and the height.What will be the new length of this building in feet? 110 133 122 111 None 14. If 0<x, y<π/2 , and sin x = cos y, then which of the statements below mustbe true?I. x = yII. 2(x + y) = πIII. cos x = sin y II and III only I and II only III only II only None 15. What is the radian measure of the smaller angle formed by the handsof a clock at 7 o’clock? 2π/3 π/2 5π/6 7π/6 2π/3 None 16. In the figure above, θ is an angle in standard position and its terminal side passes through the point \(p\left (-\frac{1}{2},\frac{\sqrt{3}}{2} \right )\) on the unit circle. What is a possible value of θ? $$\frac{2}{3}\pi $$ $$\frac{7}{6}\pi $$ $$\frac{5}{6}\pi $$ $$\frac{4}{3}\pi $$ None 17. A hot water tank with a capacity of 85.0 gallons of water is beingdesigned to have the shape of a right circular cylinder with a diameter1.8 feet. Assuming that there are 7.48 gallons in 1 cubic foot, how highin feet will the tank need to be? 5.00 5.25 4.50 4.75 None 18. The Parkside Packing Company needs a rectangular shipping box. Thebox must have a length of 1 foot, a width of 8 inches, and a volume ofat least 700 cubic inches. What is the least number of inches in heightof the box such that the height is a whole number? 3 5 8 2 None 19. By law, a wheelchair service ramp may be inclined no more than4.76°. If the base of a ramp begins 15 feet from the base of a publicbuilding, which equation could be used to determine the maximumheight, h, of the ramp where it reaches the building’s entrance? h=15 tan 4.76° h=15 sin 4.76° $$h= \frac{\tan 4.76°}{15}$$ $$h= \frac{15}{\sin 4.76°}$$ None 20. A box is constructed by cutting 3-inch squares from the corners of asquare sheet of cardboard, as shown in the accompanying diagram, andthen folding the sides up. If the volume of the box is 75 cubic inches,find the number of square inches in the area of the original sheet ofcardboard. 21 11 121 12 None 21. A rectangular fish tank has a base 2 feet wide and 3 feet long. Whenthe tank is partially filled with water, a solid cube with an edge lengthof 1 foot is placed in the tank. If no overflow of water from the tank isassumed, by how many inches will the level of the water in the tankrise when the cube becomes completely submerged? 3 1/2 1/6 2 None 22. Sophie has a hard rubber ball whose circumference measures 13inches. She wants to store it in a box. What is the number of cubicinches in the volume of the smallest cube-shaped box with integerdimensions that she can use? 81 125 64 216 None 23. What is the volume, in cubic inches, of the frustrum? 812π 1089π 324π 1,176π None 24. A wheel has a radius of 18 inches. The distance, in inches, the wheeltravels when it rotates through an angle of 2/5 π radians is closest towhich value? 13 23 11 45 None 25. The unit circle above has radius OC, angle AOB measures w radians,BA is tangent to circle O at A, and CD is perpendicular to the x-axis.The length of which line segment represents sin w? $$\bar{OB}$$ $$\bar{CD}$$ $$\bar{OD}$$ $$\bar{AB}$$ None 26. The density of lead is approximately 0.41 pounds per cubic inch. Whatis the approximate mass, in pounds, of a lead ball that has a 5 inchdiameter? 26.8 80.4 214.7 78.5 None 27. In the unit circle above, an angle that measures 4 radians intercepts arc AB. What is the length of major arc AB? $$\frac{\pi+2}{4}$$ 4 $$\frac{\pi}{2}$$ $$\frac{4}{\pi}$$ None 28. A flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 12 feet above the ground and form a right angle with each other. Cable r is attached to the ground at a point that makes tan x = 0.75.What is the value of cos x? 1.5 0.8 1.2 1.6 None 29. In the figure above, if the edge length of the cube is 4, what is the shortest distance from A to D? 4√2 4√2 +4 8 4√3 None 30. A rod 6 inches long is pivoted at one end. If the free end of the rodrotates in a machine at the rate of 165 revolutions per minute, what isthe total distance, in inches, traveled by the end of the rod in onesecond? 16.5π 29π 14.5π 33π None Time's up Please Share This Share this content Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Leave a Reply Cancel replyCommentEnter your name or username to commentEnter your email address to commentEnter your website URL (optional) Save my name, email, and website in this browser for the next time I comment.
