SAT Math Grid-ins Practice Test 34

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Question 9 questions

Time 13 minutes

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1.

In the figure above, the ratio of the circumference of circle B to the length of minor arc AC is 8:1. What is the value of x?

2. A cube and a rectangular solid are equal in volume. If the lengths of the edges ofthe rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

3. What is the maximum number of boxes with dimensions 2 inches by 3 inches by 4 inchesthat could fit in a cube-shaped container that has a volume of 1 cubic foot?

4. A solid, cone-shaped lead crystal paperweight has a height of 5 centimeters and abase diameter that is 20% larger than the height. If the density of lead crystal is3.1 g/cm3, what is the approximate mass of the paperweight? Round your answer to the nearestgram.

5. A rectangular block with a volume of 250 cubic inches is sliced into two cubes ofequal volume. How much greater, in square inches, is the combined surface area ofthe two cubes than the surface area of the original rectangular block?

6.

A locking pin is often made using a cylinder-cylinder pair in which a narrow cylinderfits tightly inside a wider cylinder. The inner cylinder protrudes from the outercylinder, usually by equal amounts on both ends. In the diagram above, the radiusof the inner cylinder is half the radius of the outer cylinder, and it protrudes fromthe outer cylinder by 4 centimeters on each end. What is the volume of the lockingpin? Round your answer to the nearest cubic centimeter.

7. In a right triangle, one angle measures x°, where sin x° =. What is cos(90° - x°)?

8. The angles of a triangle are in the ratio 1:2:3. What is the sine of the smallestangle?

9. In triangle XYZ (not shown), the measure of ∠Y is 90°, YZ = 12, and XZ = 15. Triangle HJK is similar to triangle XYZ, where vertices H, J, and K correspond to vertices X, Y, and Z, respectively, and each side of triangle HJK isthe length of the corresponding side of triangle XYZ. What is the value of tan K?