Drill 1 · Math · Geometry and Trigonometry
SAT Math: Geometry and Trigonometry (Drill 1) is a Math practice drill covering Geometry and Trigonometry. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.
SAT geometry and trigonometry questions cover area and perimeter of polygons, volume of three-dimensional solids, properties of triangles, circle equations, and basic sine, cosine, and tangent ratios. This drill applies these concepts in both pure and real-world contexts.
Question 1. A triangle has a base of 12 centimeters and a height of 9 centimeters. What is the area of the triangle, in square centimeters?
Explanation: Area of a triangle = (1/2) × base × height = (1/2)(12)(9) = 54 square centimeters. Choice D (108) is the result if you forget to multiply by 1/2.
Question 2. A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?
Explanation: By the Pythagorean theorem: c² = 5² + 12² = 25 + 144 = 169. So c = √169 = 13. The triple 5-12-13 is one of the most common Pythagorean triples on the SAT.
Question 3. A cylinder has a radius of 3 inches and a height of 10 inches. What is the volume of the cylinder?
Explanation: Volume of a cylinder = πr²h = π(3)²(10) = π(9)(10) = 90π cubic inches.
Question 4. In a right triangle, the side opposite angle θ has length 8 and the hypotenuse has length 17. What is the value of cos θ?
Explanation: First find the adjacent side: adjacent = √17² − 8² = √289 − 64 = √225 = 15. Cosine = adjacent/hypotenuse = 15/17. Choice A (8/17) is the sine, not the cosine.
Question 5. The equation (x − 2)² + (y + 3)² = 25 represents a circle in the xy-plane. What is the radius of the circle?
Explanation: The standard form is (x − h)² + (y − k)² = r². Here r² = 25, so r = 5. Choice D (25) is r², not r. The center is (2, −3).