PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry Syllabus

Math: Geometry and Trigonometry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Math: Geometry and Trigonometry in PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test), not a summary of it.

1. 1

   Lines, Angles, and Triangles

   3 topics

   • Angle Relationships
     • Vertical, complementary, and supplementary angles
     • Angles formed by parallel lines and a transversal
   • Triangle Properties
     • Triangle angle sum and exterior angles
     • Similar and congruent triangles
   • The Pythagorean Theorem
     • Finding side lengths in right triangles
2. 2

   Area, Perimeter, and Volume

   3 topics

   • Area and Perimeter of Plane Figures
     • Triangles, quadrilaterals, and composite shapes
   • Volume and Surface Area of Solids
     • Prisms, cylinders, cones, and spheres
   • Scaling and Proportional Figures
     • Effect of scale factor on area and volume
3. 3

   Circles

   3 topics

   • Circumference and Area
     • Working with radius and diameter
   • Arcs, Sectors, and Central Angles
     • Arc length and sector area
     • Radian measure
   • Circle Equations in the Coordinate Plane
     • Standard form and identifying center and radius
4. 4

   Right-Triangle Trigonometry

   4 topics

   • Sine, Cosine, and Tangent Ratios
     • Setting up trig ratios from a right triangle
   • Solving for Sides and Angles
     • Using inverse trig to find angles
   • Special Right Triangles
     • 30-60-90 and 45-45-90 relationships
   • Complementary Angle Relationships
     • Sine and cosine of complementary angles

Math: Geometry and Trigonometry flashcards for PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test)

24 of 50 cards from the Math: Geometry and Trigonometry deck — real questions with worked answers.

1. What is the sum of the measures of two supplementary angles?

   180 degrees.

2. What is the sum of the measures of two complementary angles?

   90 degrees.

3. What can you conclude about vertical angles formed by two intersecting lines?

   They are congruent (equal in measure).

4. When two parallel lines are cut by a transversal, how are alternate interior angles related?

   They are congruent.

5. When two parallel lines are cut by a transversal, how are corresponding angles related?

   They are congruent.

6. When two parallel lines are cut by a transversal, how are same-side (co-interior) angles related?

   They are supplementary (sum to 180 degrees).

7. What is the sum of the interior angles of any triangle?

   180 degrees.

8. What does the Exterior Angle Theorem state about a triangle?

   An exterior angle equals the sum of the two non-adjacent (remote) interior angles.

9. In a triangle, how do the largest angle and the longest side relate?

   The longest side is opposite the largest angle (and the shortest side is opposite the smallest angle).

10. What is the Triangle Inequality Theorem?

    The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

11. What defines an isosceles triangle, and what is true of its base angles?

    It has at least two congruent sides; the angles opposite those sides (base angles) are congruent.

12. What are the angle measures in an equilateral triangle?

    All three angles measure 60 degrees.

13. State the Pythagorean Theorem.

    In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse (side opposite the right angle).

14. A right triangle has legs 6 and 8. What is the hypotenuse?

    10 (since 6^2 + 8^2 = 36 + 64 = 100 = 10^2).

15. List three common Pythagorean triples.

    3-4-5, 5-12-13, and 8-15-17.

16. How do you find the area of a rectangle?

    Area = length x width.

17. How do you find the area of a triangle?

    Area = (1/2) x base x height.

18. What is the formula for the area of a trapezoid?

    Area = (1/2)(b1 + b2) x h, where b1 and b2 are the parallel sides and h is the height.

19. What is the formula for the area of a parallelogram?

    Area = base x height.

20. How do you find the perimeter of a rectangle?

    Perimeter = 2(length + width).

21. What is the volume of a rectangular prism (box)?

    Volume = length x width x height.

22. What is the formula for the volume of a cylinder?

    Volume = pi x r^2 x h.

23. What is the formula for the volume of a sphere?

    Volume = (4/3) x pi x r^3.

24. What is the formula for the volume of a cone?

    Volume = (1/3) x pi x r^2 x h.

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