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

The Math: Geometry and Trigonometry syllabus for PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) in full: 4 chapters, 13 topics and 16 sub-topics, every one listed below, plus 50 Math: Geometry and Trigonometry flashcards with answers.

4Chapters
13Topics
16Sub-topics
50Flashcards

Math: Geometry and Trigonometry syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  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. 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. 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. 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

PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry flashcards — 50 questions with 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).

Show the other 30 Math: Geometry and Trigonometry flashcards

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

    Volume = length x width x height.

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

    Volume = pi x r^2 x h.

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

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

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

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

  5. What is the surface area of a sphere?

    Surface area = 4 x pi x r^2.

  6. What is the volume of a pyramid?

    Volume = (1/3) x base area x height.

  7. If two figures are similar with a scale factor of k, how do their corresponding lengths compare?

    Corresponding lengths are in the ratio k to 1 (each length is multiplied by k).

  8. If two similar figures have a linear scale factor of k, what is the ratio of their areas?

    k^2 (the area scale factor is the square of the linear scale factor).

  9. If two similar solids have a linear scale factor of k, what is the ratio of their volumes?

    k^3 (the volume scale factor is the cube of the linear scale factor).

  10. What makes two triangles similar?

    Their corresponding angles are congruent and their corresponding sides are proportional (e.g., by AA, SAS, or SSS similarity).

  11. What is the formula for the circumference of a circle?

    Circumference = 2 x pi x r (or pi x d, where d is the diameter).

  12. What is the formula for the area of a circle?

    Area = pi x r^2.

  13. How is the diameter of a circle related to its radius?

    The diameter equals twice the radius (d = 2r).

  14. What is the formula for arc length given a central angle in degrees?

    Arc length = (central angle / 360) x 2 x pi x r.

  15. What is the formula for the area of a sector given a central angle in degrees?

    Sector area = (central angle / 360) x pi x r^2.

  16. How does the measure of an arc relate to its central angle?

    The arc measure (in degrees) equals the measure of its central angle.

  17. How many radians are in 360 degrees?

    2 x pi radians.

  18. What is the standard (center-radius) equation of a circle with center (h, k) and radius r?

    (x - h)^2 + (y - k)^2 = r^2.

  19. A circle has equation (x - 3)^2 + (y + 2)^2 = 25. What are its center and radius?

    Center (3, -2) and radius 5.

  20. What technique converts a general circle equation like x^2 + y^2 + Dx + Ey + F = 0 into standard form?

    Completing the square on the x-terms and the y-terms.

  21. In a right triangle, what is the sine of an angle (SOH)?

    Sine = opposite leg / hypotenuse.

  22. In a right triangle, what is the cosine of an angle (CAH)?

    Cosine = adjacent leg / hypotenuse.

  23. In a right triangle, what is the tangent of an angle (TOA)?

    Tangent = opposite leg / adjacent leg.

  24. To find an unknown angle when you know two sides of a right triangle, what do you use?

    An inverse trig function (arcsin, arccos, or arctan) of the appropriate ratio.

  25. In a 45-45-90 triangle, what is the ratio of the legs to the hypotenuse?

    1 : 1 : sqrt(2) (each leg : leg : hypotenuse).

  26. In a 30-60-90 triangle, what is the ratio of the sides opposite 30, 60, and 90 degrees?

    1 : sqrt(3) : 2.

  27. In a 30-60-90 triangle, the side opposite 30 degrees is the shortest. How long is the hypotenuse relative to it?

    The hypotenuse is twice the length of the side opposite the 30-degree angle.

  28. What is the relationship between the sine of an angle and the cosine of its complement?

    sin(x) = cos(90 - x); the sine of an angle equals the cosine of its complement.

  29. If sin(40 degrees) = 0.643, what is cos(50 degrees)?

    0.643, because 40 and 50 degrees are complementary, so cos(50) = sin(40).

  30. What value do tan(x) x tan(90 - x) equal for an acute angle x?

    1, because tan(90 - x) = 1/tan(x) (cotangent), so the product is 1.

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

What is in the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry syllabus?

PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry is split into 4 chapters: Lines, Angles, and Triangles, Area, Perimeter, and Volume, Circles and Right-Triangle Trigonometry. Together they contain 13 topics and 16 sub-topics.

How many chapters are in PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Geometry and Trigonometry?

4 chapters, containing 13 topics and 16 sub-topics. The largest chapter is Right-Triangle Trigonometry, with 4 topics.

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

Yes — a 50-card Math: Geometry and Trigonometry deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.