CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math Syllabus

Quantitative Aptitude (QA) - Geometry and Modern Math syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Aptitude (QA) - Geometry and Modern Math in CAT (Common Admission Test), not a summary of it.

1. 1

   Lines, Angles and Triangles

   3 topics

   • Lines and Angles
     • Parallel lines and transversals
     • Angle relationships
   • Triangle Properties
     • Congruence and similarity
     • Centroid, incentre, circumcentre and orthocentre
     • Pythagoras theorem and special triangles
   • Area Theorems
     • Heron's formula
     • Median and angle bisector theorems
2. 2

   Polygons and Circles

   3 topics

   • Quadrilaterals
     • Properties of parallelogram, trapezium and rhombus
     • Area relationships in quadrilaterals
   • Regular Polygons
     • Interior and exterior angles of regular polygons
     • Diagonals and area of regular polygons
   • Circles
     • Chords, tangents and secants
     • Inscribed and central angles
     • Cyclic quadrilaterals
3. 3

   Mensuration

   3 topics

   • 2D Mensuration
     • Area and perimeter of plane figures
     • Sectors and segments of a circle
   • Surface Area of Solids
     • Cube, cuboid and cylinder surface areas
     • Cone, sphere and hemisphere surface areas
   • Volume of Solids
     • Volume of prisms, pyramids and spheres
     • Frustum and combination of solids
4. 4

   Coordinate Geometry

   3 topics

   • Points and Distances
     • Distance, section and midpoint formulae
     • Collinearity of points
   • Straight Lines
     • Slope and equations of lines
     • Angle between lines and perpendicular distance
   • Areas and Circles
     • Area of triangle and polygon by coordinates
     • Equation of a circle
5. 5

   Trigonometry

   3 topics

   • Trigonometric Ratios and Identities
     • Fundamental identities
     • Values at standard angles
   • Compound and Multiple Angles
     • Sum and difference formulae
     • Double and half angle formulae
   • Heights and Distances
     • Angle of elevation and depression
6. 6

   Permutations, Combinations, Probability and Sets

   4 topics

   • Counting Principles and Permutations
     • Fundamental principle of counting
     • Permutations with restrictions and repetitions
     • Circular permutations
   • Combinations
     • Selection and grouping
     • Distribution and partitioning of identical/distinct objects
   • Probability
     • Classical probability and sample spaces
     • Conditional probability and independence
     • Bayes theorem basics
   • Set Theory
     • Venn diagrams for two and three sets
     • Inclusion-exclusion principle

Quantitative Aptitude (QA) - Geometry and Modern Math flashcards for CAT (Common Admission Test)

20 of 50 cards from the Quantitative Aptitude (QA) - Geometry and Modern Math deck — real questions with worked answers.

1. What is the sum of all angles around a point on one side of a straight line (linear pair / angles on a line)?

   180 degrees (angles on a straight line are supplementary).

2. When two parallel lines are cut by a transversal, what is the relationship between alternate interior angles and between co-interior (allied) angles?

   Alternate interior angles are equal; co-interior (same-side interior) angles are supplementary (sum to 180 degrees).

3. State the angle sum property and the exterior angle property of a triangle.

   The three interior angles sum to 180 degrees. An exterior angle equals the sum of the two remote (non-adjacent) interior angles.

4. State the triangle inequality for side lengths a, b, c.

   The sum of any two sides exceeds the third: a+b > c, b+c > a, a+c > b. Equivalently, each side lies between the difference and sum of the other two.

5. What are the four classic centers of a triangle and what is each the intersection of?

   Centroid (medians), Incenter (angle bisectors), Circumcenter (perpendicular bisectors of sides), Orthocenter (altitudes).

6. In what ratio does the centroid divide each median of a triangle?

   2:1, measured from the vertex to the midpoint of the opposite side.

7. State the Pythagorean theorem and its converse.

   In a right triangle, hypotenuse^2 = sum of squares of the other two sides (c^2 = a^2 + b^2). Converse: if c^2 = a^2 + b^2, the triangle is right-angled at the vertex opposite c.

8. State the basic area formula for a triangle and Heron's formula.

   Area = (1/2) x base x height. Heron's: Area = sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2 is the semi-perimeter.

9. How do the areas of two similar triangles relate to their corresponding sides?

   The ratio of areas equals the square of the ratio of corresponding sides (linear scale factor).

10. State the Basic Proportionality Theorem (Thales' theorem).

    A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.

11. What is the area of a triangle with two sides a, b and included angle C?

    Area = (1/2) x a x b x sin(C).

12. State the area formulas for a square, rectangle, and parallelogram.

    Square = side^2; Rectangle = length x breadth; Parallelogram = base x height.

13. State the area formula for a rhombus and a trapezium (trapezoid).

    Rhombus = (1/2) x d1 x d2 (product of diagonals halved). Trapezium = (1/2) x (sum of parallel sides) x height.

14. What distinguishes a rhombus, rectangle, and square in terms of their diagonals?

    Rhombus: diagonals bisect at right angles (unequal). Rectangle: diagonals equal and bisect (not perpendicular). Square: diagonals equal, bisect, and are perpendicular.

15. What is the relationship between a parallelogram's diagonals and the diagonals of a kite?

    Parallelogram: diagonals bisect each other. Kite: diagonals are perpendicular, and one diagonal bisects the other.

16. What is the formula for each interior angle of a regular polygon with n sides?

    Interior angle = (n-2) x 180 / n degrees. The exterior angle = 360/n degrees.

17. What is the sum of interior angles of an n-sided polygon, and the sum of exterior angles?

    Sum of interior angles = (n-2) x 180 degrees. Sum of exterior angles = 360 degrees (for any convex polygon).

18. How many diagonals does a polygon with n sides have?

    n(n-3)/2.

19. State the circumference and area formulas for a circle of radius r.

    Circumference = 2*pi*r; Area = pi*r^2.

20. What is the relationship between an inscribed angle and the central angle subtending the same arc?

    The inscribed angle is half the central angle subtending the same arc. (Angle in a semicircle is 90 degrees.)

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