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

The Quantitative Aptitude (QA) - Geometry and Modern Math syllabus for CAT (Common Admission Test) in full: 6 chapters, 19 topics and 41 sub-topics, every one listed below, plus 50 Quantitative Aptitude (QA) - Geometry and Modern Math flashcards with answers.

6Chapters
19Topics
41Sub-topics
50Flashcards

Quantitative Aptitude (QA) - Geometry and Modern Math syllabus: all 6 chapters

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

  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. 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. 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. 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. 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. 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

CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math flashcards — 50 questions with 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.)

Show the other 30 Quantitative Aptitude (QA) - Geometry and Modern Math flashcards

  1. State the formula for the length of an arc and the area of a sector with central angle theta (in degrees).

    Arc length = (theta/360) x 2*pi*r; Sector area = (theta/360) x pi*r^2.

  2. What is the tangent-radius relationship, and the length of tangents from an external point?

    A tangent is perpendicular to the radius at the point of contact. Two tangents drawn from an external point are equal in length.

  3. State the lengths of tangent segments rule: the power of a point / intersecting chords theorem.

    For two chords intersecting inside a circle, the products of their segments are equal. For a secant and tangent from an external point, (tangent)^2 = (external secant) x (whole secant).

  4. What is the relationship between the area of a circle and its inscribed square (square inscribed in a circle of radius r)?

    Inscribed square has diagonal = 2r (diameter), so side = r*sqrt(2) and area = 2r^2, while circle area = pi*r^2.

  5. State the total surface area and volume of a cube with side a, and a cuboid with dimensions l, b, h.

    Cube: TSA = 6a^2, Volume = a^3. Cuboid: TSA = 2(lb+bh+hl), Volume = l*b*h.

  6. State the curved surface area, total surface area, and volume of a cylinder (radius r, height h).

    CSA = 2*pi*r*h; TSA = 2*pi*r(r+h); Volume = pi*r^2*h.

  7. State the curved surface area, total surface area, and volume of a cone (radius r, height h, slant l).

    CSA = pi*r*l; TSA = pi*r(r+l); Volume = (1/3)*pi*r^2*h, where l = sqrt(r^2+h^2).

  8. State the surface area and volume of a sphere of radius r, and of a hemisphere.

    Sphere: SA = 4*pi*r^2, Volume = (4/3)*pi*r^3. Hemisphere: CSA = 2*pi*r^2, TSA = 3*pi*r^2, Volume = (2/3)*pi*r^3.

  9. What is the diagonal (space diagonal) of a cuboid with dimensions l, b, h?

    sqrt(l^2 + b^2 + h^2).

  10. State the distance formula between points (x1,y1) and (x2,y2).

    Distance = sqrt((x2-x1)^2 + (y2-y1)^2).

  11. State the section formula (internal division) and the midpoint formula.

    Point dividing (x1,y1)-(x2,y2) in ratio m:n internally = ((m*x2+n*x1)/(m+n), (m*y2+n*y1)/(m+n)). Midpoint = ((x1+x2)/2, (y1+y2)/2).

  12. What is the formula for the area of a triangle with vertices (x1,y1), (x2,y2), (x3,y3)?

    Area = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|.

  13. What is the slope of a line through (x1,y1) and (x2,y2), and the slope from equation ax+by+c=0?

    Slope = (y2-y1)/(x2-x1). From ax+by+c=0, slope = -a/b.

  14. What are the conditions for two lines to be parallel and perpendicular in terms of slopes?

    Parallel: equal slopes (m1 = m2). Perpendicular: product of slopes = -1 (m1*m2 = -1).

  15. State the slope-intercept and point-slope forms of a straight line.

    Slope-intercept: y = mx + c. Point-slope: y - y1 = m(x - x1).

  16. What is the perpendicular distance from point (x0,y0) to the line ax+by+c=0?

    |a*x0 + b*y0 + c| / sqrt(a^2 + b^2).

  17. State the standard equation of a circle with center (h,k) and radius r.

    (x-h)^2 + (y-k)^2 = r^2. General form: x^2 + y^2 + 2gx + 2fy + c = 0 with center (-g,-f) and radius sqrt(g^2+f^2-c).

  18. Give the values of sin, cos, and tan for 30, 45, and 60 degrees.

    sin: 1/2, 1/sqrt(2), sqrt(3)/2. cos: sqrt(3)/2, 1/sqrt(2), 1/2. tan: 1/sqrt(3), 1, sqrt(3).

  19. State the three Pythagorean trigonometric identities.

    sin^2 x + cos^2 x = 1; 1 + tan^2 x = sec^2 x; 1 + cot^2 x = cosec^2 x.

  20. State the sine and cosine addition formulas: sin(A+B) and cos(A+B).

    sin(A+B) = sinA cosB + cosA sinB; cos(A+B) = cosA cosB - sinA sinB.

  21. State the double-angle formulas for sin 2A, cos 2A, and tan 2A.

    sin2A = 2 sinA cosA; cos2A = cos^2A - sin^2A = 2cos^2A - 1 = 1 - 2sin^2A; tan2A = 2tanA/(1 - tan^2A).

  22. In a height-and-distance problem, what is the angle of elevation versus the angle of depression?

    Angle of elevation is measured upward from the horizontal to an object above the observer; angle of depression is measured downward from the horizontal to an object below. They are equal (alternate angles) for the same line of sight.

  23. How are height and horizontal distance related using the angle of elevation theta?

    tan(theta) = height / horizontal distance, so height = distance x tan(theta).

  24. State the Addition (Sum) Rule and the Multiplication (Product) Rule of counting.

    Addition rule: if a task is done in m OR n mutually exclusive ways, total = m + n. Multiplication rule: if one task in m ways AND another independently in n ways, total = m x n.

  25. State the formula for permutations of n distinct objects taken r at a time, nPr.

    nPr = n! / (n-r)!. (Order matters.)

  26. How many distinct arrangements of n objects where some are identical (p alike, q alike, etc.)?

    n! / (p! q! ...). Number of circular permutations of n distinct objects = (n-1)!.

  27. State the formula for combinations nCr and its key symmetry property.

    nCr = n! / (r!(n-r)!). Symmetry: nCr = nC(n-r); also nCr + nC(r-1) = (n+1)Cr (Pascal's rule).

  28. State the classical (theoretical) definition of probability of an event.

    P(event) = (number of favorable outcomes) / (total number of equally likely outcomes), a value between 0 and 1.

  29. State the addition rule of probability for two events and the rule for mutually exclusive events.

    P(A or B) = P(A) + P(B) - P(A and B). If mutually exclusive, P(A and B) = 0, so P(A or B) = P(A) + P(B). Complement: P(not A) = 1 - P(A).

  30. State the inclusion-exclusion principle for the union of two and three sets.

    |A∪B| = |A| + |B| - |A∩B|. |A∪B∪C| = |A|+|B|+|C| - |A∩B| - |B∩C| - |A∩C| + |A∩B∩C|.

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

What is in the CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math syllabus?

CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math is split into 6 chapters: Lines, Angles and Triangles, Polygons and Circles, Mensuration, Coordinate Geometry, Trigonometry and Permutations, Combinations, Probability and Sets. Together they contain 19 topics and 41 sub-topics.

How many chapters are in CAT (Common Admission Test) Quantitative Aptitude (QA) - Geometry and Modern Math?

6 chapters, containing 19 topics and 41 sub-topics. The largest chapter is Permutations, Combinations, Probability and Sets, with 4 topics.

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

Yes — a 50-card Quantitative Aptitude (QA) - Geometry and Modern Math 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.