GMAT quant geometry syllabus takes up approximately 10% to 15% of the entire Quant section. This means that on the test day, you could get around 3 to 6 questions overall out of 31 questions. To be able to answer these 3-6 questions you have to be thorough with the kinds of questions asked, the concepts that you will be tested on, etc. Therefore, through this article, we will acquaint you with the quant geometry syllabus to help you prepare well. So, read on!
In general, Geometry is vast and includes all kinds of concepts — shapes, measurements, and theorems. On the other hand, the GMAT geometry syllabus is restricted to basic shapes like triangles, quadrilaterals and straight lines. The exam rarely tests curves (parabola) in coordinate geometry. You are mostly asked to find the angles, side, area and perimeter of the given shape.
GMAT geometry questions mostly test your visual skills and basic measurements. So, those who have strong visual skills and are thorough with their geometry basics can do well in the GMAT Geometry section. However, GMAT test makers come up with tricky questions, so you should be very careful about the angles and lengths given in the figure. Thus, before assuming any information from the shapes, it is important to read the question carefully.
Now, let’s discuss the geometry topics in a bit more detail.
We can put this under five major categories:
- Lines and Angles
- Polygons (triangles, Quadrilaterals, etc).
- Three-Dimensional Shapes (Rectangular solids and cylinder).
- Coordinate geometry.
Let’s dive into these categories and see what concepts are tested under each:
- Lines and Angles:
We all know that a line is a one-dimensional figure, which extends both the ends infinitely. A sample figure is given below.
GMAT Questions pertaining to Lines and Angles could test your knowledge on:
- Parallel lines
- Perpendicular lines
- Different types of angles when a line intersects two or more parallel lines
- Angle in a straight line
- Vertically opposite angles when two or more lines intersect
- Sum of Interior angles of a polygon
- Sum of Exterior angles of a polygon
A Polygon is a closed figure made up of line segments (not curves) in two-dimensions.
Not all the different types (based on number of sides) of polygons are tested in the GMAT but you should be aware of all the basic rules of triangles and quadrilaterals (basic polygons).
GMAT Questions pertaining to Polygons could test your knowledge on:
- Regular Polygons
- Area of a triangle
- Perimeter of a triangle
- Different types of triangles based on its side’s length
- Different types of triangles based on its angle’s measure
- Special triangles like 300–600–900and isosceles right-angled triangle whose angles are 450–450–900.
- Similarity and Congruence of triangles
- Similar triangles applications
- Median and centroid of a triangle
- Third Side rule of a triangle
- Area and perimeter of a Quadrilateral
- Different types of Quadrilaterals (special quadrilaterals)
- Area and Perimeter of a Parallelogram
- Properties of Parallelogram
- Area and Perimeter of a Rhombus
- Properties of Rhombus
- Area and Perimeter of a Square and Rectangle
- Properties of Square and Rectangle
- Area and Perimeter of a Trapezoid
- Properties of Trapezoid
- Area and Perimeter of a Kite (convex)
- Properties of a Kite
If the set of all points on a plane are at a fixed distance from a centre, then it is a circle.
GMAT Questions pertaining to Circles could test your knowledge on:
- Radius and Diameter of the circle
- Area of the circle
- Circumference of the circle
- Arc length of the circle
- Area covered by an arc (sector area)
- Central angle theorem
- Line tangent to a circle
- Line secant to a circle
- Circles tangential to each other
- Chord of a circle
- Inscribing and circumscribing polygons in a circle
- Three – Dimensional Shapes (Rectangular Solids and Cylinder):
Three dimensional shapes are solid shapes or objects that have three dimensions i.e. length, width, and height as opposed to two-dimensional objects which have only length and width.
In the GMAT, three dimensional questions are restricted to the basic shapes like Cube, Cuboid, Cylinder and Sphere. So, knowing these four shapes are enough to answer questions based on these.
GMAT Questions pertaining to 3D basic shapes could test your knowledge on:
- Volume and surface area of the cube
- Volume and surface area of the cuboids
- Volume and surface area of the cylinder
- Volume and surface area of the sphere
- Diagonal and centre of the rectangular solids, cylinder and sphere
- Common properties between two 3D shapes when inscribed (or circumscribed) on one another
- Co – ordinate Geometry:
Locating the geometrical figures such as lines, curves, polygons, etc., in an xy-plane is called Coordinate geometry.
Sometimes questions pertaining to lines could be considered both from Algebra as well as from geometry. You can expect 700 level (difficult) questions in Coordinate Geometry. Some of the Data Sufficiency (DS) in Quant section could be challenging for you.
GMAT Questions pertaining to co-ordinate geometry could test your knowledge on:
- Equation of x and y axes
- Distance between two points in a plane
- Quadrants of the xy-plane
- Slope of a line when given two points
- Intercepts of a line
- Positive, negative and zero slopes
- Slopes when two or more lines are parallel to each other
- Slopes when two or more lines are perpendicular to each other
- Equation of a line when given a point and the slope
- Equation of a line when given two points
- Equation of line in the intercept form
- Midpoint of a line
- Centroid of a triangle
- Point dividing a line internally (section formula – Internal division)
- Point dividing a line externally (section formula – External division)
- Special lines passing through the origin (y = mx and y = -mx)
- Reflection of a point, line or shapes across x and y axes
- Reflection of a point across the special line y = x
- Point of Intersection of two lines
- Equation of circle with centre at the origin
- Equation of circle with centre not at the origin
That summarizes the concepts tested in the geometry section.
The best part of the GMAT exam is that some of the geometry questions can be solved by using logic and visual skills. Having said that, it is important to know some of the important formulae and properties of basic shapes that are listed above.
Hope this article was helpful! All the best for your GMAT exam!