SSC CGL Quantitative Aptitude Syllabus

State the alligation rule for finding the ratio in which two ingredients are mixed.

(Quantity of cheaper)/(Quantity of dearer) = (Price of dearer − Mean price)/(Mean price − Price of cheaper).

What is the formula for Simple Interest?

SI = (P x R x T)/100, where P = principal, R = rate% per annum, T = time in years.

What is the Compound Interest amount formula for annual compounding?

A = P(1 + R/100)^T; Compound Interest = A − P.

What is the difference between CI and SI for 2 years at rate R% on principal P?

Difference = P x (R/100)².

In a partnership, how is profit divided when partners invest different amounts for different times?

Profit is divided in the ratio of each partner's (capital x time) products.

If A can do a work in 'a' days and B in 'b' days, how long do they take working together?

Together they take ab/(a+b) days (combined one-day work = 1/a + 1/b).

State the fundamental relationship between speed, distance and time.

Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

How do you convert km/h to m/s and m/s to km/h?

km/h to m/s: multiply by 5/18; m/s to km/h: multiply by 18/5.

To cross a stationary pole/man, what distance does a train of length L travel?

It travels a distance equal to its own length L (Time = L / speed of train).

To cross a platform of length P, what distance does a train of length L travel?

It travels L + P (sum of train length and platform length).

For a boat with still-water speed u and stream speed v, what are downstream and upstream speeds?

Downstream speed = u + v; Upstream speed = u − v.

Given downstream speed D and upstream speed U, find speed in still water and speed of stream.

Speed in still water = (D + U)/2; Speed of stream = (D − U)/2.

What is the relative speed of two objects moving in the same direction and in opposite directions?

Same direction: difference of speeds (s1 − s2); Opposite directions: sum of speeds (s1 + s2).

Expand (a + b)² , (a − b)² and (a + b)(a − b).

(a+b)² = a² + 2ab + b²; (a−b)² = a² − 2ab + b²; (a+b)(a−b) = a² − b².

State the identity for a³ + b³ and a³ − b³.

a³ + b³ = (a + b)(a² − ab + b²); a³ − b³ = (a − b)(a² + ab + b²).

Expand (a + b + c)².

a² + b² + c² + 2ab + 2bc + 2ca.

For a pair of linear equations in two variables, what does each consistency case mean (unique, infinite, no solution)?

Unique solution: a1/a2 ≠ b1/b2 (lines intersect). Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident). No solution: a1/a2 = b1/b2 ≠ c1/c2 (parallel).

Give the quadratic formula for ax² + bx + c = 0.

x = [−b ± √(b² − 4ac)] / 2a.

For roots of ax² + bx + c = 0, what are the sum and product of roots?

Sum of roots = −b/a; Product of roots = c/a.

What does the discriminant b² − 4ac tell you about the roots of a quadratic?

> 0: two distinct real roots; = 0: two equal real roots; < 0: no real roots (complex roots).

State the Factor Theorem for polynomials.

(x − a) is a factor of polynomial p(x) if and only if p(a) = 0.

What is the slope-intercept form of a line and what do its constants mean?

y = mx + c, where m is the slope (gradient) and c is the y-intercept.

What is the sum of the interior angles of a triangle, and the exterior angle property?

Interior angles sum to 180°; an exterior angle equals the sum of the two opposite interior angles.

State the Pythagoras theorem for a right-angled triangle.

In a right triangle, (hypotenuse)² = (base)² + (perpendicular)², i.e. c² = a² + b².

What is the relationship between the radius and a tangent at the point of contact of a circle?

The tangent at any point of a circle is perpendicular (90°) to the radius drawn to the point of contact.

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

Interior angles sum = (n − 2) x 180°; sum of exterior angles = 360° (for any convex polygon).

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

Area = πr²; Circumference = 2πr.

Give the formulas for area of a triangle (base-height and Heron's).

Area = ½ x base x height; Heron's: Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2.

Give the Total Surface Area and Volume of a sphere of radius r.

TSA = 4πr²; Volume = (4/3)πr³.

Give the Volume and Curved Surface Area of a right circular cylinder (radius r, height h) and of a cone (radius r, height h, slant l).

Cylinder: Volume = πr²h, CSA = 2πrh. Cone: Volume = (1/3)πr²h, CSA = πrl where l = √(r² + h²).

Define the trigonometric ratios sin, cos and tan for an angle θ in a right triangle.

sin θ = Opposite/Hypotenuse; cos θ = Adjacent/Hypotenuse; tan θ = Opposite/Adjacent.

State the three Pythagorean trigonometric identities.

sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

Give the values of sin and cos at 0°, 30°, 45°, 60° and 90°.

sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0.

What are the trigonometric ratios of complementary angles (90° − θ)?

sin(90°−θ)=cos θ; cos(90°−θ)=sin θ; tan(90°−θ)=cot θ; sec(90°−θ)=cosec θ; cot(90°−θ)=tan θ; cosec(90°−θ)=sec θ.

In heights and distances, what do the angle of elevation and angle of depression mean?

Angle of elevation: angle above the horizontal when looking up at an object. Angle of depression: angle below the horizontal when looking down at an object.

How do you convert between degrees and radians?

Radians = Degrees x (π/180); Degrees = Radians x (180/π); note π radians = 180°.

How is the mean (arithmetic average) of grouped/ungrouped data computed?

Mean = (Σ of all values)/(number of values), or for grouped data Mean = Σ(f x x)/Σf.

How do you find the median of a data set?

Arrange data in order. If n is odd, median = the [(n+1)/2]th value; if n is even, median = average of the (n/2)th and (n/2 + 1)th values.

Define the mode and state the empirical relationship between mean, median and mode.

Mode is the most frequently occurring value. Empirical relation: Mode = 3 x Median − 2 x Mean.