PPSC Assistant Director Test Mathematics and Analytical Reasoning Syllabus

In time and work problems, if a person completes a job in n days, what is their one-day work?

One day's work = 1/n of the total job.

If A can do a job in x days and B in y days, how long do they take working together?

Together they take (x times y) / (x + y) days, since combined one-day work = 1/x + 1/y.

State the basic relationship between speed, distance, and time.

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

How do you convert a speed from km/h to m/s?

Multiply by 5/18 (km/h to m/s); multiply by 18/5 to convert m/s back to km/h.

What is a linear equation, and how many solutions does one variable linear equation have?

A linear equation has variables of degree 1 (e.g., ax + b = 0). A single-variable linear equation has exactly one solution.

State the quadratic formula for ax^2 + bx + c = 0.

x = (-b plus or minus square root of (b^2 - 4ac)) / (2a).

What does the discriminant b^2 - 4ac tell you about the roots of a quadratic?

If positive, two distinct real roots; if zero, two equal real roots; if negative, two complex (no real) roots.

For ax^2 + bx + c = 0, what are the sum and product of the roots?

Sum of roots = -b/a; product of roots = c/a.

Expand the algebraic identities (a + b)^2 and (a - b)^2.

(a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.

What is the identity for a^2 - b^2?

a^2 - b^2 = (a + b)(a - b).

Define HCF (Highest Common Factor) and LCM (Least Common Multiple).

HCF is the largest number that divides two or more numbers exactly; LCM is the smallest number that is a multiple of all the given numbers.

What is the relationship between the HCF and LCM of two numbers?

HCF x LCM = product of the two numbers.

How do you find the HCF of two numbers using the division (Euclidean) method?

Divide the larger by the smaller, then divide the divisor by the remainder repeatedly; the last non-zero remainder (the last divisor) is the HCF.

How is the LCM of fractions calculated?

LCM of fractions = LCM of numerators / HCF of denominators.

How is the HCF of fractions calculated?

HCF of fractions = HCF of numerators / LCM of denominators.

State the laws of indices for a^m x a^n and a^m / a^n.

a^m x a^n = a^(m+n); a^m / a^n = a^(m-n).

What do a^0 and a^(-n) equal (for a not zero)?

a^0 = 1; a^(-n) = 1 / a^n.

What is the power-of-a-power rule, (a^m)^n?

(a^m)^n = a^(m x n).

How is a fractional exponent a^(m/n) expressed as a root?

a^(m/n) = the nth root of (a^m), equivalently (nth root of a)^m.

What distinguishes an arithmetic progression (AP) from a geometric progression (GP)?

An AP has a constant common difference between consecutive terms; a GP has a constant common ratio between consecutive terms.

What is the formula for the nth term of an arithmetic progression?

nth term = a + (n - 1)d, where a is the first term and d is the common difference.

What is the formula for the sum of the first n terms of an AP?

Sum = n/2 x [2a + (n - 1)d], or equivalently n/2 x (first term + last term).

What is the formula for the nth term of a geometric progression?

nth term = a x r^(n-1), where a is the first term and r is the common ratio.

In coding-decoding, what is letter-position (alphabet) coding and the position numbers of A, M, and Z?

Each letter is assigned its position in the alphabet. A = 1, M = 13, and Z = 26 (forward order).

In reverse alphabet (opposite/EJOTY-type) coding, what letter corresponds to A, and what is the rule?

The opposite of A is Z. The rule is that a letter's reverse position = 27 minus its forward position (A and Z, B and Y, etc.).

In a blood-relations puzzle, who is your father's brother and your mother's sister?

Your father's brother is your paternal uncle; your mother's sister is your maternal aunt.

In direction-sense problems, if you face North and turn right, which direction do you face, and a further right turn leads where?

Facing North and turning right faces East; a further right turn faces South (each right turn is 90 degrees clockwise).

What is an analogy in reasoning, and how do you solve A : B :: C : ? type questions?

An analogy identifies a relationship between a pair. You determine the relationship between A and B, then apply the same relationship to C to find the matching term.

What does 'classification' (odd-one-out) reasoning require you to do?

Identify the common property shared by most items in a group and select the one item that does not share that property.

What is the difference between a bar graph and a pie chart in data interpretation?

A bar graph uses rectangular bars whose lengths represent values for comparison across categories; a pie chart uses sectors of a circle to show each part as a proportion (percentage) of the whole.