PPSC Test Mathematics & Analytical Reasoning Syllabus

What is the formula for average speed over a journey covering equal distances at two speeds u and v?

Average speed = 2uv / (u + v), the harmonic mean. Note it is NOT the simple average of u and v.

In time-and-work problems, how do you combine the rates of two workers A and B?

If A does a job in a days and B in b days, their one-day combined work = 1/a + 1/b, so together they finish in ab/(a+b) days.

How does the time taken by a train to cross a pole differ from crossing a platform?

To cross a pole, distance = length of train. To cross a platform, distance = length of train + length of platform. Time = distance / speed in each case.

What is the general form of a linear equation in one variable and how many solutions does it have?

A linear equation has the form ax + b = 0 (a is not 0). It has exactly one solution: x = -b/a.

What is the standard form of a quadratic equation and the quadratic formula for its roots?

Standard form: ax^2 + bx + c = 0 (a is not 0). Roots: x = (-b plus or minus sqrt(b^2 - 4ac)) / (2a).

What does the discriminant of a quadratic equation tell you about its roots?

Discriminant D = b^2 - 4ac. If D > 0, two distinct real roots; if D = 0, two equal real roots; if D < 0, no real roots (complex roots).

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

Sum of roots = -b/a; Product of roots = c/a. These come from the relationship between coefficients and roots.

What is the method for solving two linear equations in two variables?

Use substitution (solve one equation for a variable and substitute) or elimination (add/subtract equations to cancel a variable). Both yield the unique solution where the two lines intersect.

What is the BODMAS/order of operations rule used in simplification?

BODMAS: Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). Operations are performed in this priority order.

What are the algebraic identities for (a + b)^2, (a - b)^2 and a^2 - b^2?

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

What is the identity for (a + b)^3 and (a - b)^3?

(a + b)^3 = a^3 + b^3 + 3ab(a + b); (a - b)^3 = a^3 - b^3 - 3ab(a - b).

What is the identity for a^3 + b^3 and a^3 - b^3?

a^3 + b^3 = (a + b)(a^2 - ab + b^2); a^3 - b^3 = (a - b)(a^2 + ab + b^2).

What is the formula for Simple Interest (SI)?

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

What is the formula for Compound Interest amount and the interest itself?

Amount A = P(1 + R/100)^T; Compound Interest = A - P = P[(1 + R/100)^T - 1], where interest is compounded annually.

What is the key difference between simple and compound interest?

Simple interest is calculated only on the original principal each period. Compound interest is calculated on the principal plus accumulated interest, so it grows faster. For the same P, R, T, CI is always greater than or equal to SI (equal only in the first year).

For 2 years, what is the difference between compound interest and simple interest on principal P at rate R%?

Difference (CI - SI) for 2 years = P x (R/100)^2 = PR^2/10000.

How is compound interest adjusted when compounded half-yearly or quarterly?

Half-yearly: rate becomes R/2 and time becomes 2T. Quarterly: rate becomes R/4 and time becomes 4T. Use A = P(1 + rate/100)^periods.

What is an arithmetic progression (AP) and what is its general/nth term?

An AP has a constant common difference d between consecutive terms. The nth term is a_n = a + (n - 1)d, where a is the first term.

What is the sum of the first n terms of an arithmetic progression?

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

What is a geometric progression (GP) and what is its nth term?

A GP has a constant ratio r between consecutive terms. The nth term is a_n = a x r^(n-1), where a is the first term.

How do you approach a number series completion problem?

Identify the pattern between consecutive terms: check for constant difference (arithmetic), constant ratio (geometric), squares/cubes, alternating operations, or prime/Fibonacci patterns, then apply it to find the missing or next term.

In coding-decoding, what is letter-shift (Caesar) coding and how is it reversed?

In letter-shift coding each letter is moved a fixed number of positions in the alphabet (e.g. +1: CAT becomes DBU). To decode, shift each letter back by the same number of positions.

What does the positional value of letters (A=1 to Z=26) help solve in coding problems?

It lets you convert letters to numbers (and back) to detect numeric patterns. Knowing A=1, B=2, ... Z=26 (and reverse Z=1, A=26) is essential for many coding-decoding and number-letter analogy questions.

In blood relations, who is your father's brother's son and your mother's sister?

Your father's brother's son is your cousin (paternal). Your mother's sister is your aunt (maternal aunt / khala).

In blood relations, what relation is the 'daughter of my grandfather's only son'?

The grandfather's only son is your father, so his daughter is you (if female) or your sister. In standard puzzle convention it means the speaker's sister (or the speaker herself).

In direction sense, if you face North and turn 90 degrees clockwise (right), which direction do you face? And if you then turn right again?

Facing North and turning right (clockwise) you face East. Turning right again you face South. The clockwise order is North to East to South to West to North.

In direction-sense problems, how do you find the shortest (straight-line) distance between start and end points?

Resolve the net horizontal and vertical displacements, then apply the Pythagorean theorem: distance = sqrt(horizontal^2 + vertical^2).

In a circular seating arrangement, how do 'facing the centre' and 'facing outward' affect left and right?

When everyone faces the centre, a person's left/right is opposite to the observer's; when facing outward, left/right matches the normal orientation. Always fix the facing direction before deciding neighbours' left and right.

What is a syllogism, and what are its three parts?

A syllogism is a logical argument drawing a conclusion from two given premises. Its three parts are the major premise, the minor premise, and the conclusion (e.g. All A are B; All B are C; therefore All A are C).

How do Venn diagrams help solve syllogism and logical-deduction problems?

Venn diagrams represent the relationships (overlap, subset, or separation) between categories in the premises. A conclusion is valid only if it holds true in every possible diagram consistent with the premises; if any diagram contradicts it, the conclusion does not follow.

When reading a data table or chart to answer questions, what should you check first, and how do you compute percentage change and ratios between two data points?

First read the title, row/column headings, and units (and any legend on a chart). Percentage change between two values = ((new - old)/old) x 100. A ratio between two data points = value1 : value2 (or value1/value2). In a pie chart, each sector's value = (its angle/360) x total, or (its percentage) x total; the whole circle (360 degrees) represents 100% of the data.