PPSC Educators Test Basic Mathematics & Computer Studies Syllabus

What is an algebraic expression, and how does it differ from an equation?

An algebraic expression is a combination of variables, constants and operations (e.g. 3x + 2) with no equals sign. An equation states that two expressions are equal (e.g. 3x + 2 = 8).

State the formulas for (a+b)^2 and (a-b)^2.

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

State the difference of squares identity.

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

How do you solve the linear equation 2x + 5 = 15?

Subtract 5 from both sides: 2x = 10. Divide both sides by 2: x = 5.

What is the quadratic formula for ax^2 + bx + c = 0?

x = [-b ± sqrt(b^2 - 4ac)] / (2a).

What are complementary and supplementary angles?

Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees.

What is the sum of the interior angles of a triangle, and what does the exterior angle equal?

The interior angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two opposite (non-adjacent) interior angles.

Classify triangles by their sides.

Equilateral (all three sides equal), Isosceles (two sides equal), and Scalene (all sides different).

State the Pythagorean theorem.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c^2 = a^2 + b^2.

What are acute, right, obtuse, and reflex angles?

Acute: less than 90 degrees. Right: exactly 90 degrees. Obtuse: between 90 and 180 degrees. Reflex: between 180 and 360 degrees.

What are the formulas for the area and perimeter of a rectangle?

Area = length x width. Perimeter = 2 x (length + width).

What is the formula for the area of a triangle?

Area = (1/2) x base x height.

What are the formulas for the circumference and area of a circle?

Circumference = 2 x pi x r. Area = pi x r^2, where r is the radius.

What is the formula for the volume of a cuboid and of a cube?

Volume of a cuboid = length x width x height. Volume of a cube = side^3 (side cubed).

What is the formula for the volume of a cylinder?

Volume = pi x r^2 x h, where r is the base radius and h is the height.

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

Speed = Distance / Time. Therefore Distance = Speed x Time, and Time = Distance / Speed.

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

Multiply the km/h value by 5/18 to get m/s. (To convert m/s to km/h, multiply by 18/5.)

What is average speed for a journey covering distances at different speeds?

Average speed = Total distance / Total time. It is NOT simply the average of the speeds.

For relative speed, how do speeds combine for objects moving toward each other versus in the same direction?

Moving toward each other (or opposite directions): add the speeds. Moving in the same direction: subtract the speeds.

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

Their one-day work (rate) is 1/n of the job. If two people take a and b days alone, together they do (1/a + 1/b) of the work per day.

If A does a job in 10 days and B in 15 days, how long do they take working together?

Combined one-day work = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. So together they finish in 6 days.

What is an arithmetic progression (AP), and what is its nth term formula?

An AP is a sequence with 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 formula for 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 formula?

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

What is the difference between computer hardware and software?

Hardware is the physical, tangible parts of a computer (CPU, monitor, keyboard, RAM). Software is the set of programs and instructions that tell the hardware what to do (e.g. operating systems, applications).

What is the CPU, and what are its two main components?

The CPU (Central Processing Unit) is the 'brain' of the computer that processes instructions. Its main parts are the ALU (Arithmetic Logic Unit) and the CU (Control Unit).

What is the difference between RAM and ROM?

RAM (Random Access Memory) is volatile temporary memory that loses data when power is off. ROM (Read Only Memory) is non-volatile permanent memory that retains data without power and is generally read-only.

List the units of digital storage from smallest to largest (bit to gigabyte).

Bit -> Byte (8 bits) -> Kilobyte (KB, 1024 bytes) -> Megabyte (MB) -> Gigabyte (GB) -> Terabyte (TB), each step being 1024 of the previous.

What is system software versus application software, and what is an operating system?

System software manages hardware and runs the computer (e.g. the operating system). Application software performs user tasks (e.g. MS Word). An operating system (OS) is system software that manages hardware, memory, files and processes (e.g. Windows, Linux, macOS).

What do the MS Office programs Word, Excel, and PowerPoint do, and what is the difference between the Internet and the World Wide Web?

Word is a word processor (documents); Excel is a spreadsheet (calculations, tables, charts); PowerPoint creates slide presentations. The Internet is the global network of interconnected computers, while the World Wide Web (WWW) is a service of information (web pages) accessed over the Internet via browsers.