Maharashtra SSC Arithmetic (MSBSHSE) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Rational number definition

A number expressible as p/q where p and q are integers and q is not zero. Integers, fractions and terminating or recurring decimals are all rational numbers.

BODMAS order

Brackets first, then Of, then Division and Multiplication from left to right, then Addition and Subtraction from left to right. Ignoring this order gives wrong answers.

Product of unlike signs

Multiplying or dividing two numbers with different signs gives a negative result; two numbers with the same sign give a positive result. For example, (−6) × 5 = −30.

Terminating decimal test

A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors except 2 and 5. Thus 7/20 terminates but 5/12 does not.

Cross-multiplication for fractions

For positive denominators, a/b > c/d exactly when ad > bc. This compares fractions without converting them to decimals or finding a common denominator.

Simplified ratio rule

A ratio is in simplest form when both terms share no common factor other than 1. Divide both terms by their highest common factor, keeping units identical.

Proportion cross-product test

Four quantities a, b, c, d are in proportion when a : b = c : d, which is equivalent to ad = bc. Product of extremes equals product of means.

Direct variation formula

When y varies directly as x, y = kx for a constant k, so y₁/x₁ = y₂/x₂. Increasing x increases y in the same proportion.

Inverse variation formula

When y varies inversely as x, xy = k, so x₁y₁ = x₂y₂. Doubling one quantity halves the other while the product stays constant.

Mean proportional

The mean proportional between two positive numbers a and b is the square root of their product, √(ab). It satisfies a : x = x : b.

Percentage of a quantity

To find x percent of a number N, multiply N by x and divide by 100. For example, 12 percent of 250 equals 30.

Percentage change formula

Percentage change equals the change divided by the original value, multiplied by 100. Always divide by the earlier value, not the final one.

Profit percent base

Profit percent equals profit divided by cost price, times 100. Loss percent uses the same denominator. Percentages are on cost price unless marked price is specified.

Successive discount formula

Two successive discounts of a percent and b percent equal a single discount of a + b − ab/100 percent. The result is always less than a + b.

Equal percent gain and loss

Selling two articles at the same price, one at x percent gain and one at x percent loss, always yields a net loss of x²/100 percent.

Simple interest formula

Simple interest equals principal times rate times time divided by 100, with rate as annual percent and time in years. Interest is computed only on the original principal.

Compound interest formula

Amount equals P(1 + R/100)^n for annual compounding over n years; compound interest is that amount minus P. Interest is added to principal each year.

CI minus SI for two years

For two years at the same rate, compound interest exceeds simple interest by P(R/100)². This shortcut avoids computing both interests separately.

Half-yearly compounding

When interest is compounded half-yearly, halve the annual rate and double the number of periods: amount = P(1 + R/200)^(2n) for n years.

Rate varying by year

With different rates R₁, R₂, R₃ in successive years, amount = P(1 + R₁/100)(1 + R₂/100)(1 + R₃/100). Each year compounds on the previous amount.

Rectangle area and perimeter

Area of a rectangle is length times breadth; perimeter is twice the sum of length and breadth. A square is the special case with all sides equal.

Heron's formula

Area of a triangle with sides a, b, c equals √[s(s−a)(s−b)(s−c)], where s is half the perimeter (a+b+c)/2.

Circle circumference and area

Circumference equals 2πr and area equals πr² for radius r. Use π as 22/7 or 3.14 according to the question's instruction.

Cuboid volume and surface area

For a cuboid of length l, breadth b, height h: volume = lbh, total surface area = 2(lb + bh + hl), lateral surface area = 2h(l + b).

Cylinder formulas

A cylinder of radius r and height h has volume πr²h, curved surface area 2πrh, and total surface area 2πr(r + h).

Cone slant height

For a cone, slant height l equals √(r² + h²) from radius r and height h. Volume is ⅓πr²h and curved surface area is πrl.

Metric volume conversions

1 metre equals 100 centimetres, so 1 m² = 10000 cm² and 1 m³ = 1000000 cm³. One litre equals 1000 cubic centimetres.

Mean of raw data

The mean equals the sum of all observations divided by their number. It uses every value, so an extreme observation shifts it noticeably.

Median position rule

Arrange data in order. For an odd count n, the median is the ((n+1)/2)th value; for even n, average the (n/2)th and (n/2+1)th values.

Grouped data mean

For grouped data, find each class mark as the midpoint of its limits, multiply by class frequency, sum these products, then divide by total frequency.

Grouped median formula

Median = l + [(n/2 − cf)/f] × h, where l is the lower limit of the median class, cf the cumulative frequency before it, f its frequency, h the class width.

Empirical mean-median-mode relation

For moderately skewed distributions, mode approximately equals three times the median minus twice the mean. It estimates the missing measure when two are known.