Maharashtra SSC Arithmetic (MSBSHSE) key terms

A whole number with no fractional or decimal part, including positive numbers, negative numbers, and zero. On the number line, integers are the counting marks such as −3, 0 and 7.

Any number that can be written as a fraction of two integers with a non-zero denominator. Examples include 3/4, −5, 0.6 and 2.5, because each can be expressed in the form p/q.

A number written as one whole number divided by another, such as 3/5. The upper number is the numerator and the lower is the denominator, which tells how many equal parts make one whole.

A number written using place value to the right of a decimal point, such as 4.75. The digits after the point stand for tenths, hundredths and so on, so 4.75 means 4 and 75 hundredths.

The number obtained by turning a fraction upside down, so the numerator and denominator swap places. The reciprocal of 3/7 is 7/3, and multiplying a number by its reciprocal gives 1.

A straight line marked with evenly spaced points representing numbers, usually with zero in the middle, negatives to the left and positives to the right. It shows order and distance between numbers.

The distance of a number from zero on the number line, written with vertical bars. It is always non-negative, so the absolute value of −9 is 9 and the absolute value of 9 is also 9.

A comparison of two quantities of the same kind by division, written as a : b or as the fraction a/b. It tells how many times one quantity contains the other, not their difference.

A statement that two ratios are equal, such as 3 : 4 = 9 : 12. In a true proportion the product of the extremes equals the product of the means.

In the ratio a : b, the first term a is the antecedent and the second term b is the consequent. The order matters, because b : a is generally a different ratio from a : b.

A method for solving a proportion a/b = c/d by multiplying the numerator of one side by the denominator of the other, giving ad = bc. It is also used to compare two fractions.

A set of three quantities a, b, c in which a : b equals b : c, so that b² = ac. The middle quantity b is then called the mean proportional between a and c.

The middle term b in a continued proportion a : b = b : c. It equals the square root of the product ac, so the mean proportional between 4 and 25 is 10.

A relationship in which two quantities increase or decrease together, so their ratio stays constant. If y varies directly as x, then y = kx for some fixed number k.

A relationship in which one quantity increases as the other decreases, so their product stays constant. If y varies inversely as x, then xy = k, meaning y = k/x.

The fixed number k that links two varying quantities in a direct or inverse relationship. It is found by dividing y by x, or by multiplying x and y, using a known pair of values.

A fraction or ratio expressed out of 100, written with the percent sign. Thus 45% means 45 per hundred, or 45/100, which is the decimal 0.45.

The amount a shopkeeper pays to buy or produce an article before selling it. Profit or loss is calculated by comparing the selling price with this cost price.

The amount a customer actually pays when an article is sold. It may differ from the marked price after a discount, and it is compared with the cost price to find profit or loss.

The gain made when the selling price is greater than the cost price, found by subtracting cost price from selling price. Profit percent is this gain divided by the cost price, multiplied by 100.

The amount lost when the selling price is less than the cost price, found by subtracting selling price from cost price. Loss percent is this amount divided by the cost price, multiplied by 100.

The price printed on a label or listed in a catalogue before any reduction is allowed. Discount is always calculated as a percentage of this marked price, not of the cost price.

A reduction allowed on the marked price of an article, usually stated as a percentage of that marked price. Selling price equals marked price minus the discount amount.

Interest calculated only on the original principal for the whole time, never on interest already earned. The formula is I = P × R × T / 100, where T is measured in years.

Interest calculated on the principal plus interest already added, so the interest itself earns interest in later periods. The amount is A = P(1 + R/100)^n, and interest is A minus P.

The sum of money originally borrowed, lent or invested, on which interest is calculated. In simple interest problems it stays unchanged, while under compound interest it grows each period.

The total sum due at the end of a loan or investment period, equal to the principal plus the interest earned. In compound interest it is found using A = P(1 + R/100)^n.

The percentage charged or earned on the principal for each year, usually written as R% per annum. A rate of 8% per annum means 8 rupees of interest on every 100 rupees for one year.

The total length of the boundary of a closed plane figure, found by adding the lengths of all its sides. For a rectangle it equals 2 × (length + breadth).

The measure of the surface enclosed by a closed plane figure, expressed in square units such as cm². Common formulas include length × breadth for a rectangle and side² for a square.

The distance around a circle, equal to 2πr or πd where r is the radius and d the diameter. It is the circle's perimeter and is measured in ordinary length units.

The radius is the distance from the centre of a circle to any point on it; the diameter is a straight line through the centre joining two points on the circle. The diameter is twice the radius.

The total area of all the faces of a solid figure, measured in square units. For a cuboid it is 2(lb + bh + hl), and for a cube it is 6 × side².

The amount of space occupied by a solid figure, measured in cubic units such as cm³. For a cuboid it is length × breadth × height, and for a cylinder it is πr²h.

The quantity of liquid or gas a hollow container can hold, often measured in litres or millilitres. One litre equals 1000 cm³, which links capacity directly to volume.

The arithmetic average of a set of observations, found by adding all the values and dividing by how many there are. It uses every value, so a single very large value can pull it upward.

The middle value of a set of observations arranged in ascending or descending order. If the number of observations is even, the median is the mean of the two middle values.

The value that occurs most often in a set of observations. A data set may have one mode, more than one mode, or no mode if every value appears equally often.

A diagram that shows data using rectangular bars of equal width whose heights represent the frequencies. Bars are usually drawn with equal gaps between them, and the axes must be labelled.

A graph showing a continuous frequency distribution as adjacent bars with no gaps. The width of each bar represents a class interval and its height shows the frequency of that class.

The number of times a particular value or class interval occurs in a set of data. A frequency table lists each value or class alongside its count, making totals and comparisons easy.