Navy Sailor Test Mathematics Syllabus

What is the difference between direct proportion and inverse proportion?

In direct proportion, as one quantity increases the other increases (x/y is constant). In inverse proportion, as one increases the other decreases (x times y is constant).

How do you convert a fraction or decimal to a percentage?

Multiply the fraction or decimal by 100 and add the percent sign. For example, 0.25 x 100 = 25%, and 1/4 = 25%.

How do you find x% of a number N?

Compute (x/100) x N. For example, 20% of 150 = (20/100) x 150 = 30.

What is the formula for percentage increase?

Percentage increase = (Increase in value / Original value) x 100.

How do you find what percent one number is of another?

To find what percent A is of B, compute (A / B) x 100.

Define Cost Price (CP) and Selling Price (SP).

Cost Price (CP) is the price at which an item is bought. Selling Price (SP) is the price at which it is sold.

State the formulas for profit and loss in terms of CP and SP.

Profit = SP - CP (when SP is greater than CP). Loss = CP - SP (when CP is greater than SP).

State the formulas for profit percent and loss percent.

Profit% = (Profit / CP) x 100. Loss% = (Loss / CP) x 100. Both are calculated on the cost price.

How do you find Selling Price given Cost Price and Profit%?

SP = CP x (100 + Profit%) / 100. For a loss, SP = CP x (100 - Loss%) / 100.

What is discount, and on what value is it calculated?

Discount is a reduction given on the marked price (list price). Discount = Marked Price - Selling Price, and Discount% is calculated on the marked price.

State the formula for Simple Interest (SI).

SI = (P x R x T) / 100, where P is the principal, R is the rate of interest per annum, and T is the time in years.

State the formula for the amount (A) under simple interest.

Amount A = Principal + Simple Interest = P + (P x R x T)/100 = P(1 + RT/100).

State the formula for Compound Interest amount when compounded annually.

A = P(1 + R/100)^T, where A is the amount, P is principal, R is rate per annum, and T is time in years. Then CI = A - P.

How does compound interest differ from simple interest?

In simple interest, interest is calculated only on the original principal. In compound interest, interest is calculated on the principal plus accumulated interest, so it earns interest on interest.

What is the compound interest formula when interest is compounded half-yearly?

A = P(1 + R/200)^(2T): the rate is halved (R/2) and the number of periods is doubled (2T).

What is the formula for the average (arithmetic mean) of a set of numbers?

Average = (Sum of all observations) / (Number of observations).

If the average of n numbers is M, how do you find their total sum?

Sum = Average x Number of observations = M x n.

What is the average of the first n natural numbers?

The average of the first n natural numbers is (n + 1) / 2.

How is average speed for a whole journey calculated?

Average speed = Total distance / Total time taken (not the simple average of the speeds).

What is an algebraic expression, and what are its terms?

An algebraic expression is a combination of variables, constants, and operations (e.g., 3x + 5). Its terms are the parts separated by + or - signs, here 3x and 5.

What are like terms and unlike terms?

Like terms have the same variables raised to the same powers (e.g., 3x and 5x) and can be combined. Unlike terms have different variables or powers (e.g., 3x and 5y) and cannot be combined.

What is the coefficient of a term? Identify it in 7xy.

The coefficient is the numerical (or constant) factor of a term multiplying the variables. In 7xy, the coefficient is 7.

What is the difference between a monomial, binomial, and trinomial?

A monomial has one term (e.g., 5x), a binomial has two terms (e.g., x + 3), and a trinomial has three terms (e.g., x^2 + 2x + 1).

What does it mean to factorize an algebraic expression?

Factorization is expressing an algebraic expression as a product of its factors (simpler expressions which multiply to give the original).

How do you factorize an expression by taking out the common factor? Factorize 6x + 9.

Find the greatest common factor of all terms and take it outside the bracket. For 6x + 9, the common factor is 3, giving 3(2x + 3).

How do you factorize a difference of two squares?

Use a^2 - b^2 = (a + b)(a - b). For example, x^2 - 16 = (x + 4)(x - 4).

What is a linear equation in one variable, and what is its degree?

A linear equation in one variable has the form ax + b = 0 (a not equal to 0), with the variable to the first power only. Its degree is 1, and it has exactly one solution.

What is the basic rule for solving a linear equation by transposition?

Move a term to the other side of the equals sign and change its sign: a term that is added becomes subtracted, and a multiplying factor becomes a dividing factor, keeping the equation balanced.

State the algebraic identities 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 identity for (a + b)(a - b) and for (x + a)(x + b).

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