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MEAP Preparation - Grade 7 Mathematics2.25 Algebra Review

 Algebra is a branch of mathematics. In algebra, letters are used to represent numbers. Literal: The letters used to represent numbers are called literal numbers or literals. Variable: In algebra, the letter that stands for an unknown number is called a variable. The variables in 8x2y3 are x and y. Numeric Co-efficient: The number that multiplies a variable or variables is called a coefficient. It is usually written in front of the variable or variables. The coefficient in 9yz4 is 9. When the coefficient is 1, it is typically not written (i.e., 1yz4 = yz4 and 1a3 = a3). Exponent/Index and Base: The power to which a variable is raised is called an exponent. The number or variable that is multiplied by itself is called the base. In 7a5, the exponent is 5 and the base is a. When the exponent is 1, it is typically not written (i.e., 6y1z4 = 6yz4). Any variable or a number raised to the power zero gives one (i.e., x0 = 1). Term: A term is a number, variable, or the product of a number and variable(s). Examples of terms are 3x, 4x3, 7xy, x. Like Terms are terms that have the exact same variables raised to the exact same exponents. Examples of like terms: 5x2 and -6x2; 8ab3 and 9ab3 Algebraic Expression: An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It is only a phrase, not the whole sentence, so it doesn't include an equal sign. Example: 2x2 + 4y + 8xy + 15 In an algebraic expression, terms are the elements separated by plus or minus signs. The above example has four terms, 2x2, 4y, 8xy, and 15. Terms may consist of variables and coefficients, or constants. Algebraic Equation: An equation is a statement that two numbers or expressions are equal. Example: x + 5 = 12 - x Algebraic Inequalities: An algebraic inequality is a mathematical statement comparing two unequal algebraic expressions. It states that one algebraic expression is greater than (>), less than (<), greater than or equal to (>=), or less than or equal to (<=) another algebraic expression. Monomial: Any number or a variable or a product of numbers and variables is called a monomial. Each of the following is an example of a monomial: 5, -7, x, y, 6xyz, -9yz4, 2.3a3 Polynomial: An expression containing a finite sum of terms. Examples of Polynomials: 9x; x2+ 4x = 3 The following are NOT Polynomials: 6x-2 because of the negative exponent, the expression is 1/x2 has the variable in the denominator; sqrt(x) - this has a variable inside a radical Binomial: A polynomial with two terms. Example: 4x2 - 2x + 7 Trinomial: A polynomial with three terms. Example: 3x3 + 4x2 - 2x + 7 Degree of a Term: The degree of a term is the sum of the exponents on the variables contained in the term. For example, the degree of the term 4x2 is 2. Degree of a Polynomial: The degree of a polynomial is the largest degree of all its terms. Examples: The degree of 4x2 - 2x + 7 is 2. The degree of 3x3 + 4x2 - 2x + 7 is 3. Directions: Answer the following questions. Also write at least 5 examples of each of the above terms.
 Q 1: In algebraic expression, the terms are any constants, variables, or products or quotients of these.truefalse Q 2: ________ is a symbol (generally a lowercase letter) that represents an unspecified element of a set containing more than one element.constantvariableinequalityequation Q 3: A/An _______ is a mathematical statement that may use numbers, variables, or both.variablesequencesconstantexpression Q 4: In the expression 5xy, 5 is called a ___________.equationexpressionnumerical coefficientvariable Q 5: Terms are separated by plus or minus signs.falsetrue Q 6: The algebraic expression 4x3y2 is atrinomialmonomialpolynomialbinomial Q 7: The expression 3a + 4b + 3c is a binomial.falsetrue Q 8: Which of the following is an equation?2x = 105x + 3y2x2 + 4y + 8xy + 15a + b - 10c + 8d Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!