FORM ONE MATHEMATICS TOPIC 7: ALGEBRA

September 15, 2021 , ,


    •      ALGEBRA

    An algebraic expression – is a collection of numbers, variables, operators and grouping symbols.Variables - are letters used to represent one or more numbers

    Symbols to form Algebraic Expressions
    Use symbols to form algebraic expressions
    The parts of an expression collected together are called terms
    Example
    • x + 2x – are called like terms because they have the same variables
    • 5x +9y – are called unlike terms because they have different variables
    An algebraic expression can be evaluated by replacing or substituting the numbers in the variables
    Example 1
    Evaluate the expressions below, given that x = 2 and y = 3
    Example 2
    Evaluate the expressions below, given that m = 1 and n = - 2
    An expression can also be made from word problems by using letters and numbers
    Example 3
    A rectangle is 5 cm long and w cm wide. What is its area?
    Solution
    Let the area be A.
    Then
    A = length× widith
    A = 5w cm2
    Simplifying Algebraic Expressions
    Simplify algebraic expressions
    Algebraic expressions can be simplified by addition, subtraction, multiplication and division
    Addition and subtraction of algebraic expression is done by adding or subtracting the coefficients of the like terms or letters
    Coefficient of the letter – is the number multiplying the letter
    Multiplication and division of algebraic expression is done on the coefficients of both like and unlike terms or letters
    Example 4
    Simplify the expressions below
    Solution

    An equation – is a statement that two expressions are equal
    An Equation with One Unknown
    Solve an equation with one unknown
    An equation can have one variable (unknown) on one side or two variables on both sides.
    When you shift a number or term from one side of equation to another, its sign changes
    • If it is positive, it becomes negative
    • If it is negative, it becomes positive
    Example 5
    Solve the following equations
    Solution
    An Equation from Word Problems
    Form and solve an equation from word problems
    Some word problems can be solved by using equations as shown in the below examples
    Example 6
    Naomi is 5 years young than Mariana. The total of their ages 33 years. How old is Mariana?
    Solution
    Mariana is 19 years

    Simultaneous Equations
    Solve simultaneous equations
    Simultaneous equations – are groups of equations containing multiple variables
    Example 7
    Examples of simultaneous equation
    A simultaneous equation can be solved by using two methods:
    • Elimination method
    • Substitution method
    ELIMINATION METHOD
    STEPS
    • Choose a variable to eliminatee.g x or y
    • Make sure that the letter to be eliminated has the same coefficient in both equations and if not, multiply the equations with appropriate numbers that will give the letter to be eliminated the same coefficient in both equations
    • If the signs of the letter to be eliminated are the same, subtract the equations
    • If the signs of the letter to be eliminated are different, add the equations
    Example 8
    Solve the following simultaneous equations by elimination method
    Solution
    1. Eliminate y
    To find y put x = 2 in either equation (i) or (ii)
    From equation (i)
    (b)Eliminate x
    In order to find y, put x = 2 in either equation (i) or (ii)
    From equation (ii)
    (c) Given
    To find g put r = 3 in either equation (i) or (ii)
    From equation (i)
    (d) Given
    To find x, put y = - 1 in either equation(i) or (ii)
    From equation (ii)
    BY SUBSTITUTION
    STEPS
    • Make the subject one letter in one of the two equation given
    • Substitute the letter in the remaining equation and proceed as in case of elimination
    Example 9
    Solve the following simultaneous equations by substitution method
    Solution
    Linear Simultaneous Equations from Practical Situations
    Solve linear simultaneous equations from practical situations
    Simultaneous equations can be used to solve problems in real life involving two variables
    Example 10
    If 3 Mathematics books and 4 English books weighs 24 kg and 5 Mathematics books and 2 English books weighs 20 kg, find the weight of one Mathematics book and one English book.
    Solution
    Let the weight of one Mathematics book = x and
    Let the weight of one English book = y
    To find y, put x = 2.29 in either equation (i) or (ii)
    From equation(i).

    An inequality – is a mathematical statement containing two expressions which are not equal. One expression may be less or greater than the other.The expressions are connected by the inequality symbols<,>,≤ or≥.Where< = less than,> = greater than,≤ = less or equal and ≥ = greater or equal.
    Linear Inequalities with One Unknown
    Solve linear inequalities in one unknown
    An inequality can be solved by collecting like terms on one side.Addition and subtraction of the terms in the inequality does not change the direction of the inequality.Multiplication and division of the sides of the inequality by a positive number does not change the direction of the inequality.But multiplication and division of the sides of the inequality by a negative number changes the direction of the inequality
    Example 11
    Solve the following inequalities
    Solution
    Linear Inequalities from Practical Situations
    Form linear inequalities from practical situations
    To represent an inequality on a number line, the following are important to be considered:
    • The endpoint which is not included is marked with an empty circle
    • The endpoint which is included is marked with a solid circle
    Example 12
    Compound statement – is a statement made up of two or more inequalities
    Example 13
    Solve the following compound inequalities and represent the answer on the number line
    Solution

    Post a Comment

    No comments

    Subscribe to: Post Comments ( Atom )