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linear equation and graphs, Summaries of Mathematics

Mathematics

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COMMONWEALTH SECONDARY SCHOOL
SECONDARY 1 EXPRESS MATHEMATICS
Chapter 5: Linear Equations and Simple Inequalities
Name: _________________________ ( ) Class: ______ Date: _____________
Objectives:
Explore the concepts of equation and inequality
Solve linear equations in one variable
Solve fractional equations that can be reduced to linear equations
Evaluate an unknown in a formula
Formulate linear equations to solve word problems
Solve simple linear inequalities
5.1 Linear Equation (SLS: Chap 5 Linear Equations Activities 1-7)
5.1.1 Definition of a Linear Equation (Textbook page 110):
______________________ is an example of a linear equation in one variable.
5.1.2 Solving Linear Equations (Textbook page 111):
1. To solve an equation means to find the value of the unknown variable in the equation such that
this value found makes the equation become a true or valid statement. The value found for the
variable is called the solution of the equation.
2. We can use the idea of a beam balance to help us solve equations. An equation
means that both sides of the equation are equal to each other.
For example, .
In the example above is equal to . To solve the solution for we have to balance the
equation.
We do this by following 4 rules:
Rule 1: Equal numbers or variables are added to each side
Example: Solve
Rule 2: Equal numbers or variables are subtracted from each side,
Example: Solve
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COMMONWEALTH SECONDARY SCHOOL

SECONDARY 1 EXPRESS MATHEMATICS

Chapter 5: Linear Equations and Simple Inequalities

Name: _________________________ ( ) Class: ______ Date: _____________ Objectives:  Explore the concepts of equation and inequality  Solve linear equations in one variable  Solve fractional equations that can be reduced to linear equations  Evaluate an unknown in a formula  Formulate linear equations to solve word problems  Solve simple linear inequalities 5.1 Linear Equation (SLS: Chap 5 Linear Equations Activities 1-7) 5.1.1 Definition of a Linear Equation (Textbook page 110): ______________________ is an example of a linear equation in one variable. 5.1.2 Solving Linear Equations (Textbook page 111):

  1. To solve an equation means to find the value of the unknown variable in the equation such that this value found makes the equation become a true or valid statement. The value found for the variable is called the solution of the equation.
  2. We can use the idea of a beam balance to help us solve equations. An equation means that both sides of the equation are equal to each other. For example,. In the example above is equal to. To solve the solution for we have to balance the equation. We do this by following 4 rules: Rule 1 : Equal numbers or variables are added to each side Example: Solve Rule 2 : Equal numbers or variables are subtracted from each side, Example: Solve

Rule 3 : Each side is multiplied by equal numbers, Example: Solve Rule 4 : Each side is divided by equal numbers except zero. Example: Solve Example 1: Solve the following equations: (a) (b) (c) (^) (d) (e) (f) Homework: Exercise 5A (pg 118), Question: 3, 4a,c,f,h,i,k,n, 8b, 8e

5.2 Formulae

  1. A formula expresses a rule in algebraic terms. Examples of formulas which you have learnt: Example 4: Newton’s second law states that the net force F acting on a body is given by F = ma , where m is the mass and a is the acceleration of the body. The units for F , m and a are the Newton (N), the kilogram (kg) and metre per second squared (ms-2) respectively. (a) If m = 1000 kg and a = 0.05 ms-2, find the net force acting on the body. (b) If F = 100 N and a = 0.1 ms-2, find the mass of the body. Example 5: (a) If , find V when and. (b) If , find y when , , and.

5.2.1 Construction of Formula: To construct a formula, we choose letters to represent quantities before expressing the rule in algebraic terms. Example 6: Construct a formula in each of the following: (a) The perimeter P of a quadrant with radius r. (b) The total weight, W in kg of b boys weighing x kg each and g girls weighing y kg each. Homework: Exercise 5B (pg 122), Question: 2, 3, 5, 7, 9, 15 5.3 Applications of Linear Equations in Real-World Contexts 5.3.1 Algebraic Method:

  1. We use the following 5 steps to solve word problems: Step 1: ______________ the problem. Step 2: ______________ the unknown. E.g. Step 3: ______________ an equation using the information given. Step 4: ______________ the equation to find the unknown. Step 5: ______________ a final statement. Step 6: ____________ the answer. Example 7: Lucy bought 4 apples and 6 oranges. She spends a total of $3.60. If an orange costs 10 cents more than an apple, find the cost of an apple and the cost of an orange.

Example 10: A restaurant owner pays a waiter an amount of $ A per week. The amount is made up of a basic wage of $60 plus 11 cents for each of the n customers he serves. The formula connecting A and n in this case is. (a) Calculate the amount of money the waiter received in a week when he served 240 customers. (b) At the end of another week, he received $115. How many customers did he serve? (c) The owner of the restaurant decides to decrease the waiter’s basic wage to $45 but to increase the pay per customer to 17 cents. Write down the new formula connecting A and n. (d) Find the number of customers the waiter would have to serve in a week for him to receive the same amount of money whichever formula is used. Homework: Exercise 5C (pg 125), Question: 1, 2, 3, 7, 9, 11, 14 5.4 Simple Inequalities 5.4.1 Properties of Inequalities: Refer to textbook page 127: Try Investigation 5.4.2 Solving Simple Linear Inequalities: Example 11 : Solve the following inequalities (a) (b)

Example 12: A chicken pie costs 70 cents. What is the maximum number of chicken pies that one can buy with $5? Homework: Exercise 5D (pg 125), Question: 1, 2, 3, 4, 6, 7