Algebra 1
Welcome to the Algebra 1 course. This page will serve as the hub for all Algebra 1 subtopics, taking you step-by-step through the fundamentals of algebraic thinking.
Why Learn Algebra?
Algebra is much more than just solving for x. It is the language of patterns and the foundation of all advanced mathematics, science, and technology. By learning algebra, you are training your brain to think logically and solve complex problems.
Real-Life Applications
- Financial Planning: Calculating interest rates, creating budgets, and predicting future savings all require algebraic formulas.
- Architecture & Engineering: From building bridges to designing smartphones, algebra is used to determine dimensions and stress levels.
- Computer Science: Coding and algorithms are built on algebraic logic. Every video game uses algebra to calculate movement and graphics.
- Medicine: Doctors and pharmacists use algebra to calculate correct dosages based on a patient’s weight and age.
- Sports & Fitness: Analyzing player statistics or calculating the trajectory of a ball involves algebraic variables.
1. Foundations of Algebra
Variables and Expressions
In algebra, we use variables to represent unknown numbers. A variable is usually a letter like x or y.
An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables, and operations.
Examples:
- Example 1: “5 more than a number x” is written as x + 5.
- Example 2: “The product of 3 and y” is written as 3y.
- Example 3: “Half of a number z” is written as z/2.
Practice Questions:
1. Write an expression for “7 less than twice a number n“. (Click to see answer)
Answer: 2n – 7
2. Write an expression for “the sum of 10 and a number k“. (Click to see answer)
Answer: 10 + k
3. Write an expression for “9 divided by a number w“. (Click to see answer)
Answer: 9 / w
4. Write an expression for “the product of 4 and the square of x“. (Click to see answer)
Answer: 4x²
5. Write an expression for “3 less than the quotient of y and 5″. (Click to see answer)
Answer: (y / 5) – 3
Order of Operations
When an expression contains more than one operation, we use the Order of Operations (PEMDAS) to ensure accuracy.
Examples:
- Example 1: 10 + 2 × 3 = 10 + 6 = 16.
- Example 2: (5 + 3)² = 8² = 64.
- Example 3: 20 ÷ 4 + 2 = 5 + 2 = 7.
Practice Questions:
1. Evaluate 12 – 4 ÷ 2 + 1. (Click to see answer)
Answer: 11 (12 – 2 + 1 = 11)
2. Evaluate 3 × (4 + 2)². (Click to see answer)
Answer: 108 (3 × 6² = 3 × 36 = 108)
3. Evaluate 15 ÷ 3 + 4 × 2. (Click to see answer)
Answer: 13 (5 + 8 = 13)
4. Evaluate 2³ + (10 – 2) ÷ 4. (Click to see answer)
Answer: 10 (8 + 8 ÷ 4 = 8 + 2 = 10)
5. Evaluate 50 – [2 × (3 + 5)]. (Click to see answer)
Answer: 34 (50 – [2 × 8] = 50 – 16 = 34)
2. Solving Linear Equations
A linear equation is an equation for a straight line. The goal is to find the value of the variable that makes the equation true.
Examples:
- Example 1: x + 5 = 12. Subtract 5 from both sides: x = 7.
- Example 2: 3y = 15. Divide both sides by 3: y = 5.
- Example 3: 2z – 4 = 10. Add 4 then divide by 2: 2z = 14, so z = 7.
Practice Questions:
1. Solve for x: x – 8 = 20. (Click to see answer)
Answer: x = 28
2. Solve for y: 5y = 45. (Click to see answer)
Answer: y = 9
3. Solve for z: 2z + 6 = 18. (Click to see answer)
Answer: z = 6 (2z = 12, so z = 6)
4. Solve for n: n/4 = 7. (Click to see answer)
Answer: n = 28
5. Solve for x: 3x – 5 = 16. (Click to see answer)
Answer: x = 7 (3x = 21, so x = 7)
Course Curriculum
- Foundations of Algebra
- Solving Linear Equations
- Linear Inequalities
- Functions and Patterns