Exponents, Equations and Inequalities

What Will You Learn?

• 1. Exponents (Grade 9)- Mathematics revolves around two core actions: simplify and solve. Exponents provide a powerful tool for simplification, making calculations more efficient. Understanding Square and Cube Roots. Clarifying common misconceptions about square roots. The Importance of Prime Factorization. Helps simplify exponents by breaking numbers into their smallest building blocks.
• 2. Rational Exponents (Grade 10)- Moving beyond integer exponents to fractional exponents. Applying Exponential Rules to Advanced Expressions. Using foundational exponent laws to simplify and solve complex expressions. Solving Exponential Equations with university-level techniques. Tackling difficult exponential problems with structured methods for deeper understanding.
• 3. Grade 10 Equations- Up until now, we focused on simplification—breaking down expressions into their simplest forms. Now, we move beyond simplification and step into solving equations—finding unknown values. Building Mathematical Stories, we started with words (numbers), then structured them into sentences (algebraic expressions). Now, we use those sentences to create stories—equations that lead to solutions. - Linear Equations, solving for a single unknown variable using fundamental algebra. Quadratic Equations, exploring higher-order equations that involve squared terms. The techniques learned in exponents, factorization, and number systems play a crucial role in solving equations. These connections reinforce previous concepts, showing how mathematics is a continuous, structured process.
• 4. Simultaneous and Literal Equations- We delve into two different techniques for solving equations. Rather than just teaching the mechanics of these equations, we emphasize their purpose—knowing when to use them and how to apply them effectively in mathematical problems. This ensures students develop a strategic approach to problem-solving.
• 5. Word Problems- Bridging Theory with Practical Understanding. We take the techniques learned in equations and apply them to real-world situations. This helps you see mathematics as more than just numbers and symbols, but as a tool for problem-solving in daily life. We will learn about linear, quadratic and simultaneous word problems. You will understand why a specific technique is used and how to solve problems efficiently
• 6. -Linear inequalities- Unlike equations that give a single solution, inequalities describe a range of possible values that satisfy a given condition. These are useful in scenarios where there is a minimum or maximum limit rather than an exact solution. By mastering inequalities, you’ll develop an essential mathematical skill for analyzing situations where multiple values can satisfy a condition.