Grade 9 Mathematics Unit 2

on


 

TOPIC 1: DIRECTED NUMBERS

Lesson 1: Directed Numbers in Practical Situations

  • Summary: Understanding and applying positive and negative numbers in real-life contexts such as temperature changes, financial transactions, and elevation.
  • Example:
    • Situation: A temperature drops from 5°C to -3°C.
    • Explanation: The change in temperature is calculated as -3 - 5 = -8°C.

Lesson 2: Adding Directed Numbers

  • Summary: Learning how to add positive and negative numbers.
  • Example:
    • Problem: Add -4 and 7.
    • Solution: -4 + 7 = 3
    • Explanation: Start at -4 on the number line, move 7 units to the right to reach 3.

Lesson 3: Subtracting Directed Numbers

  • Summary: Understanding subtraction of directed numbers, including subtracting negative numbers.
  • Example:
    • Problem: Subtract -3 from 5.
    • Solution: 5 - (-3) = 5 + 3 = 8
    • Explanation: Subtracting a negative is equivalent to adding the positive.

Lesson 4: Multiplying Directed Numbers

  • Summary: Rules for multiplying positive and negative numbers.
  • Example:
    • Problem: Multiply -6 by 4.
    • Solution: -6 * 4 = -24
    • Explanation: A positive times a negative gives a negative product.

Lesson 5: Dividing Directed Numbers

  • Summary: Rules for dividing positive and negative numbers.
  • Example:
    • Problem: Divide -18 by -3.
    • Solution: -18 ÷ -3 = 6
    • Explanation: A negative divided by a negative gives a positive quotient.

Lesson 6: Solving Mixed Problems

  • Summary: Combining all operations with directed numbers in complex calculations.
  • Example:
    • Problem: Calculate 4 + (-3) * 2 - 6 / (-2).
    • Solution: 4 - 6 + 3 = 1
    • Explanation: Follow the order of operations (PEMDAS/BODMAS).

TOPIC 2: INDICES

Lesson 7: Squares and Square Roots

  • Summary: Understanding squares and square roots, including their properties and notation.
  • Example:
    • Problem: Find the square and square root of 16.
    • Solution: The square of 4 is 16, and the square root of 16 is 4.

Lesson 8: Multiplication Laws of Indices

  • Summary: Rules for multiplying powers with the same base.
  • Example:
    • Problem: Simplify 2^3 * 2^4.
    • Solution: 2^(3+4) = 2^7
    • Explanation: Add the exponents when multiplying like bases.

Lesson 9: Division Laws of Indices

  • Summary: Rules for dividing powers with the same base.
  • Example:
    • Problem: Simplify 5^6 / 5^2.
    • Solution: 5^(6-2) = 5^4
    • Explanation: Subtract the exponents when dividing like bases.

Lesson 10: Zero and Negative Indices

  • Summary: Understanding the meaning of zero and negative exponents.
  • Example:
    • Problem: Evaluate 7^0 and 3^-2.
    • Solution: 7^0 = 1; 3^-2 = 1/9
    • Explanation: Any number to the power of zero is 1, and a negative exponent indicates a reciprocal.

Lesson 11: Scientific Notation

  • Summary: Expressing large and small numbers in scientific notation.
  • Example:
    • Problem: Express 4500 in scientific notation.
    • Solution: 4.5 x 10^3
    • Explanation: Move the decimal point to create a number between 1 and 10, then multiply by the appropriate power of ten.

Lesson 12: Combined Index Operations

  • Summary: Applying multiple index laws in a single expression.
  • Example:
    • Problem: Simplify (3^2 * 3^-4) / 3^3.
    • Solution: 3^(2 - 4 - 3) = 3^-5 = 1/3^5
    • Explanation: Combine all index laws to simplify.

TOPIC 3: ALGEBRAIC EXPRESSIONS

Lesson 13: Number Patterns

  • Summary: Recognizing and continuing number patterns and sequences.
  • Example:
    • Problem: Find the next two terms in the sequence 2, 5, 8, 11, ...
    • Solution: 14, 17
    • Explanation: The sequence increases by 3 each time.

Lesson 14: Algebraic Expressions

  • Summary: Introduction to expressions involving variables and constants.
  • Example:
    • Problem: Write an expression for "5 times a number x, decreased by 7".
    • Solution: 5x - 7
    • Explanation: 5 times x means multiplication, and decreased by 7 means subtraction.

Lesson 15: Simplifying Algebraic Expressions

  • Summary: Combining like terms and using distributive properties.
  • Example:
    • Problem: Simplify 3x + 2x - 4.
    • Solution: 5x - 4
    • Explanation: Combine like terms (3x and 2x).

Lesson 16: Evaluating Algebraic Expressions

  • Summary: Substituting values into expressions to find their numerical value.
  • Example:
    • Problem: Evaluate 2x^2 - 3 when x = 3.
    • Solution: 2(3)^2 - 3 = 18 - 3 = 15
    • Explanation: Substitute 3 for x and calculate.

Lesson 17: Factorization

  • Summary: Breaking down expressions into factors, including finding common factors.
  • Example:
    • Problem: Factorize 12x^2 - 6x.
    • Solution: 6x(2x - 1)
    • Explanation: Factor out the greatest common factor, 6x.

TOPIC 4: EQUATIONS

Lesson 18: Simple Equations

  • Summary: Solving equations involving one variable.
  • Example:
    • Problem: Solve 2x + 3 = 11.
    • Solution: x = 4
    • Explanation: Subtract 3 from both sides, then divide by 2.

Lesson 19: Solving Equations Involving Grouping Symbols

  • Summary: Solving equations with parentheses or brackets.
  • Example:
    • Problem: Solve 3(x + 4) = 21.
    • Solution: x = 3
    • Explanation: Divide both sides by 3, then subtract 4.

Lesson 20: Solving Equations Involving Unknowns on Both Sides

  • Summary: Handling equations with variables on both sides.
  • Example:
    • Problem: Solve 4x - 7 = 2x + 5.
    • Solution: x = 6
    • Explanation: Subtract 2x and add 7 to both sides, then divide by 2.

Lesson 21: Equations Involving Fractions

  • Summary: Solving equations that contain fractions.
  • Example:
    • Problem: Solve (x/3) + 2 = 5.
    • Solution: x = 9
    • Explanation: Subtract 2, then multiply by 3.

Lesson 22: Changing Subjects of Simple Equations

  • Summary: Rearranging equations to solve for a specific variable.
  • Example:
    • Problem: Make y the subject in the equation x = 2y + 3.
    • Solution: y = (x - 3)/2
    • Explanation: Isolate y by subtracting 3 from both sides and dividing by 2.

Lesson 23: Transposing Formulae

  • Summary: Manipulating formulae to solve for different variables.
  • Example:
    • Problem: Transpose the formula P = 2L + 2W to solve for W.
    • Solution: W = (P - 2L)/2
    • Explanation: Subtract 2L and divide by 2.

Lesson 24: Solving Word Problems

  • Summary: Translating real-life situations into equations and solving them.
  • Example:
    • Problem: A total of $150 is divided between two people such that one person receives $30 more than the other. How much does each person get?
    • Solution: Let x be the amount one person gets. Then the other gets x + 30. Solve x + (x + 30) = 150 to find x = 60. The amounts are $60 and $90.
    • Explanation: Formulate and solve the equation based on the problem description.

 

Comments

Post a Comment

Ads