Podcast
Questions and Answers
Solve for $x$: $3(x + 2) = 5x - 4$
Solve for $x$: $3(x + 2) = 5x - 4$
- $x = 8$
- $x = 5$ (correct)
- $x = 6$
- $x = 7$
The expansion of $(a + b)^2$ is $a^2 + b^2$
The expansion of $(a + b)^2$ is $a^2 + b^2$
False (B)
Expand and simplify: $(x + 3)(x - 4)$
Expand and simplify: $(x + 3)(x - 4)$
x^2 - x - 12
If $2x + 5 = 11$, then $x$ = ____
If $2x + 5 = 11$, then $x$ = ____
Match the following expressions with their simplified forms:
Match the following expressions with their simplified forms:
Solve for $x$: $3x + 7 = 22$
Solve for $x$: $3x + 7 = 22$
Expand the following expression: $4(2x - 3)$
Expand the following expression: $4(2x - 3)$
Solve for $x$: $5x - 10 = 2x + 5$. The value of x is ______.
Solve for $x$: $5x - 10 = 2x + 5$. The value of x is ______.
Match the expression with its expanded form:
Match the expression with its expanded form:
Expand: $2(3y - 5)$
Expand: $2(3y - 5)$
Solve for $x$: $5x - 9 = 3x + 5$. Therefore, x = ______
Solve for $x$: $5x - 9 = 3x + 5$. Therefore, x = ______
Match the equation to its solution set:
Match the equation to its solution set:
The expression $(a + b)^2$ is equivalent to $a^2 + b^2$.
The expression $(a + b)^2$ is equivalent to $a^2 + b^2$.
Expand and simplify: $2(x - 3) + 5(x + 2)$
Expand and simplify: $2(x - 3) + 5(x + 2)$
If $y = 4x - 9$ and $x = 3$, then $y$ = ____.
If $y = 4x - 9$ and $x = 3$, then $y$ = ____.
Match the following expressions with their expanded forms:
Match the following expressions with their expanded forms:
Solve for $x$: $5x - 10 = 3x + 4$, $x$ = ______
Solve for $x$: $5x - 10 = 3x + 4$, $x$ = ______
What is the solution to the linear equation $3x + 7 = 22$?
What is the solution to the linear equation $3x + 7 = 22$?
Is the expression $(a + b)^2$ equivalent to $a^2 + b^2$?
Is the expression $(a + b)^2$ equivalent to $a^2 + b^2$?
Solve for $y$: $2y - 5 = 11$. Therefore, $y$ = _______
Solve for $y$: $2y - 5 = 11$. Therefore, $y$ = _______
Which of the following is the expanded form of the binomial $(2x - 3)^2$?
Which of the following is the expanded form of the binomial $(2x - 3)^2$?
Expand the following expression: $4(2x + 3y - 5)$
Expand the following expression: $4(2x + 3y - 5)$
Is $3x + 5 = 2x - 1$ equivalent to $x = -6$?
Is $3x + 5 = 2x - 1$ equivalent to $x = -6$?
Solve for x: $2(x + 3) = 16$, $x$ = _____
Solve for x: $2(x + 3) = 16$, $x$ = _____
What is the solution to the equation $3x + 7 = 22$?
What is the solution to the equation $3x + 7 = 22$?
Is the following statement true or false? $(a + b)^2 = a^2 + b^2$
Is the following statement true or false? $(a + b)^2 = a^2 + b^2$
Solve for x: $5x - 10 = 2x + 5$. x = _______
Solve for x: $5x - 10 = 2x + 5$. x = _______
Flashcards
What is a linear equation?
What is a linear equation?
An equation where the highest power of the variable is 1. When graphed, it forms a straight line.
What is a binomial?
What is a binomial?
An algebraic expression with two terms, connected by a plus or minus sign.
What does 'expanding brackets' mean?
What does 'expanding brackets' mean?
The process of multiplying each term inside the brackets by the term outside the brackets.
What is meant by simplifying?
What is meant by simplifying?
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What does 'solving an equation' mean?
What does 'solving an equation' mean?
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What is a constant?
What is a constant?
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What is a coefficient?
What is a coefficient?
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What are like terms?
What are like terms?
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What is a solution to an equation?
What is a solution to an equation?
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What is a variable?
What is a variable?
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What is a term?
What is a term?
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What is a 'solution'?
What is a 'solution'?
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What does 'simplify' mean?
What does 'simplify' mean?
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Expanding Brackets
Expanding Brackets
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Combining Like Terms
Combining Like Terms
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Simplifying Expressions
Simplifying Expressions
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Solving Equations
Solving Equations
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What is the coefficient?
What is the coefficient?
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What is a 'root' of an equation?
What is a 'root' of an equation?
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What is an identity?
What is an identity?
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What is 'expanding'?
What is 'expanding'?
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What does 'evaluating' mean?
What does 'evaluating' mean?
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What is the additive identity?
What is the additive identity?
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What is an equation?
What is an equation?
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What is the Distributive Property?
What is the Distributive Property?
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What is an extraneous solution?
What is an extraneous solution?
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What is meant by 'inverse operations'?
What is meant by 'inverse operations'?
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What is an identity equation?
What is an identity equation?
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How to Expand Brackets
How to Expand Brackets
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Solving simple linear equations
Solving simple linear equations
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Expanding single brackets
Expanding single brackets
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Combining algebraic terms
Combining algebraic terms
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Binomial Expansion
Binomial Expansion
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Solve an equation with variables on both sides
Solve an equation with variables on both sides
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Study Notes
- Solving Linear Equations
- The objective is to isolate the variable on one side.
- Inverse operations reverse the operations on the variable.
- Addition and subtraction are inverse operations.
- Multiplication and division are inverse operations.
- Maintain equality by performing the same operation on both sides.
- Simplify both sides before isolating the variable by combining like terms.
Examples of Solving Linear Equations
- Solve for x: x + 5 = 12 => x = 12 - 5 => x = 7
- Solve for y: y - 3 = 8 => y = 8 + 3 => y = 11
- Solve for z: 4z = 20 => z = 20 / 4 => z = 5
- Solve for a: a / 2 = 9 => a = 9 * 2 => a = 18
- Solve for b: 2b + 3 = 11 => 2b = 11 - 3 => 2b = 8 => b = 8 / 2 => b = 4
Binomials
- A binomial is an algebraic expression containing two terms.
- Terms are connected by a plus or minus sign.
- Examples: x + y, a - b, 2m + 3n, p^2 - q^2.
Expanding Brackets
- Expanding brackets involves multiplying the outside term by each inside term.
- Use the distributive property: a(b + c) = ab + ac.
- Pay attention to signs when expanding.
Examples of Expanding Brackets
- Expand: 3(x + 2) = 3x + 6
- Expand: -2(y - 4) = -2y + 8
- Expand: a(2a + 5) = 2a^2 + 5a
- Expand: x(x - 3) = x^2 - 3x
- Expand: 5(2b + 1) = 10b + 5
Expanding Two Binomials
- Use FOIL (First, Outer, Inner, Last) or distributive property.
- (a + b)(c + d) = ac + ad + bc + bd
Examples of Expanding Two Binomials
- Expand: (x + 1)(x + 2) = x^2 + 2x + x + 2 = x^2 + 3x + 2
- Expand: (y - 3)(y + 4) = y^2 + 4y - 3y - 12 = y^2 + y - 12
- Expand: (2a + 1)(a - 2) = 2a^2 - 4a + a - 2 = 2a^2 - 3a - 2
- Expand: (b - 5)(b - 1) = b^2 - b - 5b + 5 = b^2 - 6b + 5
- Expand: (x + 3)(x - 3) = x^2 - 3x + 3x - 9 = x^2 - 9
Year 9 Level Algebra Questions
- Includes solving linear equations, simplifying expressions, expanding brackets, and basic factoring.
Simplifying Expressions
- Combine like terms.
- Like terms have the same variables to the same powers.
- Examples: 3x + 2x = 5x, 4y^2 - y^2 = 3y^2, 5ab + 2ab - ab = 6ab
Examples of Simplifying Expressions
- Simplify: 2x + 3y + 4x - y = 6x + 2y
- Simplify: 5a - 2b - 3a + 7b = 2a + 5b
- Simplify: 4m^2 + 2m - m^2 + 3m = 3m^2 + 5m
- Simplify: 7p - 3q + q - 4p = 3p - 2q
- Simplify: 6xy + 2x - 3xy + 4x = 3xy + 6x
Basic Factoring
- Breaking down an expression into its factors.
- Look for common factors.
- Examples: 4x + 8 = 4(x + 2), 3y^2 - 6y = 3y(y - 2)
Examples of Basic Factoring
- Factor: 5a + 10 = 5(a + 2)
- Factor: 2b - 6 = 2(b - 3)
- Factor: 4x^2 + 8x = 4x(x + 2)
- Factor: 6y - 9y^2 = 3y(2 - 3y)
- Factor: 7m^2 + 14m = 7m(m + 2)
Solving Equations with Fractions
- Eliminate fractions by multiplying by the least common denominator (LCD).
- LCD is the smallest multiple divisible by all denominators.
Examples of Solving Equations with Fractions
- Solve for x: x / 3 = 5 => x = 5 * 3 => x = 15
- Solve for y: 2y / 5 = 4 => 2y = 4 * 5 => 2y = 20 => y = 20 / 2 => y = 10
- Solve for z: (z + 1) / 2 = 3 => z + 1 = 3 * 2 => z + 1 = 6 => z = 6 - 1 => z = 5
- Solve for a: (a - 2) / 4 = 1 => a - 2 = 1 * 4 => a - 2 = 4 => a = 4 + 2 => a = 6
- Solve for b: (3b + 1) / 5 = 2 => 3b + 1 = 2 * 5 => 3b + 1 = 10 => 3b = 10 - 1 => 3b = 9 => b = 9 / 3 => b = 3
Quiz on Linear Equations, Binomials, Expanding Brackets, and Year 9 Algebra
- Consist of 30 questions focusing on linear equations, binomials, expanding brackets, and general year 9 level algebra.
- Questions should focus on direct algebraic manipulation and not be word problems.
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