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Questions and Answers
If two lines are perpendicular and one has a gradient of 2, what is the gradient of the other line?
If two lines are perpendicular and one has a gradient of 2, what is the gradient of the other line?
- $-\frac{1}{2}$ (correct)
- $\frac{1}{2}$
- -2
- 2
What condition must be met to ensure that two lines are parallel?
What condition must be met to ensure that two lines are parallel?
- Their gradients must be equal. (correct)
- Their y-intercepts must be equal.
- Their gradients must be negative reciprocals of each other.
- The product of their gradients must be -1.
Which of the following represents the correct application of the distributive property?
Which of the following represents the correct application of the distributive property?
- $a + (b + c) = ab + ac$
- $a(b + c) = ab + ac$ (correct)
- $a(b + c) = ab + c$
- $a(b - c) = ab + ac$
When solving linear inequalities, what operation requires reversing the inequality symbol?
When solving linear inequalities, what operation requires reversing the inequality symbol?
What does the 'c' represent in the linear equation $y = mx + c$?
What does the 'c' represent in the linear equation $y = mx + c$?
How do you determine which region to shade when graphing an inequality such as $2x + 3y < 6$?
How do you determine which region to shade when graphing an inequality such as $2x + 3y < 6$?
What is the formula to find the midpoint $M$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$?
What is the formula to find the midpoint $M$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$?
What is the first step in solving equations with algebraic fractions?
What is the first step in solving equations with algebraic fractions?
In the context of solving simultaneous equations, what is 'elimination'?
In the context of solving simultaneous equations, what is 'elimination'?
What should be the initial step when applying simultaneous equations to solve a word problem?
What should be the initial step when applying simultaneous equations to solve a word problem?
Flashcards
Midpoint and Length of a Line Segment
Midpoint and Length of a Line Segment
A line segment joining points (x1, y1) and (x2, y2) has a midpoint M and a length/distance d.
Parallel and Perpendicular Lines
Parallel and Perpendicular Lines
Parallel lines have the same gradient. Perpendicular lines have gradients m1 and m2 such that m1 * m2 = -1.
Graphs of Linear Relations
Graphs of Linear Relations
In the form y = mx + c, 'm' represents the gradient and 'c' represents the y-intercept.
Linear Equations vs. Inequalities
Linear Equations vs. Inequalities
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Simultaneous Equations
Simultaneous Equations
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Solving Linear Equations
Solving Linear Equations
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Applications of Simultaneous Equations
Applications of Simultaneous Equations
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Review of Algebra
Review of Algebra
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Equations with Algebraic Fractions
Equations with Algebraic Fractions
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Finding a Rule for a Graph
Finding a Rule for a Graph
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Study Notes
Midpoint and Length of a Line Segment
- For a line segment joining points (x₁, y₁) and (x₂, y₂), the midpoint M is ((x₁+x₂)/2, (y₁+y₂)/2).
- Length or distance is calculated as d=√((x₂-x₁)²+(y₂-y₁)²)
Review of Algebra
- Combine like terms when adding or subtracting (e.g., 2x + 4x + y = 6x + y).
- Multiply terms (e.g., 3x * 2y = 6xy).
- Divide terms (e.g., 4ab ÷ (2b) = 2a).
- Expand expressions: a(b + c) = ab + ac and a(b - c) = ab - ac.
Equations with Algebraic Fractions
- For more complex algebraic fractions, an example is provided.
- To solve equations, combine fractions by adding or subtracting.
- Multiply both sides of the equation by the denominator.
Parallel and Perpendicular Lines
- Parallel lines share the same gradient (e.g., y = 2x + 7 and y = 2x - 4).
- For perpendicular lines with gradients m₁ and m₂, m₁ * m₂ = -1, or m₂ = -1/m₁.
- An example is y = 3x + 4 and y = -⅓x + 2.
Finding a Rule for a Graph
- For points (x₁, y₁) and (x₂, y₂), the gradient (m) = (y₂-y₁) / (x₂-x₁).
- To find the line equation y = mx + c: find the gradient first.
- Then substitute a point if c is not known, using y = mx + c or y - y₁ = m(x - x₁).
Graphs of Linear Relations
- In y = mx + c, m represents the gradient, and c is the y-intercept.
- The gradient, m=rise/run
- To graph: use the gradient and y-intercept, or locate the x-intercept (y = 0) and y-intercept (x = 0).
Linear Inequalities
- Equations contain a '=' sign, while inequalities use >, ≥, <, or ≤.
- When solving linear inequalities, reverse the inequality symbol when multiplying or dividing by a negative number.
Solving Linear Equations
- Steps include using inverse operations, collecting like terms on one side, and finding a common denominator.
Simultaneous Equations
- Solve two equations with two unknowns: use substitution when one pronumeral is the subject (e.g., y = x + 4); or use elimination by adding or subtracting multiples of equations to eliminate one variable.
Applications of Simultaneous Equations
- Problem solving steps include: defining unknowns using pronumerals, forming two equations, solving them simultaneously, and answering the question in words.
Regions on the Cartesian Plane
- Inequalities with two variables represent the region above or below the line.
- For y ≥ x - 3, shade above the line; for y > x - 3, use a dashed line.
- To decide which region to shade for an inquality like 2x + 3y < 6, test point (0, 0).
- Two or more half planes form an intersecting region.
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