Podcast
Questions and Answers
The city bus company carries, on average, ______ passengers daily.
The city bus company carries, on average, ______ passengers daily.
3500
Each passenger pays ______ to ride the bus.
Each passenger pays ______ to ride the bus.
$2.25
For every ______ increase in bus fare, the company loses 50 customers.
For every ______ increase in bus fare, the company loses 50 customers.
$0.25
The farmer has enough materials for ______ meters of fencing.
The farmer has enough materials for ______ meters of fencing.
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The height of the tennis shot as a function of time is expressed as ______.
The height of the tennis shot as a function of time is expressed as ______.
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The maximum height of the tennis ball is found using the ______ of the equation.
The maximum height of the tennis ball is found using the ______ of the equation.
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In solving the quadratic equation, the ______ indicates the nature of its roots.
In solving the quadratic equation, the ______ indicates the nature of its roots.
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To find the dimensions of the grassed area, the total amount of fencing is ______.
To find the dimensions of the grassed area, the total amount of fencing is ______.
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The vertex can be found from the ______ form of a parabola.
The vertex can be found from the ______ form of a parabola.
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To find the x-intercepts of a quadratic function, one method is ______.
To find the x-intercepts of a quadratic function, one method is ______.
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The maximum height of a batted ball is determined by identifying the ______ of the quadratic function.
The maximum height of a batted ball is determined by identifying the ______ of the quadratic function.
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When transforming from vertex to standard form, it is sometimes referred to as ______.
When transforming from vertex to standard form, it is sometimes referred to as ______.
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A common method to solve quadratic equations is the ______ formula.
A common method to solve quadratic equations is the ______ formula.
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Drawing a ______ can help visualize problems involving areas and dimensions.
Drawing a ______ can help visualize problems involving areas and dimensions.
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The area of both the photo and mat backing is given as ______ square cm.
The area of both the photo and mat backing is given as ______ square cm.
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When using the vertex form, we first determine how it changed from ______ = x.
When using the vertex form, we first determine how it changed from ______ = x.
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Ms. Johannsen has $3300 consisting of $50 bills and $______ bills.
Ms. Johannsen has $3300 consisting of $50 bills and $______ bills.
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A pole casts a shadow which is 5.6m long. The sun is at an angle of ______ to the ground.
A pole casts a shadow which is 5.6m long. The sun is at an angle of ______ to the ground.
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To solve by ______, you match coefficients, add or subtract, solve, substitute, and solve again.
To solve by ______, you match coefficients, add or subtract, solve, substitute, and solve again.
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Town B is 8km directly ______ of town A.
Town B is 8km directly ______ of town A.
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In the equation y = 2x + 5, the slope is ______.
In the equation y = 2x + 5, the slope is ______.
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The angle of depression from the top of a 150m cliff to a ship in the sea is ______°.
The angle of depression from the top of a 150m cliff to a ship in the sea is ______°.
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When solving systems, a ______ is the point where two lines intersect.
When solving systems, a ______ is the point where two lines intersect.
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Ms. Gardner invested $9000, combining low risk bonds yielding ______% per year.
Ms. Gardner invested $9000, combining low risk bonds yielding ______% per year.
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A triangle has angles of 110°, 40° and ______°.
A triangle has angles of 110°, 40° and ______°.
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The vertical radio tower is held in position by a wire which is ______m long.
The vertical radio tower is held in position by a wire which is ______m long.
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The elimination method works best when the coefficients are easy to ______.
The elimination method works best when the coefficients are easy to ______.
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Brooke can see the top of a nearby building at an angle of elevation of ______°.
Brooke can see the top of a nearby building at an angle of elevation of ______°.
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In solving by substitution, the steps are isolate, substitute, solve, ______, and solve again.
In solving by substitution, the steps are isolate, substitute, solve, ______, and solve again.
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A golfer hits her ball a distance of ______m so that it finishes 31m from the hole.
A golfer hits her ball a distance of ______m so that it finishes 31m from the hole.
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To classify systems, you analyze the slopes and ______ of the equations.
To classify systems, you analyze the slopes and ______ of the equations.
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Two scouts travel 3.7km on a bearing of ______°T.
Two scouts travel 3.7km on a bearing of ______°T.
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The equation of a line can be represented as 𝑦 = 𝑚𝑥 + ______
The equation of a line can be represented as 𝑦 = 𝑚𝑥 + ______
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To find the distance between two points A(-3, 4) and B(-8, 10), you use the ______ formula.
To find the distance between two points A(-3, 4) and B(-8, 10), you use the ______ formula.
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To determine if a triangle is right-angled, you can use the ______ theorem.
To determine if a triangle is right-angled, you can use the ______ theorem.
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A quadrilateral TUNE with vertices T(0, 10), U(4, 2), N(−2, −1), and E(−6, 7) can be classified as a ______.
A quadrilateral TUNE with vertices T(0, 10), U(4, 2), N(−2, −1), and E(−6, 7) can be classified as a ______.
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The midpoint between two points can be found using the ______ formula.
The midpoint between two points can be found using the ______ formula.
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The equation of the median of a triangle passes through a vertex and the ______ of the opposite side.
The equation of the median of a triangle passes through a vertex and the ______ of the opposite side.
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The shortest distance from a point to a line is represented by a ______ line.
The shortest distance from a point to a line is represented by a ______ line.
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The formula for a circle with its center at the origin is ______.
The formula for a circle with its center at the origin is ______.
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The destroyer sails 25km on a bearing of ______°T.
The destroyer sails 25km on a bearing of ______°T.
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The cruiser sails 30km on a bearing of ______°T.
The cruiser sails 30km on a bearing of ______°T.
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Competitors run 230m directly ______ to point B.
Competitors run 230m directly ______ to point B.
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They cycle 260m from point C directly to point ______.
They cycle 260m from point C directly to point ______.
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The bearing of C from A has been recorded as ______°T.
The bearing of C from A has been recorded as ______°T.
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In factored form, a quadratic looks like ______.
In factored form, a quadratic looks like ______.
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The vertex form of a quadratic is represented as ______.
The vertex form of a quadratic is represented as ______.
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Standard form of a quadratic generally looks like ______.
Standard form of a quadratic generally looks like ______.
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Study Notes
Linear Systems
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Classifying systems: Linear systems can have one solution, no solutions, or infinitely many solutions. Identifying the type of solution depends on whether the lines are parallel, coincident, or intersecting.
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Solving by graphing: Graphing linear equations allows visualizing the point of intersection (POI). Graphing requires determining the slope and y-intercept to plot the lines accurately. Accurately plotting lines is critical to finding the POI.
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Solving by substitution: Isolating a variable in one equation, substituting it into the other equation, and then solving for the variables. Repeated substitution and solution steps will determine the POI.
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Solving by elimination: Matching coefficients of variables in both equations, adding or subtracting the equations to eliminate a variable, then substituting the result into one original equation to find the other variable. Consistent application of the method will reveal the solution's POI.
Applications
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Interest problems: Calculating interest earned on investments with different interest rates and amounts. Algebraic methods will solve for the investments.
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Concentration problems: Determining the quantity of different components (e.g., different bills). Algebraic methods are used to find the unknown quantities
Analytic Geometry
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Finding equation of a line: Calculating equations of lines using given points and slopes. The equations can be written in the form y = mx + b or Ax + By = C
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Working with perpendicular lines: Understanding the relationship between slopes of perpendicular lines. Perpendicular lines have negative reciprocal slopes.
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Midpoint between two points: Calculating midpoint using the formula. The formula involves averaging x and y coordinates.
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Distance between two points: Calculating the distance using the distance formula. This formula uses x and y coordinates.
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Classifying triangles: Identifying different triangle types by evaluating sides and angles. Classifying triangles involves criteria such as equal sides and angles.
Classifying Quadrilaterals
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Identifying properties of different quadrilaterals: Various quadrilaterals (squares, rectangles, rhombi, kites, parallelograms, trapezoids). Specific properties define these quadrilaterals.
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Perpendicular Bisector: Calculating the equation of a line that cuts a segment in half at a 90-degree angle. The perpendicular bisector formula uses the midpoint and slope of the given line segment.
Triangles
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Median: A line segment connecting a vertex of a triangle to the midpoint of the opposite side. Calculating midpoint is critical to finding the median equation.
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Altitude: A line segment from a vertex perpendicular to the opposite side (or its extension). Calculating altitudes involves determining the equation of a line segment perpendicular to the base.
Shortest Distance from a Point to a Line
- Calculating the shortest distance: The shortest distance between a point and a line is the length of the perpendicular segment from the point to the line.
Circles
- Equation of a circle: Determine the equation of circles. Identifying centers and radii is critical to determining the circle equation
Trigonometry
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Pythagorean Theorem: The relationship between sides in a right-angled triangle (a² + b² = c²).
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Similar Triangles: Recognizing and using similar triangles to solve problems. Identifying similar shapes, evaluating ratios of sides and using similarity to solve.
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Primary Trigonometric Ratios (SOH CAH TOA): The ratios of sides in right triangles. Identifying and using sine, cosine, and tangent ratios.
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Sine Law: Useful for finding unknown sides or angles in triangles with at least one given angle and its opposite side.
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Cosine Law: Useful for finding unknown sides or angles in triangles with at least three given sides or two sides and the included angle .
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Area of a Triangle: Calculating areas of triangles using different formulas (base x height / 2) or using the SAS formula (half the product of two sides and the sine of the included angle).
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Applications: Using trigonometry to solve practical word problems (e.g., finding heights, distances, angles of elevation and depression).
Solutions to Quadratic Equations
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By Factoring: Solving quadratic equations by factoring. Factoring involves recognizing common factors and using special products.
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Using the Quadratic Formula: Solving quadratic equations using the quadratic formula. Formula: x = (-b ± √(b²-4ac))/2a
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Applications of Solutions to Quadratic Equations: Real-life problems solvable with quadratic equations. Appropriate situations and application contexts.
Forms of a Quadratic
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Factored Form: y = a(x - m)(x - n). Understanding how the factored form represents roots/zeros/x-intercepts.
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Vertex Form: y = a(x - h)²+k. Understanding how the vertex form represents the vertex (h, k)
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Standard Form: y = ax² + bx + c. Understanding how the standard form represents the quadratic expression without factorization.
Transformations of Quadratics
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Identify and describe transformations of quadratics. Reflecting, stretching, compressing, and shifting parabolas.
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Finding the Vertex: Finding the vertex using the formula x = -b/2a.
Calculator Steps
- Calculator functions for quadratic functions and equations.
Quadratics Word Problems
- Using quadratic equations to model and solve real-world problems. Identifying and applying mathematical models appropriately to the scenario in question.
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Description
This quiz covers the classification of linear systems and methods for solving them, including graphing, substitution, and elimination. Understand how to identify the type of solution and accurately find points of intersection. Test your knowledge on these essential algebraic techniques.
