Math 2 Part 1 BYU Course Flashcards
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Questions and Answers

What is the coefficient in the monomial 4x²?

  • 4x
  • 2
  • 4 (correct)
  • x²

    • What is a polynomial?

    A series of monomials.

    What is a term in a polynomial?

    Each item separated by an addition or subtraction sign.

    What is the graph of a quadratic equation called?

    <p>A parabola.</p> Signup and view all the answers

    What does the term quadratic refer to?

    <p>A function or an equation whose graph is a parabola.</p> Signup and view all the answers

    What does the discriminant tell you about a quadratic equation?

    <p>Number of solutions</p> Signup and view all the answers

    What are the points where the graph crosses the x-axis called?

    <p>X-intercepts or roots.</p> Signup and view all the answers

    What happens if the quadratic term is negative?

    <p>The parabola opens down.</p> Signup and view all the answers

    The perimeter of any polygon is the sum of the length of its ______.

    <p>sides</p> Signup and view all the answers

    The formula for the perimeter of a rectangle can be written as P = ______.

    <p>2l + 2w</p> Signup and view all the answers

    The area of the polygon is the measure of the region ______ the polygon.

    <p>inside</p> Signup and view all the answers

    The formula for the area of a rectangle can be written as A = ______.

    <p>lw</p> Signup and view all the answers

    What is a linear equation?

    <p>An equation that represents a line.</p> Signup and view all the answers

    What is the Slope-intercept Formula?

    <p>y = mx + b</p> Signup and view all the answers

    The ______ is the vertical line on a coordinate plane.

    <p>y-axis</p> Signup and view all the answers

    What does it mean for lines to be parallel?

    <p>Run the same way and have the same slant, so they will not intersect.</p> Signup and view all the answers

    What is meant by vertical shift in graphing?

    <p>When the b value moves the line vertically, up and down from the usual position.</p> Signup and view all the answers

    What is a line to fit on a scatter plot?

    <p>A line drawn as close as possible to all the points on a scatter plot.</p> Signup and view all the answers

    How is standard form expressed?

    <p>Ax + By = C</p> Signup and view all the answers

    What is a scatter plot?

    <p>A collection of data points on a graph.</p> Signup and view all the answers

    What is a fitted line?

    <p>A straight line that goes through the center of data points.</p> Signup and view all the answers

    What is a prediction equation?

    <p>An equation suggested by the points of a scatter plot used to predict other points.</p> Signup and view all the answers

    Define correlation in statistics.

    <p>A relationship between two variables.</p> Signup and view all the answers

    What does causation imply?

    <p>When one variable causes the other variable.</p> Signup and view all the answers

    What does graphing linear functions involve?

    <p>Graph the boundary line, decide on its type, shade regions, and test points.</p> Signup and view all the answers

    What is a boundary in graphing?

    <p>Separates the coordinate plane into two regions.</p> Signup and view all the answers

    What do exponents tell us?

    <p>How many times the base is used as a factor.</p> Signup and view all the answers

    Define the base in an expression.

    <p>A number that is multiplied repeatedly.</p> Signup and view all the answers

    What is a power in mathematics?

    <p>The whole expression involving exponents.</p> Signup and view all the answers

    What is an exponential function?

    <p>A function that repeatedly multiplies an initial amount by the same positive number.</p> Signup and view all the answers

    What is scientific notation?

    <p>A method of writing very large or very small numbers using powers of 10.</p> Signup and view all the answers

    What does the equality property of exponential functions state?

    <p>When the bases are equal, we can set the exponents equal to each other.</p> Signup and view all the answers

    What shape is formed by joining three segments?

    <p>Triangle.</p> Signup and view all the answers

    What are the vertices of a triangle?

    <p>The points A, B, and C in triangle ABC.</p> Signup and view all the answers

    What term describes the segments of a triangle?

    <p>Sides.</p> Signup and view all the answers

    How can triangles be classified?

    <p>By the size of their angles.</p> Signup and view all the answers

    What is an equiangular triangle?

    <p>A triangle where all three angles have the same measure.</p> Signup and view all the answers

    How is an equilateral triangle defined?

    <p>A triangle that has three congruent sides.</p> Signup and view all the answers

    What is an isosceles triangle?

    <p>A triangle that has two congruent sides.</p> Signup and view all the answers

    Define a scalene triangle.

    <p>A triangle that has no congruent sides.</p> Signup and view all the answers

    Can a triangle be both right and obtuse?

    <p>No, it is impossible.</p> Signup and view all the answers

    What is the longest side of a right triangle called?

    <p>Hypotenuse.</p> Signup and view all the answers

    The longer sides of a triangle are opposite the angles with the largest measure.

    <p>True</p> Signup and view all the answers

    What does congruent mean in geometry?

    <p>Two figures are identical.</p> Signup and view all the answers

    What are CPCTC?

    <p>Corresponding Parts of Congruent Triangles are Congruent.</p> Signup and view all the answers

    What are the two special types of segments in a triangle?

    <p>Altitude of a triangle and median of a triangle.</p> Signup and view all the answers

    Define an angle bisector.

    <p>A line or ray that divides an angle into two congruent angles.</p> Signup and view all the answers

    What is a polygon?

    <p>Union of three or more coplanar segments where exactly two segments intersect at each endpoint.</p> Signup and view all the answers

    What do we call the segments of a polygon?

    <p>Sides.</p> Signup and view all the answers

    What are the two types of polygons?

    <p>Concave and Convex.</p> Signup and view all the answers

    What is a diagonal of a polygon?

    <p>A segment connecting any two nonconsecutive vertices of the polygon.</p> Signup and view all the answers

    How many diagonals can be drawn from each vertex of a hexagon?

    <p>Three.</p> Signup and view all the answers

    What is a convex polygon?

    <p>A polygon where all diagonals lie completely within the polygon.</p> Signup and view all the answers

    Define a concave polygon.

    <p>A polygon that has at least one diagonal that lies outside the polygon.</p> Signup and view all the answers

    How do you calculate the sum of the measures of the interior angles of a polygon?

    <p>Multiply the number of triangles by 180°.</p> Signup and view all the answers

    What is the sum of the measures of the exterior angles of any convex polygon?

    <p>360°.</p> Signup and view all the answers

    What does it mean for a polygon to be equilateral?

    <p>A polygon where all sides are congruent.</p> Signup and view all the answers

    What defines an equiangular polygon?

    <p>A polygon where all interior angles are congruent.</p> Signup and view all the answers

    How many sides would a regular polygon have if each interior angle measures 144°?

    <ol start="10"> <li></li> </ol> Signup and view all the answers

    What is a quadrilateral?

    <p>A polygon with four sides.</p> Signup and view all the answers

    What are consecutive sides in a quadrilateral?

    <p>Sides that share a common vertex.</p> Signup and view all the answers

    Define opposite sides in a quadrilateral.

    <p>Sides that do not intersect.</p> Signup and view all the answers

    What are parallelograms?

    <p>Quadrilaterals with two pairs of parallel opposite sides.</p> Signup and view all the answers

    What is a trapezoid?

    <p>A quadrilateral with one pair of parallel opposite sides.</p> Signup and view all the answers

    What defines a rectangle?

    <p>An equiangular quadrilateral.</p> Signup and view all the answers

    How do you determine if a parallelogram is a rectangle?

    <p>If its diagonals are congruent.</p> Signup and view all the answers

    What are the bases and legs of a trapezoid?

    <p>Bases are the parallel sides, and legs are the sides that are not parallel.</p> Signup and view all the answers

    What is the altitude of a trapezoid?

    <p>Any segment from one base to the other that is perpendicular to both bases.</p> Signup and view all the answers

    Define the median of a trapezoid.

    <p>The line segment that is parallel to the bases.</p> Signup and view all the answers

    What is an isosceles trapezoid?

    <p>A trapezoid with congruent legs.</p> Signup and view all the answers

    What is meant by translation in geometry?

    <p>The transformation of sliding a shape up, down, or sideways.</p> Signup and view all the answers

    What is a rotation in geometric transformation?

    <p>Turning a shape to change its orientation.</p> Signup and view all the answers

    What does reflection mean in geometry?

    <p>Flipping a shape over to face a different direction.</p> Signup and view all the answers

    What is a translation vector?

    <p>It indicates the length and direction of a transformation.</p> Signup and view all the answers

    What is a ratio?

    <p>The fraction of two measurements, expressed as a/b.</p> Signup and view all the answers

    What is the geometric mean?

    <p>A common type of proportion in geometry.</p> Signup and view all the answers

    What is a proportion?

    <p>An equation where two ratios are equal.</p> Signup and view all the answers

    What does cross multiplication refer to in algebra?

    <p>An algebraic method to change fractions into multiplication.</p> Signup and view all the answers

    What are similar polygons?

    <p>Polygons that have the same shape but not necessarily the same size.</p> Signup and view all the answers

    Define similarity transformation.

    <p>A transformation producing similar figures.</p> Signup and view all the answers

    What are rigid transformations?

    <p>Transformations that preserve the shape and size of figures.</p> Signup and view all the answers

    What are similar triangles?

    <p>Triangles with two angles congruent to two angles of another triangle.</p> Signup and view all the answers

    What is a radical expression?

    <p>An expression involving roots, such as the square root.</p> Signup and view all the answers

    What is a rational approximation?

    <p>An answer that is estimated rather than exact.</p> Signup and view all the answers

    Define rational numbers.

    <p>Any number that can be expressed as a fraction.</p> Signup and view all the answers

    What are irrational numbers?

    <p>Real numbers that cannot be expressed as fractions.</p> Signup and view all the answers

    State the Pythagorean theorem.

    <p>a² + b² = c²</p> Signup and view all the answers

    What does rationalizing the denominator involve?

    <p>Multiplying the numerator and denominator by the same radical expression.</p> Signup and view all the answers

    What is a monomial?

    <p>An expression that is a numeral, variable, or product of both.</p> Signup and view all the answers

    Study Notes

    Linear Equations and Graphing

    • Linear Equation: Represents a straight line in a coordinate plane.
    • Slope-Intercept Formula: y = mx + b, where m is the slope and b is the y-intercept.
    • Y-Axis: Vertical line representing output values (y).
    • Parallel Lines: Run in the same direction without intersecting.
    • Vertical Shift: Changes the position of a line vertically by modifying the b value.
    • Fitted Line: Drawn close to scatter plot data points for trend analysis.
    • Standard Form: Written as Ax + By = C, a common way to express linear equations.
    • Scatter Plot: Displays data points on a graph for visual analysis of relationships.
    • Prediction Equation: Derived from scatter plot data to forecast additional points.
    • Correlation vs. Causation: Correlation indicates a relationship, while causation implies one variable influences another.

    Graphing Linear Inequalities

    • Identify and graph the boundary line using slope-intercept form.
    • Use dotted lines for < and >; solid lines for ≤ and ≥.
    • Shade regions based on the inequality direction (above or below the line).
    • Test a point in the shaded region to confirm it's part of the solution.

    Triangles

    • Triangle Types: Classifications include acute (all angles < 90°), obtuse (one angle > 90°), and right (one angle = 90°).
    • Equilateral Triangle: All sides and angles are congruent.
    • Isosceles Triangle: Two sides and angles are congruent.
    • Scalene Triangle: No congruent sides or angles.
    • Triangle Properties: Longer sides are opposite larger angles; no triangle can be both right and obtuse.

    Triangle Segments

    • Hypotenuse: Longest side in a right triangle.
    • Altitude: Perpendicular segment from a vertex to the opposite side.
    • Median: Segment from a vertex to the midpoint of the opposite side.

    Polygons

    • Polygon: Formed by three or more connected segments with non-intersecting sides.
    • Types of Polygons: Classified as convex or concave.
    • Diagonals: Segments connecting non-consecutive vertices.
    • Convex Polygon: All diagonals remain inside the polygon.
    • Concave Polygon: At least one diagonal extends outside.
    • Sum of Interior Angles: For an n-gon, equals (n - 2) × 180°.

    Quadrilaterals

    • Quadrilateral: Four-sided polygon with angles summing to 360°.
    • Parallelograms: Quadrilaterals with two pairs of parallel sides.
    • Trapezoids: One pair of parallel sides.
    • Rectangle: Equiangular quadrilateral with congruent diagonals.
    • Isosceles Trapezoid: Has congruent legs and base angles.

    Transformations

    • Translations: Movement of shapes up, down, left, or right.
    • Rotations: Turning shapes around a fixed point.
    • Reflections: Flipping shapes across a line.
    • Rigid Transformations: Preserve shape and size; includes translations, rotations, and reflections.

    Ratios and Proportions

    • Ratio: Comparison of two measurements as a fraction.
    • Proportion: Equality of two ratios, commonly solved using cross multiplication.
    • Geometric Mean: Calculated for proportions, establishing a relationship between values.

    Quadratic Functions

    • Quadratic Function: Represents a parabolic graph with a squared term.
    • Vertex: Highest or lowest point in a parabola, related to the direction it opens.
    • Discriminant: Determines the number of real solutions (b² - 4ac); zero for one solution, positive for two, and negative for none.

    Exponential Functions

    • Exponential Growth/Decay: Models changing quantities, expressed in forms like y = a(1±r)ᵡ.
    • Scientific Notation: Represents large or small numbers using powers of 10.

    Rational and Irrational Numbers

    • Rational Numbers: Numbers expressible as fractions.
    • Irrational Numbers: Non-repeating and non-terminating decimal representations.

    Miscellaneous

    • Rationalizing the Denominator: Process to eliminate radicals from the denominator of fractions.
    • Monomial: A singular term in mathematics, including numbers and variables.
    • Polynomial: A sum of two or more monomials.### Perimeter of a Rectangle
    • Farmers calculate the perimeter of a pasture for fencing material.
    • The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where l is length and w is width.

    Area of a Polygon

    • The area of a polygon measures the space inside it.
    • Example application: Area calculation determines the amount of carpet needed for a room.
    • Area is expressed in square units, representing how many squares fit in the region.
    • For rectangles, the area (A) can be calculated using the formula A = lw, where l is length and w is width.
    • Visualizing the rectangle as a partition of squares simplifies understanding of area.

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    Test your knowledge with these flashcards covering key concepts from the Math 2 Part 1 BYU online course. This quiz includes definitions and formulas related to linear equations and the slope-intercept formula. Perfect for students wanting to reinforce their understanding of algebraic principles.

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