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 (C)</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. (A), The vertex is a maximum. (B)</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 (A)</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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