Mathematics Class Quiz

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Questions and Answers

What is the value of n in the equation 125n = 14810?

  • 11 (correct)
  • 13
  • 12
  • 14

What is the cartesian equation obtained by eliminating t from the equations x = t - 5 and y = t^2?

  • x = (y + 5)^2
  • x = (y - 5)^2
  • y = (x - 5)^2
  • y = (x + 5)^2 (correct)

If a matrix A has no inverse, what is the condition its determinant needs to satisfy?

  • Determinant must be negative
  • Determinant must be positive
  • Determinant must be zero (correct)
  • Determinant must be equal to 1

For which of the following values of x does the matrix A = [[2, 1], [x, 3]] have no inverse?

<p>1 (D)</p> Signup and view all the answers

What is the value of the derivative of the function y = 2x^2 - 4x + 3 at the point x = 2?

<p>8 (B)</p> Signup and view all the answers

In the expression (tan45° + tan60°)/(1 - tan45°tan60°), what is the value of the expression?

<ul> <li>2 - √3 (C)</li> </ul> Signup and view all the answers

What is the cartesian equation obtained by eliminating t from the equations x = t^2 and y = 2t - 3?

<p>(y + 3)^2 = 4x (C)</p> Signup and view all the answers

Find the equation of the tangent line to the curve y = 2x^2 - 4x + 3 at the point x = 2.

<p>y = 4x - 5 (D)</p> Signup and view all the answers

Express the number 15 as the difference of two squares.

<p>16 - 1 (A)</p> Signup and view all the answers

What is the value of the expression: x^3 - 2x^2 + 3x when x = 3?

<p>16 (C)</p> Signup and view all the answers

Which of the following points lies on the curve represented by the equation x^2/9 + y^2/16 > 1?

<p>(3, 4) (C)</p> Signup and view all the answers

What is the value of (\sqrt{3} * \sqrt{5}) based on the binary operation defined by (a * b = a^2 + b^2 - 2ab)?

<p>4 (D)</p> Signup and view all the answers

Which of the following expressions represents the difference of two squares for the number 21?

<p>25 - 4 (D)</p> Signup and view all the answers

Which of the following lines is perpendicular to the line represented by (x = 5 - 4y)?

<p>y = -\frac{1}{4}x + 5 (A)</p> Signup and view all the answers

What is the value of (cos(2A)) if (sin(2A) = \frac{1}{2})?

<p>1 (D)</p> Signup and view all the answers

Which of the following pairs of equations represents perpendicular lines?

<p>3x + 5y = -10 and 5x - 3y = 10 (A)</p> Signup and view all the answers

What is the value of (cos(A + B)) if (cos(A) = \frac{3}{5}) and (sin(B) = \frac{12}{13}) and both angles A and B are in the first quadrant?

<p>(\frac{56}{65}) (C)</p> Signup and view all the answers

Which of the following statements is true about the lines with equations (x + 2y = -5) and (2x + y = 5)?

<p>The lines are perpendicular. (C)</p> Signup and view all the answers

Flashcards

Even Product Rule

If the product of two integers is even, then at least one is even.

Odd Product Rule

If the product of two integers is odd, then both integers must be odd.

Odd Sum Rule

If the sum of two integers is odd, then exactly one of them is odd.

Even Difference Rule

If the difference of two integers is even, it doesn't mean both integers are even.

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Rational Function Range

Identify numbers not in the range of a rational function, such as y values from equations.

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Tangent Line Equation

The equation of the tangent to a curve at a certain point can be found using derivatives.

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Angle Between Vectors

The cosine of the angle between two vectors involves their dot product and magnitudes.

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Matrix Inverse

The inverse of a matrix exists if its determinant is non-zero; used in solving equations.

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Kite

A quadrilateral with diagonals that are perpendicular and only one pair of congruent angles.

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Perpendicular lines

Lines that intersect at a right angle (90 degrees).

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Parallel lines

Lines that never intersect and have the same slope.

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Cosine addition formula

cos(A + B) = cosAcosB - sinAsinB; relates angles through trigonometric components.

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Intercepts of a line

Points where a line crosses the x-axis and y-axis.

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Sum of a linear series

The total of terms in a sequence defined by a linear formula.

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Matrix Determinant

Only square matrices have determinants.

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Binary operation

A mathematical operation combining two elements to produce another.

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Evaluating expressions

The process of calculating the value of a mathematical expression.

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Inverse Matrix

A matrix has an inverse only if its determinant is non-zero.

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Inequality Solution

Point A(2, 3) is a solution for x²/4 + y²/9 > 1.

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Eliminating Parameter

Eliminate t from x = t² + 1, y = 2t + 3 to get (y - 3)² = 4(x - 1).

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Finding n in 125n = 14810

n = 11 when solving 125n = 14810.

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Evaluating Tan Expression

Evaluate (tan45° + tan60°)/(1 - tan45°tan60°) to get -2 - √3.

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No Inverse Condition

Matrix A has no inverse when its determinant equals zero.

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Exact Square and Cube

A number that is both a perfect square and a perfect cube.

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