Grade 10 Academic Mathematics Final Exam Review: Algebra Big Ideas

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Questions and Answers

What is the correct method to solve a linear system graphically?

  • Using quadratics to find the solution
  • Using the substitution method
  • Using the elimination method
  • Plotting the graphs of the equations and finding the point of intersection (correct)

Which property of parabolas is represented by the equation y=a(x-h)^2+k?

  • Minimum value
  • Y-intercept
  • Axis of symmetry
  • Maximum value (correct)

What is the appropriate method to solve a quadratic equation if it cannot be easily factored?

  • Applying the properties of parabolas
  • Solving it by graphing
  • Using the quadratic formula (correct)
  • Using the difference of squares

Which trigonometric function is represented by the acronym SOH in the context of similar triangles?

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

What is the first step when solving a problem using linear systems by substitution?

<p>Solving for one variable in one of the equations (D)</p> Signup and view all the answers

In the context of quadratic expressions, what method would be most suitable for factoring a perfect square trinomial?

<p>Using the square root property (D)</p> Signup and view all the answers

When graphing a quadratic equation, what do the intercepts represent?

<p>X and Y coordinates at which the graph crosses the axes (B)</p> Signup and view all the answers

What is a fundamental property of exponential laws involving negative exponents?

<p>$a^{-n} = 1/a^n$ (A)</p> Signup and view all the answers

Which method is used to determine the equation of a line algebraically given specific information?

<p>$ax+by+c=0$ form (D)</p> Signup and view all the answers

Flashcards

Solving Linear Systems Graphically

Plotting the graphs of the equations and finding the point of intersection.

Parabola's Vertex

Maximum or minimum value of the parabola (y=a(x-h)^2+k).

Solve Quadratic Equations

Using the quadratic formula when factoring is difficult.

SOH (Sine)

Sine = Opposite / Hypotenuse in a right triangle.

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Substitution Method (Linear Systems)

Solve for one variable in one of the equations.

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Factoring Perfect Square Trinomials

Using the square root property to factor.

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Quadratic Graph Intercepts

X and Y coordinates at which the graph crosses the axes.

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Negative Exponents

$a^{-n} = 1/a^n$, flipping the base across the fraction.

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Line Equation Form

ax + by + c = 0 represents linear equations.

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