Algebra 1 Semester 2 Final Exam Flashcards
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Questions and Answers

Solve the system of equations: -2x - y = -19, x - y = 11

(10, -1)

Zoe has 36 coins (quarters and nickels) that are worth $3.00. How many nickels does she have?

30

Zoe has 36 coins (quarters and nickels) that are worth $3.00. How many quarters does she have?

6

Simplify: (3x³y⁶z)²

<p>9x⁶y¹²z²</p> Signup and view all the answers

Simplify: (-a²b²c²)³(2ab³c)²

<p>-4a⁸b¹²c⁸</p> Signup and view all the answers

Simplify: 5x⁰(-10x³)

<p>-50x³</p> Signup and view all the answers

Simplify: (x² - x + 1) + (9x² - 9x + 10)

<p>10x² - 10x + 11</p> Signup and view all the answers

Simplify: (x² - x + 1) - (9x² - 9x + 10)

<p>-8x² + 8x - 9</p> Signup and view all the answers

Simplify: (x² - x + 1)(9x² - 9x + 10)

<p>9x⁴ - 18x³ + 28x² - 19x + 10</p> Signup and view all the answers

Factor: x² + 3x - 4

<p>(x + 4)(x - 1)</p> Signup and view all the answers

Solve: x² + 3x - 4 = 0

<p>x = 1, x = -4</p> Signup and view all the answers

Factor: 6x² + 5x - 6

<p>(2x + 3)(3x - 2)</p> Signup and view all the answers

Solve: 6x² + 5x - 6 = 0

<p>x = 2/3, x = -3/2</p> Signup and view all the answers

Factor: 2x² + 7x + 3

<p>(2x + 1)(x + 3)</p> Signup and view all the answers

Solve: 2x² + 7x + 3

<p>x = -½, x = -3</p> Signup and view all the answers

Find the vertex of the quadratic equation: y = x² - x - 2

<p>(½, -2¼)</p> Signup and view all the answers

Simplify: √72

<p>6√2</p> Signup and view all the answers

Simplify: √45

<p>3√5</p> Signup and view all the answers

Simplify: √108

<p>6√3</p> Signup and view all the answers

Simplify: √120

<p>2√30</p> Signup and view all the answers

Simplify: 5√2 + 2√98

<p>19√2</p> Signup and view all the answers

Simplify: 4√20 - √5

<p>7√5</p> Signup and view all the answers

Simplify: 3√20 - √45 + 4√80

<p>19√5</p> Signup and view all the answers

Solve the system of equations: y = 2x + 5, y = 2x - 5

<p>No solution</p> Signup and view all the answers

Solve the system of equations: y = 5x - 7, -3x - 2y = -12

<p>(2, 3)</p> Signup and view all the answers

Solve the system of equations: -4x - 2y = -12, 4x + 8y = -24

<p>(6, -6)</p> Signup and view all the answers

Factor: 4x(8x + 1)

<p>32x² + 4x</p> Signup and view all the answers

Factor: (5x + 2)(7x - 2)

<p>35x² + 4x - 4</p> Signup and view all the answers

Factor: 3x²(5x³ - 2x + 5)

<p>15x⁵ - 6x³ + 15x²</p> Signup and view all the answers

Solve: (-2x³ + x - 3x²) - (-7x² - 8x - 8)

<p>-2x³ + 4x² + 9x + 8</p> Signup and view all the answers

Solve: (-2x³ + x - 3x²) + (-7x² - 8x - 8)

<p>-2x³ - 10x² - 7x - 8</p> Signup and view all the answers

Solve: x² - 16 = 0

<p>x = 4, x = -4</p> Signup and view all the answers

Find the vertex of the quadratic equation: x² + 16x + 64 = 0

<p>(-8, 0)</p> Signup and view all the answers

Find the vertex of the quadratic equation: -x² - 10x - 30 = 0

<p>(-5, -5)</p> Signup and view all the answers

Study Notes

Systems of Equations

  • Solve the system: -2x - y = -19 and x - y = 11 results in (10, -1).
  • Solving y = 5x - 7 and -3x - 2y = -12 gives intersection point (2, 3).
  • The system y = 2x + 5 and y = 2x - 5 has no solution as lines are parallel.
  • For -4x - 2y = -12 and 4x + 8y = -24, the solution is (6, -6).

Coin Problems

  • Zoe has 36 coins worth $3.00 and has 30 nickels.

Quadratic Expressions

  • y = x² - x - 2 has vertex at (½, -2¼).
  • Find vertices of quadratics: x² + 16x + 64 at (-8, 0) and -x² - 10x - 30 at (-5, -5).

Simplifying Expressions

  • Simplifying (3x³y⁶z)² results in 9x⁶y¹²z².
  • (-a²b²c²)³(2ab³c)² simplifies to -4a⁸b¹²c⁸.
  • 5x⁰(-10x³) results in -50x³.
  • (x² - x + 1) + (9x² - 9x + 10) simplifies to 10x² - 10x + 11.
  • (x² - x + 1) - (9x² - 9x + 10) simplifies to -8x² + 8x - 9.
  • (x² - x + 1)(9x² - 9x + 10) expands to 9x⁴ - 18x³ + 28x² - 19x + 10.

Factoring

  • x² + 3x - 4 factors to (x + 4)(x - 1).
  • 6x² + 5x - 6 factors to (2x + 3)(3x - 2).
  • 2x² + 7x + 3 factors to (2x + 1)(x + 3).

Solving Quadratics

  • x² + 3x - 4 = 0 has solutions x = 1 and x = -4.
  • 6x² + 5x - 6 = 0 gives solutions x = 2/3 and x = -3/2.
  • 2x² + 7x + 3 = 0 solves to x = -½ and x = -3.

Radical Simplification

  • √72 simplifies to 6√2.
  • √45 simplifies to 3√5.
  • √108 simplifies to 6√3.
  • √120 simplifies to 2√30.
  • 5√2 + 2√98 simplifies to 19√2.
  • 4√20 - √5 simplifies to 7√5.
  • 3√20 - √45 + 4√80 simplifies to 19√5.
  • 3√250 + 5√160 simplifies to 35√10.

Polynomial Factoring

  • 4x(8x + 1) represents 32x² + 4x.
  • (5x + 2)(7x - 2) expands to 35x² + 4x - 4.
  • 3x²(5x³ - 2x + 5) represents 15x⁵ - 6x³ + 15x².
  • (-2x³ + x - 3x²) - (-7x² - 8x - 8) simplifies to -2x³ + 4x² + 9x + 8.
  • Adding polynomials forms -2x³ - 10x² - 7x - 8.

Roots of Quadratics

  • x² - 16 = 0 gives roots x = 4 and x = -4.

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Test your knowledge with these flashcards designed for the Algebra 1 Semester 2 Final Exam. Each card contains a problem or equation related to systems of equations, coin problems, and simplification of expressions. Perfect for review and mastering the concepts before the final exam.

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