Algebra 1 Semester 2 Final Exam Flashcards

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?

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

Simplify: (3x³y⁶z)²

9x⁶y¹²z² Signup and view all the answers

Simplify: (-a²b²c²)³(2ab³c)²

-4a⁸b¹²c⁸ Signup and view all the answers

Simplify: 5x⁰(-10x³)

-50x³ Signup and view all the answers

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

10x² - 10x + 11 Signup and view all the answers

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

-8x² + 8x - 9 Signup and view all the answers

Simplify: (x² - x + 1)(9x² - 9x + 10)

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

Factor: x² + 3x - 4

(x + 4)(x - 1) Signup and view all the answers

Solve: x² + 3x - 4 = 0

x = 1, x = -4 Signup and view all the answers

Factor: 6x² + 5x - 6

(2x + 3)(3x - 2) Signup and view all the answers

Solve: 6x² + 5x - 6 = 0

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

Factor: 2x² + 7x + 3

(2x + 1)(x + 3) Signup and view all the answers

Solve: 2x² + 7x + 3

x = -½, x = -3 Signup and view all the answers

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

(½, -2¼) Signup and view all the answers

Simplify: √72

6√2 Signup and view all the answers

Simplify: √45

3√5 Signup and view all the answers

Simplify: √108

6√3 Signup and view all the answers

Simplify: √120

2√30 Signup and view all the answers

Simplify: 5√2 + 2√98

19√2 Signup and view all the answers

Simplify: 4√20 - √5

7√5 Signup and view all the answers

Simplify: 3√20 - √45 + 4√80

19√5 Signup and view all the answers

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

No solution Signup and view all the answers

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

(2, 3) Signup and view all the answers

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

(6, -6) Signup and view all the answers

Factor: 4x(8x + 1)

32x² + 4x Signup and view all the answers

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

35x² + 4x - 4 Signup and view all the answers

Factor: 3x²(5x³ - 2x + 5)

15x⁵ - 6x³ + 15x² Signup and view all the answers

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

-2x³ + 4x² + 9x + 8 Signup and view all the answers

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

-2x³ - 10x² - 7x - 8 Signup and view all the answers

Solve: x² - 16 = 0

x = 4, x = -4 Signup and view all the answers

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

(-8, 0) Signup and view all the answers

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

(-5, -5) 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.