Abeka 10th Grade Algebra 2 Test 02

Questions and Answers

What type of linear equation is x + 1 = x + 1?

identity

What would a rational equation be multiplied by to clear the equation of fractions?

least common denominator

What type of number contains both a real part and an imaginary part, for example, 7 − 3i?

complex

Rewrite 2x + 4x^2 = 9 in standard form.

4x² + 2x - 9 = 0 Signup and view all the answers

What is the imaginary form of √-16?

4i Signup and view all the answers

Which of the following correctly states the number of solutions for |3x + 20| > -12?

All real numbers Signup and view all the answers

Which of the following correctly states the types of real solutions for the discriminant 16?

Unequal, rational Signup and view all the answers

Which of the choices correctly translates the following problem? "The area of a yard is 24 square feet. If the width is 3 feet less than the length, state the dimensions of the yard."

x(x - 3) = 24 Signup and view all the answers

What type of interval best describes -2 ≤ x < 8?

Bounded, mixed Signup and view all the answers

Match the following equations with their solutions:

3x − 4 = 8 = x = 4 ax = 2x + 5 = x = 5/a - 2 2|x + 2| = 4 = x = -4, 0 x^2 − 3x − 10 = 0 = x = -2, 5 Signup and view all the answers

What are the values for a, b, and c in the equation -2x = -3x^2 + 11?

a = 3; b = -2; c = -11 Signup and view all the answers

When simplifying the expression 3i/(2 - i), by which of the following would you multiply both numerator and denominator?

2 + i Signup and view all the answers

Solve for x: 3x − 4 = 8.

x = 4 Signup and view all the answers

Solve for x: ax = 2x + 5.

x = 5/a - 2 Signup and view all the answers

Solve for x: 2|x + 2| = 4.

x = -4, 0 Signup and view all the answers

Solve for x: x^2 − 3x − 10 = 0.

x = -2, 5 Signup and view all the answers

Solve for x: x^2 − 15 = 1.

x = ±4 Signup and view all the answers

Solve for x: x^2 + 8x + 4 = 0.

A.--- Signup and view all the answers

Solve for x: x^2 + 3x + 8 = 0.

C.--- Signup and view all the answers

Solve the inequality: -8x < 8.

(-1, ∞) Signup and view all the answers

Solve the inequality: 4 ≤ 2x ≤ 10.

[2, 5] Signup and view all the answers

Solve the inequality: |x + 1| > 3.

(-∞, -4) or (2, ∞) Signup and view all the answers

What is the value of i^15?

-i Signup and view all the answers

Simplify the expression: (2 + 7i) − (4 − 8i).

-2 + 15i Signup and view all the answers

Multiply (6 − 2i) (1 + i).

8 + 4i Signup and view all the answers

Simplify: 3/(6+i).

18/37 - 3i/37 Signup and view all the answers

Solve the equation: 1/2z + 3z = 5/3z − 11.

z = -6 Signup and view all the answers

Solve for x: 3/x - 2 = 8/x + 6.

x = 34/5 or x = 6 4/5 Signup and view all the answers

Solve the equation: 2/x = 3/x+1 + 2/x+1.

x = 2/3 Signup and view all the answers

Solve for x: √3x + 1 = 4.

x = 3 Signup and view all the answers

Solve for x: √5x + 5 = √4x + 1.

x = 4 Signup and view all the answers

The denominator of a fraction is 4 more than its numerator. If the fraction equals 1/3, what is the fraction?

2/6 Signup and view all the answers

Study Notes

Linear Equations and Solutions

An equation like x + 1 = x + 1 is classified as an identity.
The least common denominator is used to eliminate fractions in rational equations.
Solutions to absolute value inequalities, such as |3x + 20| > -12, encompass all real numbers.

Complex Numbers

A number with both real and imaginary parts, exemplified by 7 − 3i, is termed complex.

Quadratic Equations

The standard form of the equation 2x + 4x² = 9 is 4x² + 2x - 9 = 0.
The type of solutions indicated by a discriminant of 16 corresponds to unequal, rational roots.

Algebraic Expressions and Simplification

The imaginary form of √-16 is represented as 4i.
Simplifying the expression 3i/(2-i) requires multiplying by 2 + i in both the numerator and denominator.

Solving Equations and Systems

For the equation 3x − 4 = 8, the solution is x = 4.
The equation ax = 2x + 5 can be solved to find x = (5/a - 2).
Absolute value equations like 2|x + 2| = 4 yield solutions x = -4, 0.

Finding Roots

For the quadratic x² − 3x − 10 = 0, the solutions are x = -2, 5.
The equation x² − 15 = 1 results in solutions x = ±4.

Inequalities

The inequality -8x < 8 has the solution (-1, ∞).
The compound inequality 4 ≤ 2x ≤ 10 translates to the interval [2, 5].

Absolute Value and Complex Numbers

The absolute value inequality |x + 1| > 3 results in two intervals: (-∞, -4) or (2, ∞).
The complex number i raised to an exponent, i^15, simplifies to -i.

Operations with Complex Numbers

The result of (2 + 7i) − (4 − 8i) is -2 + 15i.
The product (6 − 2i)(1 + i) computes to 8 + 4i.
The fraction 3/(6+i) simplifies to 18/37 - (3i/37).

Additional Algebraic Problems

For the equation 1/2z + 3z = 5/3z - 11, the solution is z = -6.
In the equation 3/x - 2 = 8/x + 6, solutions are found at x = 34/5 or x = 6 4/5.
The equation 2/x = 3/(x+1) + 2/(x+1) simplifies to find x = 2/3.
Solving √3x + 1 = 4 leads to x = 3.
The equation √5x + 5 = √4x + 1 gives the solution x = 4.

Fraction Problems

A fraction where the denominator is 4 more than its numerator, resulting in a value of 1/3, equates to 2/6.

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Description

Challenge your knowledge with this quiz based on the Abeka 10th Grade Algebra 2 curriculum. It covers fundamental concepts such as linear equations, rational equations, complex numbers, and standard form. Perfect for reviewing key algebraic principles before tests!