Abeka 10th Grade Algebra 2 Test 01

Questions and Answers

In the expression $2(3 + 5) - 4^2$, which operation should be done first?

Parentheses (correct)

Addition

Subtraction

Exponentiation

Which of the following algebraic properties was applied to the expression $(a + c) + x$ to get the expression $a + (c + x)$?

Associative (correct)

Identity

Distributive

Commutative

Which of the following shows the distributive property done correctly on the expression $-3(4x - 5)$?

-3(4x + 5)

-12x + 15 (correct)

-3(4x) - 3(-5)

-12x - 15

Which of the following correctly expands $(w + y)^3$?

$w^3 + 3w^2y + 3wy^2 + y^3$ Signup and view all the answers

Which of the following is a prime expression?

$x^2 + 16$ Signup and view all the answers

Which of the following is the correct sum for $3 adical{2} + adical{8}$?

$5 adical{2}$ Signup and view all the answers

What is the term for the root that matches the radicand in sign?

Principal root Signup and view all the answers

Which of the following is a like radical with $-2 adical{3}5$?

$12 adical{3}$ Signup and view all the answers

In order to multiply radicals, which of the following needs to be true?

The indices are the same. Signup and view all the answers

Which of the following is the conjugate of $ adical{2} - 7$?

$ adical{2} + 7$ Signup and view all the answers

What is twice w decreased by four?

2w - 4 Signup and view all the answers

What is the product of x and y if it is twenty?

xy = 20 Signup and view all the answers

Evaluate $3xy + z^3$ when it is equal to -25.

-25 Signup and view all the answers

What does the expression $12z^2 / 2y^2$ simplify to?

3/2 Signup and view all the answers

What is $(-2x^2)^2 · x^4y$ equal to?

4x^8y Signup and view all the answers

Simplify $6w^2z^{-1} / 3wz^4$.

2w/z^5 Signup and view all the answers

What does $(w + 4) - (w^2 + 5w + 2)$ simplify to?

-w^2 - 4w + 2 Signup and view all the answers

What does $(4a + b)(a - 5b)$ expand to?

4a^2 - 19ab - 5b^2 Signup and view all the answers

Expand $(2x - y)(2x + y)$.

4x^2 - y^2 Signup and view all the answers

What does $(2q + 3)^2$ expand to?

4q^2 + 12q + 9 Signup and view all the answers

Simplify $8x^3 + 3x^2 / 2x$.

4x^2 + 3x Signup and view all the answers

What does $x^3 - 6x^2 + 9x$ factor to?

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

What does $9y^2 - 121$ factor to?

(3y + 11)(3y - 11) Signup and view all the answers

Factor $a^5 - b^5$.

(a - b)(a^4 + a^3b + a^2b^2 + ab^3 + b^4) Signup and view all the answers

What does $x^4 - 81$ factor to?

(x^2 + 9)(x + 3)(x - 3) Signup and view all the answers

What does $x^2 - 4x - 21$ factor to?

(x + 3)(x - 7) Signup and view all the answers

What does $3x^2 + 19x + 20$ factor to?

(3x + 4)(x + 5) Signup and view all the answers

What does $w^2 - 12w + 36$ factor to?

(w - 6)^2 Signup and view all the answers

What does $x/x^2 - 6x$ simplify to?

1/(x - 6), x ≠ 0 Signup and view all the answers

What does $5/x + 2$ divided by $6/x^2 - x - 6$ equal?

5(x - 3)/6, x ≠ -2, 3 Signup and view all the answers

Simplify $3/x + 4 + 4/x - 3$.

(7x + 7)/(x + 4)(x - 3), none Signup and view all the answers

What is $ adical{12} + 2 adical{27}$ equal to?

$8 adical{3}$ Signup and view all the answers

What is $^3 adical{3x} imes ^3 adical{9x^4}$?

$3x^3 adical{x^2}$ Signup and view all the answers

What is $^4 adical{12x^3} / ^4 adical{6x^7}$?

$1/x imes ^4 adical{2}$ Signup and view all the answers

What is $9/x - adical{7}$?

$9x + 9 adical{7}/x^2 - 7$ Signup and view all the answers

Study Notes

Operations and Properties

Prioritize operations in expressions: Parentheses first as seen in 2(3 + 5) − 4^2.
The associative property allows rearranging grouping in addition, exemplified by (a + c) + x becoming a + (c + x).

Distributive Property

Distributing -3 across (4x − 5) results in -12x + 15.
Correctly expanding (w + y)^3 gives w^3 + 3w^2y + 3wy^2 + y^3.

Radicals and Like Terms

Identify primes: x^2 + 16 is a prime expression.
Simplifying radicals: The sum of 3√2 + √8 equals 5√2.
Principal root refers to the root matching the radicand's sign.

Conjugates and Like Radicals

Conjugate of √2 - 7 is √2 + 7.
A like radical for -2^3√5 is 12^3√5.

Multiplying Radicals

Multiplication of radicals requires the same indices.

Algebraic Expressions and Operations

"Twice w decreased by four" translates to 2w - 4.
The product of x and y expressed as xy = 20.
Evaluating expressions: 3xy + z^3 equals -25.

Simplifying Expressions

12z^2/2y^2 simplifies to 3/2.
(-2x^2)^2 · x^4y results in 4x⁸y.
Simplifying 6w^2z^-1/3wz^4 yields 2w/z⁵.

Polynomial Expressions

(w + 4) − (w^2 + 5w + 2) simplifies to -w² - 4w + 2.
The expansion of (4a+b)(a−5b) gives 4a² - 19ab - 5b².
Expanding (2x − y)(2x + y) results in 4x² - y².
Squaring (2q + 3) results in 4q² + 12q + 9.

Factoring and Roots

8x^3 + 3x^2/2x simplifies to 4x² + 3x.
The expression x^3 − 6x^2 + 9x factors as x(x - 3)².
9y² - 121 factors to (3y + 11)(3y - 11).
a^5 - b^5 is factored as (a - b)(a⁴ + a³b + a²b² + ab³ + b⁴).
x^4 - 81 factors to (x² + 9)(x + 3)(x - 3).
The quadratic x² - 4x - 21 factors as (x + 3)(x - 7).
3x² + 19x + 20 factors to (3x + 4)(x + 5).
w² - 12w + 36 factors to (w - 6)².

Rational Expressions and Equations

The expression x/x² - 6x simplifies to 1/x - 6 (note x ≠ 0).
5/x + 2 divided by 6/x² - x - 6 results in 5(x - 3)/6 (note x ≠ -2, 3).
The combined fractions 3/x + 4 + 4/x - 3 simplify to (7x + 7)/((x + 4)(x - 3)).

Simplifying Radicals

The expression √12 + 2√27 simplifies to 8√3.
Combined cube roots ^3√3x * ^3√9x^4 simplifies to 3x^3√x².
Dividing fourth roots ^4√12x³/^4√6x⁷ simplifies to 1/x ^4√2.

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