Algebra 2 Honors Midterm Exam

Write the expression 8^(5/3) in radical form, and simplify. Round to the nearest whole number if necessary.

(^3√8)^5 → 2^5 → 32

Add x+9/x-2 + -8x-39/x^2+x-6. Identify any x-values for which the expression is undefined.

(x+6)/(x+3); x≠2 x≠-3

Evaluate logv4 1/16 by using mental math.

-2

For h(x)=2x^2+6x-9 and k(x)=3x^2-8x+8, find h(x)-2k(x).

-4x^2+22x-25

Simplify lne^-5x.

-5x

Write the expression ^11√10^8 by using rational exponents.

10^8/11

Use synthetic substitution to evaluate the polynomial P(x)=x^3-4x^2-5 for x=4.

11

Express 8√-84 in terms of i.

16i√21

The amount of money in a bank account can be expressed by the exponential equation A=300(1.005)^12t where A is the amount in dollars and t is the time in years. About how many years will it take for the amount in the account to be more than $900?

18 years

Find the number and type of solutions for x^2-9x=-8.

2 real solutions; x = 1 or 8

Simplify 2z^3-6z^2/z^2-3z. Identify any z-values for which the expression is undefined.

2(z^2-1); z≠0

Evaluate logv9 243. If necessary, round your answer to the nearest tenth.

2.5

Simplify the expression (27)^1/3 ⋅ (27)^2/3.

27

Simplify logv7 x^3 - logv7 x.

2logv7 x

Simplify the expression logv4 64.

3

Multiply 6i(4-6i). Write the result in the form a+bi.

36 + 24i

Find the complex conjugate of 3i+4.

3i-4

Factor the expression 81x^6+24x^3y^3.

3x^2(3x+2y)(9x2-6xy+4y^2)

Write the logarithmic equation logv4 16=2 in exponential form.

4^2=6

Simplify the expression ^4√256z^16. Assume that all variables are positive.

4z^4

Find the product (5x-3)(x^3-5x+2).

5x^4 -3x^3 -25x^2 +25x -6

Write a function that transforms f(x)=2x^3+4 in the following way: stretch vertically by a factor of 6 and shift 5 units left.

6(2x^3+9)

Add. Write your answer in standard form. (5a^5-a^4) + (a^5+7a^4-2)

6a^5 +6a^4 -2

Multiply 8x^4y^2/3z^3 ⋅ 9xy^2z^6/4y^4. Assume that all expressions are defined.

6x^5z^3

Identify the degree of the monomial -5r^3s^5.

8

Consider the function f(x)=-4x^2-8x+10. Determine whether the graph opens upward or downward. Find the axis of symmetry, the vertex and the y-intercept. Graph the function.

downward; aos: x = -1; vertex: (-1, 14); y-int: (0, 10)

Write a quadratic function that fits the points (0,6), (2,4), and (3,6).

f(x)=x^2-3x+6

Graph f(x)=5x-1. Then, write and graph the inverse.

f^-1(x)= x/5 + 1/5

f(x)=0.9^x is transformed 4 units left, compressed vertically by a factor of 1/2, and reflected across the x-axis. Write the transformed function g(x).

g(x)=-1/2(0.9^(x+4))

Let g(x) be the transformation, vertical translation 3 units down, of f(x)=-4x+8. Write the rule for g(x).

g(x)=-4x+11

What function is vertically stretched by a factor of 3 and translated 4 units right from the parent function?

g(x)=3(x^2-4)

The parent function f(x)=√x is stretched horizontally by a factor of 4, reflection across the y-axis, and translated left 2 units. Write the square-root function g.

g(x)=√-1/4x+2

Identify the leading coefficient, degree, and end behavior of the function P(x)=-5x^4-6x^2+6.

lc = -5; d = 4; eb = as x → -∞, P(x) → -∞, as x → +∞, P(x) → -∞

Express logv2 64 - logv2 4 as a single logarithm. Simplify, if possible.

logv2 16; 4

Write the exponential equation 2^3=8 in logarithmic form.

logv2 8 = 3

Distance that sound travels through air d varies directly as time t, and d=1,675 ft when t=5s. Find t when d=5,025 ft.

t = 15s

Find the zeros of the function f(x)=x^2+6x+18.

unfactorable, no zeros

Divide by using synthetic division. (x^2-9x+10) ÷ (x-2)

x -7 -4/x-2

Identify holes in the graph of f(x)= x^2+8x+12/x+2. Then graph.

x = -2

Solve the equation x^2=3-2x by completing the square.

x = -3 and 1

Factor x^3+5x^2-9x-45.

x = -5, -3, and 3

Solve (-3+18)^(1/2)=x.

x = -6 or 3

Solve the polynomial equation 3x^5+6x^4-72x^3=0 by factoring.

x = 0, -4, and 6

Identify the axis of symmetry for the graph of f(x)=x^2+2x-3.

x = 1

Solve 8^(x+8)=32^x.

x = 12

Find the zeros of g(x)=4x^2-x+5 by using the Quadratic Formula.

x = 1±i√79/8

Identify the roots of -3x^3-21x^2+72x+540=0. State the multiplicity of each root.

x = 5 and -6 with multiplicity of 2

Solve the equation 2x^2+18=0

x = ±3i

Subtract -6x^2+x-3/x^2+9 - -2x-4/x^2+9. Identify any x-values for which the expression is undefined.

x is always defined

The area of a rectangle is equal to x^2+10x+16 square units. If the length of the rectangle is equal to x+8 units, what expression represents its width?

x+2

Write a quadratic function in standard form with zeros 6 and -8.

x^2+2x-48

Find the product (x-2y)^3.

x^3 -6x^2y -6xy -8y^3

Divide 5x^3/3x^2y ÷ 25/3y^9. Assume that all expressions are defined.

xy^8/5

Use inverse operations to write the inverse of f(x)=x/4-5.

y=4x-20

Find the absolute value |-7-9i|.

≈ 11.4