Midterm Review Packet Name: ______

Algebra 2

Due date: The day that you take the Algebra 2Midterm Exam (January 20 or January 21).

Directions: Complete each problem. Show all work. This review packet can be used during the Midterm Exam. The Midterm covers Units 0-3. This packet highlights the types of problems that could be on the exam. On the last page. you may write definitions, formulas, examples, graphs, etc. from Units 0, 1, 2, and 3 on the last page front and back. No other notes will be allowed during the exam.

  • By completing this review packet and making your “Study Sheet”, you can earn EXTRA CREDIT towards your 2nd quarter grade. ALL work must be shown to earn credit.
  • Remember! Notes, homework, tests, and quizzes from Units 0-3 are also great resources!
  1. Solve
  1. Evaluate
  1. Solve | 4w− 1 | + 2 = 9.
  1. Let and .

a.Find

b.Find

c.Find

d.Find

e.Find

f.Find

  1. Identify the domain and range of the relation.

D: ______

R: ______

Is the relation a function? Explain your reasoning.

  1. What is the parent function of g(x)? + 2

Parent function:f(x)= ______

In words, describe the transformation from f(x) to g(x).

  1. Graph y = x2 -8x + 15.

Axis of symmetry: ______

Vertex: ______

x-intercepts: ______

  1. Solve the equation by factoringx2 – 8x + 15 = 0.
  1. What is the repationship between the solutions of the quadratic equation and the x-intercepts?
  1. Classify the following polynomials by degree and number of terms.
  1. -2x4
  1. 3x + 7
  1. x5 – 5x4 + x3 + 6x2 – x + 1
  1. x3 + 4x2– 3
  1. Write (x + 2)(x – 1)(x – 3) in standard form.
  1. Write x3 + 6x2 + 8x in factored form.
  1. Solve the equation in two different ways. x2 + 2 = -14
  1. Find the zeros of f(x) = (x – 6)3(x + 5)2 and state the multiplicity.
  1. Write a quartic polynomial equation in standard form with zeros at and 3i.
  1. Use the equation f(x) = x3 +5x2 + x + 5.
  1. Use the Rational Root Theorem to find the possible rational roots of the function. Mind your p’s and q’s 
  1. List any actual roots.
  1. Graph the function. Find the coordinates of the relative maximum and relative minimum.

Rel. Max. ______

Rel. Min. ______

x-intercept(s) ______

  1. Find all roots of the equation.
  1. (2x2 + 3x – 7) (x – 2)
  1. Divide using long division.
  1. Divide using synthetic division.
  1. Is (x – 2) a factor of (2x2 + 3x – 7)? Explain your reasoning.
  1. Simplify each expression completely.
  1. (-2i)(4i) + 7i
  1. Solve the equation. log2 (x + 1) = 4
  1. Solve the equation. 33x = 729
  1. Evaluate log483. Round to the nearest hundredth.
  1. Write the inverse function. y = log3 (x – 7)
  1. A population of penguins is growing at a rate of 7% per year. If the initial population was 400, what will the population be in 5 years? Write an exponential function and solve.
  1. Evaluate ln 3. Round the nearest tenth.
  1. Solve ln x = 9
  1. Solve e2x = 34

Study Sheet

Organize your notes from Units 0, 1, 2, and 3. You may write definitions, formulas, examples, graphs, etc. in your own handwriting. Utilize the front and back of this page. This study sheet can be used during the exam.

No other notes will be allowed.