Algebra IB Midterm Review

Unit 1 Polynomials

100

Identify the leading coefficient, degree, and constant for the given polynomial. 

6x³- 8x² + 4x - 9

Leading Coefficient: 6

Degree: 3 

Constant: -9

200

Write the polynomial in standard form and identify the leading coefficient, degree, and constant. 

10x - 7x⁴ +5x³ - 3 + 6x²

Standard Form: -7x⁴ +5x³ +6x² +10x - 3

Leading Coefficient: -7 

Degree: 4 

Constant: -3 

300

Find the sum between the polynomials: 

(2x² - 4x + 16) + (-5x² +10x - 20) 

-3x² +6x - 4 

400

What is the result when 4x² -17x + 38 is subtracted from 

2x² -5x +25? 

-2x²+12x -11

500

What is the products of (3x-1)(4x+9)

12x² + 23x - 9 

Unit 2 Factoring

100

Factor the polynomial: 

5x² - 35x

5x(x - 7) 

200

Factor the polynomial: 

36x⁵ + 16x²

4x²(9x³ + 4) 

300

Factor the trinomial: 

x² - 49 

(x + 7)(x - 7) 

400

Factor the polynomial: 

x² -2x - 24 

(x + 4)(x - 6) 

500

Factor the polynomial completely: 

3x² - 15x + 18 

3(x - 3)(x - 2) 

Unit 3 Solving Quadratics by Factoring

100

Solve the equation: 

(2x + 3)(x - 1) = 0 

x = -3/2 and x = 1

200

Solve the equation: 

2x² + 8x = 0 

x = 0 and x = -4 

300

Solve the equation: 

x² - 64 = 0 

(x + 8)(x - 8) 

400

Solve the equation: 

x² + 7x  - 18 = 0 

x = -9 and x = 2

500

Solve the equation: 

2x² -10x + 8 = 0 

x= 1 and x = 4

Unit 4 Radicals

100

Describe the transformation: 

(Square root of x) + 5

Vertical shift up 5 units.

200

Simplify the radical in simplest radical form. 

Square root of 45 

3 radical 5

300

Determine the number and answer in simplest radical form. 

(Square root of 27) - (Square root of 12)

Radical 3 

400

Rationalize the denominator. 

9/(square root of 13) 

(9 square root of 13)/13 

500

Rationalize the denominator.

5/radical 8 

(5 radical 2)/4 

Unit 5 More on Solving Quadratics

100

Solve the equation using the square root method. 

3x² = 27 

x = -3 and x = 3 

200

Solve the equation using the square root method. 

(x - 3)² - 49 = 0 

x = -4 and x = 10 

300

Determine the discriminant and the number of solution(s). Identify of they are rational or irrational. 

x² +3x - 1 = 0 

- radical 13 and radical 13

Two Solutions

Irrational 

400

Solve the quadratic equation using the quadratic formula. 

x² - 5x - 14 = 0 

x = -2 and x = 7 

500

Solve the Quadratic Equation by Completing the Square. 

x² - 2x - 15 = 0 

x = 5 and x = -3