Algebra IB Final Exam Study Guide and Practice Problems
LAWS OF EXPONENTS#25
BASE, EXPONENT, AND VALUE
In the expression 25 , 2 is the base, 5 is the exponent, and the value is 32.
25 means 2 · 2 · 2 · 2 · 2 = 32x3 means x · x · x
LAWS OF EXPONENTS
Here are the basic patterns with examples:
1)xa . xb = xa + bexamples: x3 . x4 = x3 + 4 = x7;27 · 24 = 211
2)= xa - bexamples: x10÷ x4 = x10 - 4 =x6;= 2-3 or
3)(xa)b =xabexamples: (x4)3 = x4 · 3 = x12;(2x3)4 = 24·x12 = 16x12
4) and examples: ;
5)examples: ;
Quadratic Formula:
Additional Notes:
1
Algebra 1 Final Exam Practice Problems
Write each expression in simple radical (square root) form.
1. / 2. / 3. / 4.Find the GCF.
5. 2x, 8 / 6. 4x2, 20x / 7. 4x, 18Simplify the following expressions.
8. / 9. / 10.Calculate the expressions using order of operations.
11. / 12.Solve the following using proportions.
13. / 14. Mike can mow 3 lawns in 4 hours. How many lawns could he mow in 12 hours?Solve each equation.
15. = / 16. / 17.What property did you use here? ______
Solve the following systems of equations. For #20, write the equations first!
18. 3x – 2y = -25x – 2y = 10 / 19.
/ 20. Edda has a poodle that weighs 4 pounds and gains 3 pound per year. Walden has a young sheltie that weighs 7 pounds and gains 2 pounds every year. When will the two dogs weigh the same amount?
Find the slope and y-intercept. Then determine the equation of the line in y = mx + b form.
21. / 22.m = ______
b = ______
y = ______/ m = ______
b = ______
y = ______
Solve the inequality and represent your solution on a number line.
23. / 24.Graph and shade correctly for the following inequalities. If it is a system, remember to shade only the overlap!
25. 2x – 3y ≤ 5 / 26. y < 3Simplify the following expressions.
27. / 28. / 29. / 30.Answer the questions about the box and whisker plot below.
31. What is the upper quartile? ______
32. What is the median? ______
Using the graph to the right, are the following questions TRUE or FALSE?
33. The oldest person has the highest starting salary. ______
34. The youngest person has the lowest starting salary. ______
35. Person B is older than Person A. ______
Identify the type of correlation shown in each scatter plot.
36.
a. / b. / c.______/ ______/ ______
46.Match the rules stated in words with one of the algebraic expressions listed on the right.
______a. two more than three times a number1) 5x – 7
______b.sevenless than five times a number2) 3t + 2
______c.twice the sum of a number and negative eight3) 2 ( m + (-8) )
Answer the following questions about probability.
37. Suppose you choose a marble from a bag containing 3 red marbles, 3 white marbles, and 5 blue marbles. You return the first marble to the bag and then choose again. Find P(red and blue).
______
38. In a bag containing 3 red marbles, 3 white marbles, and 6 blue marbles, what is the P(white marble)?
______
Use the double distributive property or FOIL and combine like terms.
39. ( x + 4 ) ( x + 1 ) / 40. ( x – 2 ) ( x – 2 )41. ( x + 5 ) ( x – 3 ) / 42. ( m + 3 ) ( m – 5 )
Factor using any method.
43. x2 – 11x + 10 / 44. x2 + 4x - 12 / 45. 2x2 + 3x – 201