Final Exam Information. Practice Problems for Final Exam

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1 Final Exam Information When:... What to bring: Pencil, eraser, scientific calculator, 3x5 note card with your own handwritten notes on (both sides). How to prepare: Look through all your old tests and quizzes. Learn from your previous mistakes. Look through your homework as well as in-class work sheets. Do some of the review problems in the book. Do the Final Review below, and make sure you really know it. Create study groups. Ask tutors or myself when you have questions. Get a good night s sleep before taking the final. Practice Problems for Final Exam 1. Consider the set of numbers ,,, 0, - 17, 1 π, List those numbers that are real numbers integers (c) rational numbers (d) irrational numbers. Insert <, >, or = in the boxes to make a true statement Simplify as completely as possible ( )

2 4. Evaluate the following expressions ( 1) (c) (d) 131 ( 1) 9 36 (e) 8 (f) 3 8 (g) 49 (h) x y 5. Evaluate the given expression for x = -1, and y = 1 ( x ) 3 + 5( y x) 6. Perform the indicated operations and simplify each algebraic expression as completely as possible. ( 3a + 7b) (5 b + 5a ) 5 4 3xy 5 15xy (c)

3 (d) (3x 5) (e) ( x 3)( x 3x+ 4) (f) 7x 5 5 7x (g) 5( ) 7. The two triangles below are similar. Find the length of side x and write your answer in decimal form. 9 x 8 6 Find the length of side x in the right triangle below and write your answer in decimal form, rounded to two decimals. 7 1 x

4 8. Write an equation for the phrase and solve. Ten less than twice a number is four times the number. Find the number. 9. Consider the following picture when you answer the questions below x x - 5 x - x Express the perimeter of the white rectangle as an algebraic expression (as simplified as possible) Express the area of the gray region as an algebraic expression (as simplified as possible)

5 10. Divide the expression using long division 4y + 8y + 3 y 1 Factor completely or state that the polynomial is prime 11. x x 35x y 14y 6 (c) 4 x Perform the division and simplify completely ( x 1) x 11x + 5 4x 1

6 13. Consider the following equation: x + 4x + 5 x 4 For what value(s) of x is the expression undefined Perform the subtraction and simplify as completely as possible 14. Solve the inequality. Express the solution set in set-builder notation or interval notation and graph the set on a number line. 4x + 17 > Solve each equation. Clearly show your solution, or identify that the equation has no solution or is true for all real numbers. 6x + 6x + 1 = 0 x 1 6= 0 (c) ( a + 1) = 81 (d) V 1 3 = π rh solve for r (volume of a cone)

7 16. Graph each equation (you might have to simplify the equation first and/or put it in a more familiar form) y = -x 4 y + 4 = x + y (c) x+y = -4 (d) y = 4

8 17. Consider the following system of linear equations 3x+ 6y = 6 5x y = 14 Graph the two lines in the coordinate system to the right, and use the graphs to find the solution to the system of equations. y x Now confirm your answer in by solving the system algebraically, using the substitution or addition method. 18. Find the slope-intercept equation of the line that goes through (0,) and (-3,5)

9 19. Given the equation y 3x= 7 Find the x-intercept Find the y-intercept 0. A batter hits a baseball into the air. The formula y = 16x + 64x+ 5 models the baseball s height above the ground, y, in feet, x seconds after it is hit. How high is the ball after seconds? When will the ball hit the ground? Round to the nearest tenth of a second. 1. You are choosing between two long-distance telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all long-distance calls. Plan B has a monthly fee of $3 with a charge of $0.1 per minute for all long-distance calls. For how many minutes of long distance calls will the costs for the two plans be the same? What would be the cost for each plan? If you make approximately 15 long-distance calls per month, each averaging 30 minutes, which plan should you select?

10 . Josh s backyard has a rectangular shape with a perimeter of 1040 ft. The length of his backyard is 00 ft more than the width. What is the width and length of his backyard? 3. John needs to get a ladder for his house to clean the leaves off of the roof. His house is 10 feet tall and he puts the ladder 5 feet from his house. How long does the ladder have to be? (Assume the ground in perfectly level and at a right angle to the house.) 4. A receipt shows that you bought an item for $31.50, including a 5% sales tax. What was the price of the item (before the sales tax)? 5. A person s hair length is proportional to the number of years it has been growing. After years, a persons s hair grows 8 inches. The longest moustache on record was grown by Kalyan Sain of India. Sain grew his moustache for 17 years. How long was each side of the moustache? Use a proportion to solve the problem.

11 6. In a sports league of n teams in which each team plays every other team twice, the total number N of games to be played is given by N = n n. How many games must be played in a league of 7 teams? The Colchester Youth Soccer League plays a total of 40 games. How many teams are in the league? 7. Determine if each of the following statements are true T or false F. If you multiply an inequality by a negative number, you have to reverse the inequality sign. If you add a negative number to both sides of an inequality, you have to reverse the inequality sign. (c) You can only use the Pythagorean theorem on right triangles (d) If a quadratic equation has a solution, you can always solve it by using the quadratic formula. (e) Two parallel lines have the same slope (f) If a system of linear equations has no solution it is because the corresponding lines have different slopes. (q) 0 = 0 (h) The measures of the angles in a triangle always add up to 90 (i) 0.% can be written as the decimal.00 (j) A natural number must be positive (k) The expression 4x 7x 5 + is a trinomial (l) The 4 in the above expression is a constant (m) 63 is a prime number