Alg Summer Review STA Summer Review for Students Entering Algebra This packet will be collected and graded the first week of school. There will also be a test over this material the first week of school. It will be your first test grade. You must show all work on a separate sheet of notebook paper. Students are epected to know from memory all other relevant formulas, including: - Sum of the angles in a triangle - Pythagorean Theorem - Area and perimeter of triangles, rectangles, and squares - All formulas for linear equations (slope formula, slope-intercept and point-slope forms) In order to be prepared for the beginning eam, students should be able to do all of the following problems and related problems as well. The answers are provided for you to check your work. Show work where necessary. Practice problems. Translate to an algebraic epression: seven less than twice a number. Translate to an algebraic epression: three-fifths of a number. Use the commutative law of multiplication to write an epression equivalent to: wd s. Use the associative law of addition to write an epression equivalent to: wd s. Use the distributive law to write an epression equivalent to: wd s. Simplify: 0 87 8 8 8 7 9 e. 8 m m 7 m 7. Evaluate: y y for and y 8. Add: a b a b ab a b a b 9. Subtract: y y 7y y y y page of
Alg Summer Review 0. Simplify and write the final answers with positive eponents only: 0 0 z z 7 e. a b c a c g. y h. y i. j. v w v w ab bc n v k. y y z. Multiply: 7 8y y 7 7y a a a. Divide: y y 9 y y. Convert to decimal notation: 7. 0. Convert to scientific notation: 0 09.... Multiply and write your answer in scientific notation: 70 0 0. Divide and write your answer in scientific notation:.. 0 0 7 page of
Alg Summer Review 7. Factor completely: 8 e. y y 9 8 g. h. 0 8. Solve for the indicated variable: A bh, for b Q p q, for q r y t, for 9. Simplify: 0 89 00 0. Solve the equations for and simplify your answer if possible:... 0 7 g. 9 7 9 e. h. 0 i. 0 j. k. 7 7 0 l. m. 0. Find an equation of the vertical line containing the point, and state its slope.. Find an equation of the horizontal line containing the point, and state its slope.. For the linear equation y, state the slope and graph the line.. For the linear equation, state the slope and graph the line. page of
Alg Summer Review. For the linear equation y : Find the and y intercepts Find the slope Graph the line. Find the slope of the linear equation y 7. Find an equation of the line containing the point, with slope m 8. Find the slope of the line from the graph: 9. Find the slope of the line passing through the points, and, 7 Find an equation of the line described in part (a). 0. Solve the system of equations by graphing: y y. Solve the systems of linear equations by any method: y y0 y7 7y 0y y. In a class of 0 students, % work full time. How many students in that class work full time?. On a test of items, a student got correct. What percent were correct? page of
Alg Summer Review. A computer is on sale for a % reduction. If the sale price is $7.0, what was the original price?. Rent in Austin has increased by % since 990. If monthly rent for a bedroom apartment is now $80, what would rent have been for the same apartment in 990? Round your answer to the nearest cent.. The sum of three consecutive odd integers is 87. What are the integers? 7. The second angle of a triangle is times as large as the first. The third angle is degrees less than the sum of the other two angles. Find the measure of each angle. 8. The length of a rectangle is feet less than times its width. If the perimeter of the rectangle is feet, what are the dimensions of the rectangle? 9. Two angles are complementary if the sum of their angles is 90 degrees. One of two complementary angles is degrees more than twice the other. Find the measure of each angle. 0. There were 00 tickets sold for a volleyball game. Tickets for students were $ each and for adults were $ each. The total amount collected was $0. How many of each type of ticket were sold?. Clear Shine window cleaner is % alcohol and Sunstream window cleaner is 0% alcohol. How much of each should be used to make 90 ounces of a cleaner that is 0% alcohol?. Emilio wishes to mi peanuts worth $. per pound with almonds worth $.80 per pound to make 80 pounds of a miture worth $. per poun How much of each should he use?. The length of a rectangle is one foot less than three times the width. Find the length and width if the area is 0 square feet.. A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is feet long, what are the dimensions of the garden?. The length of one leg of a right triangle is meters. The length of the hypotenuse is 8 meters longer than the other leg. Find the lengths of the hypotenuse and the other leg of the triangle.. Two angles are supplementary if the sum of their angles is 80 degrees. One of two supplementary angles is 8 degrees less than three times the other. Find the measure of each angle. 7. A sample of light bulbs contained defective bulbs. How many defective bulbs would you epect in a batch of 000 light bulbs? 8. Solve and graph the solution on a number line: w 7 9 y y page of
Alg Summer Review 9. List all value(s) of for which each rational epression is undefined: 9 0 0. Simplify (reduce), if possible: a a a 0 a 0 y y. Perform the indicated operation. If possible, simplify (reduce) your answer: 7 a a 0 9 y 7 y y y y g. a a 8 a 8a 8 a h. 8 7 e. a a a a i. y y y y page of
Alg Summer Review Answers 8n v. n 7. n. dw s. wd s. wd s. 7. 9 e.. g. h. i. j. k. 8 y 9y 80v w 8a bc z 9 y y y 7 8y 9y a a a 8. a b ab. y y 9. y y y. 700 0...... 9 0 0. 0 z e. a b c page 7 of
Alg Summer Review 8. 9. 0. y e. cannot be factored g. h. A b h y t r q p Q 0 7 0. 0 7 or e., 7 or g., h., i., j., k. l. m. 7 7 0. equation: slope: undefined. equation: y slope: 0. slope: 0. slope: undefined page 8 of
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Alg Summer Review -intercept =,0 y-intercept = 0, slope = 0. solution:,. 7. y 7 8. 9. undefined m y. Dependent (infinitely many solutions), 7 Inconsistent (no solution). students work full time.. 87 %. $80.. $8 9., 9, and 7.. 7., 90, and 7 degrees 8. width: 7 feet length: feet 9. and degrees 0. 70 student tickets and 0 adult tickets page 0 of
Alg Summer Review. 0 oz. of Clear Shine (%) and 0 oz. of Sunstream (0%),. pounds of peanuts and pounds of almonds. length: 9 feet width: 0 or feet 0.. width: feet length: feet. hypotenuse: m other leg: m. a a or a a. 7 and degrees 7. 7 defective light bulbs 8a 8. or y 0 w or w w 0 a e. 7 7 or y or y y y 9. 0 0 g. h. a 0 a or a a i. y y or y y y page of