Solve for the variable by transforming equations:

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1 Cantwell Sacred Heart of Mary High School Math Department Study Guide for the Algebra 1 (or higher) Placement Test Name: Date: School: Solve for the variable by transforming equations: 1. y + 3 = x = 3. x = w w = (x 4) + 5 = n = 36 n x + = x Simplify: 8. x y + 3x y 9. Add x + 5xy 6y and8x + 6xy+ y Add. 10. (4c - 3cd 5d ) + ( -c + 6cd d )

2 CSHM Study Guide for Algebra 1 Placement Test Spring (6a ab) + ( a + 5 ab b ) Subtract. 1. (4c - 3cd 5d ) - (-c + 6cd d ) 13. (6a ab) ( a + 5 ab b ) Simplify (4 x )(3 x ) (6 x y)( xy (3 x ) 3 3 ( ab)( 5 ab )( ab ) 3 6hk 0hk (3 y ) y y (3 x )(4 x) (5 x )( x ) 0. ( 5a ) 3 6y 5 1. ( ) Simplify.. 4x y( 5x 3xy+ 4y ) 3. ( ) 1 3 x y x xy+ y 1 x y x xy y 4. ( ) 5. x(x 3) + 3x(x + )

3 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Solve. 6. y(3-y) + (y -6) = (3a 1) 5(1 a) = 8 Simplify. 8. (a + 3)(51 1) 9. (x 1)(x + 3x + 4) 30. (3x 4)(x - x + 1) Multiply. Arrange the terms in each factor in order of decreasing degree of one of the variables. 31. (4 + x)(x - 4x + 3) 3. (y 3x)(x + y - xy) Solve. Explain your answer 33. Two jets leave St. Louis at 8:00 A.M., one flying east at a speed km/h greater than the other, which is traveling west. At 10:00 A.M. the planes are 480 km apart. Find their speeds. 34. A rectangular flower garden is 8 ft longer than it is wide. It is surrounded by a brick walk ft wide. The area of the walk is 176 ft. Find the dimensions of the flower garden. 3

4 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Simplify. 35. x yz x y z 36. 6x y 9xy 3 ( x 37. )3 3 x ( xy 38. )7 7 xy Find the missing factor t 4 = (t)( ) 40. x y 4 ( x y) 8 = 7 ( ) Divide. Assume that no denominator equals zero xy 1x 4x 6ab 1ab 4. 4ab Simplify. 43. (a b)(a + b) 44. (x + 3y)(x + y) ( x x)( x + 1) 46. (x 5)(x + 5) 4

5 CSHM Study Guide for Algebra 1 Placement Test Spring (x 6y)(x + 6y) Factor. 48. b a - 5b Simplify. Write each square as a trinomial. 50. (x + 5) 51. (ab 3) Decide whether each trinomial is a perfect square. If it is, factor it. If it is not, write not a perfect square. 5. k + 10k y - 8y k + 180k Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime. 55. a + 10a x - 19x a + 1a 45 5

6 CSHM Study Guide for Algebra 1 Placement Test Spring y - 14y x - 3x u - 8u ax x + ay y Solve: 6. (x 1)(x + 3) = x(x 10) = x - 7x + 1 = Find two consecutive positive odd integers whose product is 143. Simplify. Give any restrictions on the variables x 3 y a a 5 36 a 81 ( x 7 )( x 4 ) 68. ( 7 x)( x+ ) Multiply. Express each product in simplest form x 3 x 4 6

7 CSHM Study Guide for Algebra 1 Placement Test Spring de f e f d 5 4 x 3 x 71. x x a 4 3 4b 5 Divide. Give your answers in simplest form. 74. ab a 4 b 3n m 1mn 76. x x 9 x x 6 4 x + x 6 Simplify. 77. x 4x x 6x Solve x 3 = 30 5 x 1 = x + 3 4x 9 = 3 5 7

8 CSHM Study Guide for Algebra 1 Placement Test Spring 017 w w = n n + = x + 1 x 1 = x + 4 = is 0% of what number? 87. What percent of 60 is 45? Simplify x (3 ) ab 91. ( ) 3 Simplify. Write your answers in scientific notation ( 4 10 )( 7 10 ) 6 State whether each ordered pair is a solution of the given equation. Show why or why not. 94. x y = 5 a. (6, 1) b. (3, - ) 8

9 CSHM Study Guide for Algebra 1 Placement Test Spring m 3n = 6 a. (6, ) b. (9, 4) Solve for y in terms of x x + y = xy + x = 4 Solve each equation if x and y are whole numbers x + y = xy + = 9 Graph each equation x y = x 3y = 6 Find the slope of the line through the given points. 10. (5, 6), (, 4) 9

10 CSHM Study Guide for Algebra 1 Placement Test Spring (1, 4) ( 3, 0) Find the slope of each line x + y = x 5y = 10 State the slope and the y-intercept y = - x x + y = 6 Graph the following equations y = - x y= x

11 CSHM Study Guide for Algebra 1 Placement Test Spring 017 State whether the lines whose equations are given are parallel. State why or why not x y = 5 x y = x y = 6 y x = 6 Write an equation in slope-intercept form of each line described. 11. slope ; passes through (3, - 1) 113. slope -1, passes through (3, 1) 114. (4, 5), (, 1) 115. (-, 8), (1, ) 116. y intercept 1; x intercept 4 Find the values for each given function with the set of real numbers as the doman f(x) = 3x a. f() b. f(-) c. f(-4) 11

12 CSHM Study Guide for Algebra 1 Placement Test Spring g(x) = x - 1 a. g(4) b. g(-4) c. g(0) Graph each linear function f(x) = - x g(x) = 5 Find the vertex and axis of symmetry of the graph of each equation. Then use the vertex and at least four other points to graph the equation. 11. y = - x 1

13 CSHM Study Guide for Algebra 1 Placement Test Spring y = x - 3x Systems of equations. Solve by the graphing method. 13. x y = 3 x + y = 5 Solve by the substitution method: 14. y = x + x + y = 6 13

14 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Solve by elimination 15. x + y = 4 x + y = x y = 1 3x + y = - Solve each inequality. Graph the solution set. 17. x b> 3 b 19. r 3<3r x 1< - 4 or x 1 > < y

15 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Solve. 13. x + = x 5 = Solve and graph the solution set x t > 3 Graph the following inequalities x y y > 3 15

16 CSHM Study Guide for Algebra 1 Placement Test Spring y< x + 3 Graph the following systems of inequalities y x < 3x + y > y > x 1 y < x + 16

17 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Find the indicated square root ± 7 Simplify. Leave your answers in simplest radical form x x y 148. Solve. 3mn mn x = x 9 = = 45x 15 Use the Pythagorean Theorem to solve for the missing side. 15. a = 3, b = 4, c =? 153. a = 7, b =?, c = a =?, b = 16, c = 0. Simplify

18 CSHM Study Guide for Algebra 1 Placement Test Spring x= = 3a x = m 36 = m 5c 3 4= 7 Solve. Express irrational solutions in simplest radical form. If the equation has no solution write No solution x = x = x = (x 3) = x - 9 = (x + 3) - 4 = 68 Use the Quadratic Formula to solve each equation. Give any irrational roots in simplest radical form x + 5x = 0 18

19 CSHM Study Guide for Algebra 1 Placement Test Spring x + 3x 10 = x = 8x x + x = 178. A landscaper wants to design a formal garden which is rectangular. The length will be 6m longer than the width. If the area of the garden is to be 135 m, find the length and width. Draw a diagram to illustrate the solution. Diagram: Geometry 179. Find the area of the triangle in square feet. 4 ft. 3.5 ft What is the volume of a cube that has an edge of 3 centimeters? 181. The perimeters of the two rectangles are equal. What is the width of the second rectangle? 19

20 CSHM Study Guide for Algebra 1 Placement Test Spring A shoe box is most like a A. Cone B. Cylinder C. Rectangular Prism D. Sphere 183. Which item is most like a cylinder? A. basketball B. box of cookies C. can of soup D. desk 184. The strings of a guitar are most like the following types of line segments. a. parallel b. intersecting c. collinear d. perpendicular For questions Using the diagram describe the following: 185. A point: 186. A line: 187. The point where two lines intersect: 188. Three collinear points: 189. The point where a line and a plane intersect. 0

21 CSHM Study Guide for Algebra 1 Placement Test Spring 017 Vocabulary. Define the following terms. Try to give answers that are not straight textbook or internet answers 190. Equation: 191. Expression: 19. Term: 193. Power: 194. Exponent 195. Coefficient: 196. Factor: 197. Slope: 198. Variable: 199. Simplify: 00. Root: 01: Zeros (of a quadratic equation): 0. Solution: 03. Absolute Value: 04. Outlier: 05. Vertical line: 06. Horizontal line: 1