XEI 504 Worksheet CRS SKILL Expressions Equations and Inequalities XEI 504 Name_________________________________________ Period____________ LEVEL DESCRIPTION Level 1 – ALL students must attain XEI 303 Combine like terms mastery at this level XEI 402 Add and subtract simple algebraic expressions XEI 405 Multiply two binomials Level 2 – MOST students will attain mastery of the focus skill in isolation . Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will attain XEI 601 Manipulate expressions and equations mastery of the extension skill. Level 1 1. Simplify each expression. a) 3x2 − 7x2 c) 4b + 6 – 4 + 2b + 19 e) 10p3 + 7p2 – 2p3 + b) 12x+9x d) 4c + 18d – 11c + 5d f) b – 3a + 6a – 2b + a g) 5(a – 8) − 6a i) 2(7 − 4n3) + 8(3n3 + 5) k) 11(x + 2) − 4(3x − 7) h) 2(3.7p – 1.6r) + 3(1.5p − 7.2r) j) (-­‐5.9m – 2.7n) – (1.2m – 6.2n) l) 6(m3 + n2) − (2m3 − n) 1 2. Simplify each expression by using the distributive property. a. -­‐2(a + 5) b. -­‐4(2 + 3x) c. 5(-­‐3n + 9) d. -­‐7(m + 8) e. -­‐10(-­‐5 – 8n) f. 3(-­‐2b – 9) g. 4(2m – 4) h. -­‐8(-­‐9x – 3) i. –(x + 9) 3. Simplify the expression by using the distributive property and combining like terms: a. -­‐12n + 3(n + 6) b. -­‐5x + 3(7x – 5) c. 15n − 7(n + -­‐8) d. -­‐9x + -­‐4(3x – 2) e. 12x2 + 6(x + 9) f. -­‐5y + 3(7y +10) 2 Use the box method to find the area of each of the following rectangles. 4. (x + 5) by (x + 6) 7. (2x + 2) by (x + 3) Area: _____________ Area: _____________ 5. (2x + 1) by (x + 7) 8. (x + 8) by (x + 9) Area: _____________ Area: _____________ 6. (x + 7) by (x + 5) 9. (2x – 4) by (x + 5) Area: _____________ Area: ___________ 10. Rewrite without parentheses. a. (x + 3)(x + 4) b. (x + 6)(x + 3) c. (x -­‐ 5)(x + 2) d. (x + 8)(x -­‐ 9) e. (y − 5)(4y + 3) f. (4x + 3)(-­‐7x + 5) 3 Level 2 Find each sum or difference. 1. (4a -­‐ 5) + (3a + 6) 3. (7x2 -­‐ 8) + (3x2 + 1) 5. 5a2 + 3a2x -­‐ 7a3 (+) 2a2 -­‐ 8a2x + 4 7. 2x + 6y -­‐ 3z + 5 4x -­‐ 8y + 6z -­‐ 1 (+) x -­‐ 3y + 6 9. (5x2 -­‐ x -­‐ 7) + (2x2 + 3x + 4) 11. (5x + 3z) + 9z 13. (5a2x + 3ax2 -­‐ 5x) + (2a2x -­‐ 5ax2 + 7x) 2. (3p2 -­‐ 2p + 3) -­‐ (p2 -­‐ 7p + 7) 4. (x2 + y2) -­‐ (-­‐x2 + y2) 6. 5x2 -­‐ x -­‐4 (-­‐) 3x2 + 8x -­‐7 8. 11m2n2 + 2mn -­‐ 11 (-­‐) 5m2n2 -­‐ 6mn + 17 10. (5a + 9b) -­‐ (4b + 2a) 12. 6p -­‐ (8q + 5p) 14. (x3 -­‐ 3x2y + 4xy2 + y3) -­‐ (7x3 -­‐9x2y + xy2 + y3) 4 Multiply the following polynomials. 15. (a + 3) (a2 + 7a + 6)
16. (y -­‐ 5) (4y2 – 3y + 2) 17. (x -­‐ 6) (x2 – 7x -­‐ 8 ) 18. (3b2 – 4b) (2b2 – b + 7) 5 Level 3 Find the PERIMETER of the shape. Equation: Perimeter = Sum of all the sides 19. 20. 21. 3 – 2x 9x – 3y + 2 4x -­‐ 8 3a -­‐
b
2y – 3x -­‐ 3 3a -­‐
b
11 + y 12 + 5x + 7y 3a -­‐ b 22. 23. 24. 7 + 3x 3b – 4a + 5 4z + 3 4z + 3
6 + 2a 2 – 2 5x
6 +
2
a 3b – 4a + 5 25. 26. 27. 3x2 + 5x + 7 3ab + 4a2 3x2 – 4x 3x2 – 4x 6x -­‐ 3 6x -­‐ 3 2a2 3b2 2
7 – 2x 3x + 5x + 7 7 – 2x 2
6b – 5ab 5x2 + 7x + 3 6 Find the area of each shape. 28. 29. n+ 5 x + 7 n x + 2 + 5 30. 2x + 5 31. x + 7 x + 3 x -­‐ 3 5x -­‐ 7 Find the missing side of a shape. 32. 33. 34. 2
2
5x
– 3x + 2
9ab
+
8a
???
2
2x – 5
???
4a2 – 4ab
3x2 + 9x
7b2 – 2ab
Perimeter
Perimeter
Perimeter
2
2
2
5x
+
7x
+
12
14x2 + 4x – 8
9b – 2ab + 12a
???
7 35. A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b, what is the length of the third side? 36. For a rectangle with length of 3x + 4 and perimeter of 10x + 18, what is the width of the rectangle? 37. A rectangle has a perimeter of 12y2 – 2y + 18 and has a width of 4y2 – y + 6. What is the length of the rectangle? Level 4 38. If g(x) = -­‐2x + 4 and f(x) = 10x – 5, find g(x) + 3f(x). 39. If h(x) = 5x2 – 10x and g(x) = -­‐12x2 – 14, find h(x) – g(x). 40. If the width of a rectangle is six more than twice its length. Find the expression for the perimeter of the rectangle in terms of length (l). Use formula for perimeter of a rectangle. 41. The width of a rectangle is twice its length. Find the alegabric expression for the perimeter of the rectangle. 8 42. The length of a rectangle is five more than its width. Find the algebraic expression for the perimeter of the rectangle. 43. The side of a regular octagon is 3x – 2. Find expression for the perimeter. f(x) = -­‐x2 + 3x g(x)= 5x2 -­‐ 8 h(x)= -­‐17x – 22 Given the functions above, find the following. 44. g(x) – h(x) 45. f(x) + h(x) 46. f(x) – g(x) 47. -­‐2h(x) + g(x) 48. 8f(x) – 3g(x) 9 Level 5 Solve for the indicated variable in the parenthesis. 49. P = IRT (T) 50. A = 2(L + W) (W) 51. y = 5x -­‐ 6 (x) 52. 2x -­‐ 3y = 8 (y) 53. x + y = 5 (x) 3 54. y = mx + b (b) ax + by = c (y) 56. A = (1/2)h(b + c) (b) V = LWH (L) 58. A = 4πr2 (r2) V = πr2h (h) 60. 7x -­‐ y = 14 (x) A = x + y (y) 2 62. R = E (I) l 55. 57. 59. 61. 10 63. Write the following in slope-­‐intercepts form (y = mx + b). a. 10x − 5(y + 2) = 25 b. Mixed Review Use the given functions to evaluate each expression. g ( x ) = 3x − 2 f ( x ) = x 2 + 1 64 f ( 3) 6y − 3x
= −3 10
65. g (1) 66. f ( −2 ) 67. g ( −4 ) 68. 3 f ( 5 ) 69. 4g ( −1) 70. f ( x ) + 4 71. g ( t ) 72. f ( h ) 73. g ( 2x ) 11