Westhill Institute
Vestigia Nulla Retrorsum Department of Curriculum and Academic Programs Subject: Math Grade / Group: 701 Teacher’s Name: Ana Isabel Almeida L. Semester Examination or Guide: Date: 23 – 05 -­‐ 2011 Grade: 7th Student Name __________________________________________________________ By signing this document, I affirm that I have neither given nor received help with this guide. __________________________________________________________ Student’s Signature Advanced Math
Study Guide
Monomials and Polynomials
Write each fraction in lowest terms.
1.
2.
54j
27j3
4.
12k5
14f5u5
5.
-2f6u4 - 2u5
7.
4c2 + 4cq + q2
8.
16c2 + 8ct + t2
16c2 - t2
13.
13tc + 3t2 + 4c2
14.
400k2 - 200kq
-6a2 - 13ar - 7r2
24e2 + 24ex + 6x2
9.
25xf - 28x2 + 8f2
12e2 + 8ew + w2
384f2 - 192fu
256uf - 128u2
12.
-27c4u3
-6c2u4
15.
15e2 + 41es + 12s2
4e2 - w2
17.
440k2 - 220kq
19.
9a2 - p2
16pa + 5p2 + 3a2
64f2 - 49x2
16c2 - t2
16.
6.
27e4x4
6e2 + 5ex + x2
11.
48a2p + 24ap2
44pa + 22p2
9e4x5
8c2 + 20cq + 8q2
10.
3.
36k4
12e2 + 7es + s2
44h2s - 22hs2
18.
10e2 + 23et + 9t2
22h2s - 11hs2
20.
36a2 - 49r2
8e2 + 6et + t2
21.
-35c3s4
6e2 + 7ex + x2
-5c3s3 - 5s5
36e2 - x2
Polynomials
Add.
1. (14x + 5) + (10x + 5)
2. (10x + 12) + (6x + 20)
3. (19x2 + 12x + 12) + (7x2 + 10x + 13)
4. (17x2 + 20x + 11) + (15x2 + 11x + 17)
5. (-15x2 - 5x + 9) + (-6x2 - 19x - 16) + (-15x2 - 14x - 6. (-13x2 - 13x - 10) + (19x2 - 19x - 5)
13) + (9x2 - 14x + 20)
7. (4x2 - 6x + 7) + (-19x2 - 15x - 18)
8. (-13x2 - 5x - 14) + (-14x2 - 20x + 8)
2 9. (20x7 - 10x6 - 9x5 - 14x4 + 18x) + (-6x6 - 12x5 9x4 - 9x)
10. (-20x2 + 13x - 4) + (11x2 - 13x - 10)
11. (-14x2 - 15x - 17) + (14x2 + 9x - 17)
12. (-10x6 + 18x3 + 13) + (7x6 - 7x2 + 17)
13. (11x2 + 5x + 6) + (18x2 + 17x + 17)
14. (4x2 - 19x + 15) + (-18x2 + 15x + 16)
15. (-7x2 + 14x + 17) + (19x2 - 6x - 20) + (-14x2 18x + 20) + (20x2 + 19x + 17)
16. (-14x7 + 19x6 - 17) + (5x5 - 10x4 + 18)
17. (9x6 - 4) + (10x5 - 15x4 + 14)
18. (-17x6 - 6x3 - 20x) + (-10x4 + 9x3 - 18)
19. (20x2 + 15x + 13) + (-19x2 + 17x + 5)
20. (5x6 + 9x3 - 6x) + (-9x7 - 20x2 - 6x)
Subtract.
1. (6x + 14) - (9x + 5)
2. (6x + 19) - (14x + 5)
3. (14x2 + 13x + 12) - (7x2 + 20x + 4)
4. (19x2 + 9x + 16) - (5x2 + 12x + 7)
5. (15x2 - 9x + 9) - (13x2 + 15x + 5) - (-16x2 + 20x + 6. (-9x2 - 4x - 4) - (-9x2 - 11x + 12)
16) - (-7x2 + 10x - 10)
7. From 19x2 + 11x + 15 subtract -5x2 - 6x - 6
8. (-18x2 + 7x - 14) - (-20x2 + 17x - 12)
9. Subtract -10x2 + 16x - 15 from -6x2 + 19x + 19
10. (17x5 + 19x2 + 15) - (9x7 - 11x - 17)
11. (4x2 + 15x - 18) - (9x2 - 5x + 19) - (-5x2 + 18x 20) - (-4x2 - 7x + 15)
12. (20x6 - 13x5) - (-7x6 + 7x5 - 20x3 - 4x2)
13. How much greater is -12x2 - 19x + 8 than -15x2
+ 17x - 18?
14. How much greater is -16x2 - 7x - 5 than 18x2 +
13x - 8?
15. Subtract 4x4 - 14x3 + 11 from -14x6 - 9x5 - 12x2
16. From -16x2 + 13x - 13 subtract -19x2 - 11x + 12
17. (17x2 + 7x - 14) - (-6x2 - 5x - 18)
18. (8x3 - 8x - 4) - (-16x6 + 9x3 - 6x2)
19. (-18x2 + 4x - 16) - (15x2 + 4x - 13)
20. How much greater is -19x2 + 5x - 6 than -5x2 16x - 17?
Use FOIL.
1. (11x + 11) (11x + 10)
2. (9x + 9) (3x + 3)
3. (8x + 11) (5x + 11)
4. (9x + 7) (6x + 4)
5. (11x + 5) (-11x + 12)
6. (8x + 11) (-3x + 6)
7. (6x + 3) (-5x + 2)
8. (7x + 7) (5x - 4)
9. (-10x + 11) (7x + 5)
10. (-9x + 5) (-10x - 6)
11. (8x - 13) (20x + 11)
12. (16x - 19) (8x - 8)
13. (18x - 20) (-12x - 6)
14. (10x - 11) (-14x + 9)
3 15. (-20x - 12) (-19x - 15)
16. (-14x + 11) (-9x + 19)
17. (-7x - 11) (19x - 14)
18. (6x + 7) (20x - 9)
19. (12x - 13) (-12x + 12)
20. (16x + 13) (-8x + 15)
Multiply.
1. (-2x2 - 4x + 11) (5x - 12)
2. (-11x + 3) (-10x2 - 7x - 9)
3. (4x2 + 12x + 10) (-9x2 + 8x + 2)
4. (7x2 - 6x - 8) (-2x + 2)
5. (10x5 + 3) (-2x2 - 11x + 2)
6. (-12x - 3) (12x2 - 11x + 3)
7. (-10) (2x2 + 8x + 3)
8. (2x6 + 3x5) (-5x - 12)
9. (6x7 - 8x2 + 7) (-4x - 3) (-6x2 - 7x - 11)
10. (-9x2 + 11x + 2) (8x2 + 6x - 7)
11. (8x5 + 3x4 + 2x3) (5x + 10) (12x2 + 6x + 6)
12. (-7x + 11) (-12x + 3)
13. (4x3 + 5x2 - 12x) (-12x - 2) (7x2 - 9x + 12)
14. (7x + 3) (7x2 + 3x + 10)
15. (9) (8x2 - 2x + 3)
16. (-12x + 12) (4x2 - 11x + 11)
17. (-6x4 + 11x2 + 3x) (10x + 4) (4x - 4)
18. (-3x6 - 6x3) (11x - 6) (10x - 10)
19. (-11x7 + 11x6 + 11x2) (9x3 - 7x2 - 4x + 6) (-7x 11)
20. (-3x + 8) (-4x3 + 8x2 - 2x + 12)
Divide.
1.
28x2
2.
7x2
3.
24x4
48x4
4.
32x4
5.
9x
90x7
6.
88x
22x9
12x3
108x3
8.
20x11
9.
35x
45x
6x8
7.
42x2
72x10
54x2
10.
4 21x3
-15x3
22x9
-15x3
11. (-40x12 + 30x10 12. (77x11 + 33x10 +
4
3
10x + 30x + 80x) ÷
99x6 + 88x5 + 44x) ÷
2
20x
11x3
13. (-40x12 - 20x11 25x9 - 30x2) ÷ 15x3
14. (32x11 + 12x7 + 20x4
- 28x2) ÷ 8x2
15. (18x10 - 9x8 + 72x7 + 16. (6x11 + 24x9 - 27x8 +
9x5 + 36x2) ÷ 36x2
3x6 - 3x5) ÷ 24x
17. (112x12 - 72x10 +
40x9 - 144x8) ÷ (136x5)
18. (14x12 - 18x11 12x10 - 18x5) ÷ 28x7
19. (36x12 + 96x11 - 54x8 20. (192x12 + 72x11 +
+ 96x) ÷ 102x5
84x8 - 36x3 - 216x2)
÷ (-120x8)
Add, Subtract, Multiply, and Divide.
1. (12x + 14) - (6x + 17)
2.
32x2
28x2
3. [(12x2 + 14x + 13) - (10x2 + 10x + 4)] × [(-5x6 +
10x4 + 3x) (-5x - 12)]
4. x (9x2 + 2x + 8)
5. (-10x + 12) (9x - 4)
6. (11x6 + 4x5 + 7x) (-8x + 8)
7. (88x12 + 55x11 + 99x3) ÷ 11x2
8. [(16x2 - 5x - 8) + (20x2 - 9x + 8)] × [(9x - 3) (-5x 11)]
9. (-5x + 6) (5x + 5)
10. (-20x5 - 17x4 + 17x3) - (16x7 + 9x6 - 10x)
11. (8x) (-4x + 9)
12. (-10x2 + 4x + 3) (5x2 + 4x + 5)
13. (-14x8 + 6x6 + 12x4 - 10x3) ÷ 4x3
14.
-36x11
63x5
15. (-14x + 13) (-15x - 10)
16. x (x2 + 4x + 4)
17. (-6x - 12) (-8x - 9)
18.
39x2
-42x3
19. (108x7 + 168x5 - 132x4 + 120x2) ÷ 168x8
20. (20x2 - 8x + 19) - (6x2 + 6x + 20) - (-13x2 - 10x
+ 16) - (20x2 + 6x - 14)
5 Factoring perfect squares
1. 49x2 - 100
2. x2 + 16x + 64
3. x2 - 9
4. 25x2 - 120x + 144
5. x2 - 10x + 25
6. x2 - 16
7. 81x2 - 144xy + 64y2
8. 49x4 - 121
9. 16x2 - 24x + 9
10. 49x4 + 168x2 + 144
11. 9x2 - 25
12. 16x4 - 49
13. 25x4 - 110x2 + 121
14. x2 + 6x + 9
15. 64x4 + 144x2 + 81
16. 25x2 - 36
17. 81x2 - 100
18. 4x2 + 36xy + 81y2
19. 16x4 - 25
20. 49x2 - 28x + 4
21. 25x2 - 90xy + 81y2
22. 81x4 - 16
23. 9x4 + 48x2 + 64
24. x2 - 2x + 1
25. 49x2 - 42x + 9
26. x2 - 121
27. x2 - 144
28. 25x4 - 4
29. 16x2 - 56xy + 49y2
30. 25x4 - 20x2 + 4
Factoring Trinomials
1. x2 - 14x + 45
2. x2 + 17x + 60
3. x2 - 18x + 80
4. x2 - 10x + 16
5. x2 - 6x + 9
6. x2 - 7x + 6
7. x2 + 20x + 99
8. x2 + 3x - 18
9. x2 - 3x - 88
10. x2 - 16x + 48
11. x2 + 11x + 30
12. x2 - 14x + 33
13. x2 + x - 30
14. x2 - 3x - 70
15. x2 + 8x - 9
16. x2 - 16x + 55
17. x2 + 6x - 72
18. x2 + 5x - 50
19. x2 + 10x + 24
20. x2 + 6x - 16
21. x2 - 5x + 4
22. x2 - 16x + 60
23. x2 + 8x - 20
24. x2 - 4x + 3
25. x2 + 2x - 35
26. x2 - 5x - 24
6 27. x2 - 6x + 8
28. x2 + x - 90
29. x2 - 100
30. x2 - 16
One-Step Equations
Solve each equation.
Y+1 = 4
Y-1 = 0
Y-1 = 1
Y+18 = 24
X+19 = 24
Y-1 = 2
4Y+11 = 27
Z+24 = 30
2Y+23 = 29
5X+2 = 27
3Y+8 = 26
4X+3 = 27
4Y+2 = 10
2Y+12 = 22
7 4Y+11 = 27
2Y+7 = 19
Z+24 = 30
Y+17 = 20
8