Unit: Polynomials Calculator Permitted ‐ SHOW YOUR WORK Final Review Math 9 Name:________________________ Date: ________ Part 1: Anatomy 1. Anatomy ‐ Identify the various components of the following polynomials: Polynomial Degree Type Var(s) Coefficient(s) Constant(s) a) 3x2 – 2x ‐ 1 b) ‐8 c) x3y2 ‐ 2x2y3 – x2y2 d) x2 ‐ 16 e) ‐ x5y4z3 2. Collect like terms to simplify (reorder variables if necessary): a) x ‐ y ‐ 2y ‐ x b) x2 ‐ 3x + 3x2 ‐ 3 c) b + a + b ‐ 2a ‐ b d) xy + 1 ‐ 2yx ‐ 2 e) 3x y3z2 ‐ 2z2xy3 + y3z2x f) x2 + 3x ‐ x2 ‐ 2 Part 2: Monomials 3. Multiply the following monomials: a) (2x3)(‐3x2) b) (x3)(‐x2)(‐2x3) c) (‐3x)(‐2x)(‐2x) d) (2x2y) (3x2y3) e) (2x3y)(‐3xy2)(‐x2y) f) (‐x2)(‐x2)(‐x2)(‐x2)(‐x2) 4. Divide the following monomials; use only positive powers (leave in fraction form if necessary): 15x 8
10x 4
12x 4
a) b) c) 5x 3
2x
3x 7
Unit: Polynomials Final Review Math 9 Part 3: Binomials 5. Multiply: a) (x + 3)(x + 2) b) (x + 2)(2x + 1) c) (2x + 5)(2x + 5) d) (x + 3)(x ‐ 5) e) (2x – 1)(x + 3) f) (2x + 1)(3x – 4) g) (x – 6)(3x – 4) h) (4x – 3)(2x – 5) i) (x – 5)(x – 5) 6. Multiply: a) (x + 2)2 b) (x – 3)2 c) (3x – 4)2 Part 4: Polynomials 7. Multiply: a) (x + 3)(x2 + 2x + 3) b) (x2 + 3x + 4)(x + 1) c) (2x + 5)(x2 +3x ‐ 2) e) (x – 1)(x2 + 5x – 3) f) (x2 – 3x + 4)(x – 5) d) (x – 2)(x2 – 3x – 5) Answers: 1. (a)2,tri,x,3,-2,-1 (b) 0,mono,none,none,-8 (c) 5,tri,x,y,1,-2,-1,0 (d) 2,bi,x,1,-16 (e) 12,mono,x,y,z,-1,0
2.(a) -3y (b) 4x2-3x-3 (c) -a+b (d) -xy-1 (e) 2xy3z2 (f) 3x-2 3. (a) -6x5 (b) 2x8 (c) -12x3 (d) 6x4y4 (e) 6x6y4 (f) -x10 4. (a) -3x5 (b) 3
-4/x3 5. (a) x2+5x+6 (b) 2x2+5x+2 (c) 4x2+20x+25 (d) x2-2x-15 (e) 2x2+5x-3 (f) 6x2-5x-4 (g) 3x2-22x+24 (h) 8x2-26x+15
5x (c).
2
2
2
2
3
2
3
2
3
2
(i) x -10x+25 6. (a) x +4x+4 (b) x -6x+9 (c) 9x -24x+16 7. (a) x +5x +9x+9 (b) x +4x +7x+4 (c) 2x +11x +11x-10
(d) x3-5x2+x+10 (e) x3+4x2-8x+3 (f) x3-8x2+19x-20
Unit: Polynomials Review Math 9 Part 5: Grids 1.
Model:
Model:
(x
++22)(x
+ 33+)) 5)
(2x+
1)(3x
(x
)(x
+
Model:
(2x – 5)(2x + 3)
Model:
A:
(4x + 5)(2x + 3)
5.
Model:
(2x – 3)(3x – 2)
8.
Model:
3.
Model:
(4x + 9)(4x + 9)
A:
(2x + 5)(4x – 7)
A:
A:
7.
Model:
A:
A:
4.
2.
6.
Model:
(4x + 9)(4x – 9)
A:
(5x – 4)(3x – 7)
A:
9.
Model:
A:
17
(4x – 9)(4x – 9)
Unit: Solving Final Review Calculator Permitted ‐ SHOW YOUR WORK Math 9 Name:________________________ Date: ________ Part 1: Solving Equations 1. Solve the following Equations: a) 2x – 5 = 2 b) 2. Solve the following Equations: a) 5 – 3x + 7 = –5x + 9 b) d) 2(x + 1) = 3x ‐ 5 e) 4. Solve the following Equations: x 4x  3
= b) a) 3
2
20 = –5(x + 2) c) x
– 19 = –20 4
5x – 20 – 4x + 9 = 5 + 2x – 4 c) 2x – 15x – 12 = 9 – 3x – 2 8 ‐ 2(x ‐ 3) = 3(x ‐ 5) + 2 f) 7 + 2(x2 ‐ 3) = 2x2 + 13 ‐ 3x2 x  3 2x  3
= + 2 4
3
Unit: Solving Final Review Math 9 Part 2: Plot the following Inequalities: 1. x > 0 < | | | | | | | | | | > 4. x < 0 & x > 2 < | | | | | | | | | | > 7. 2 ≤ x ≤ 4 < | | | | | | | | | | > 2. x ≤ ‐4 3. x < 3/2 < | | | | | | | | | | > < | | | | | | | | | | > 5. x < ‐3 & x > 2 6. x ≤ ‐2 & x ≥ 2 < | | | | | | | | | | > < | | | | | | | | | | > 8. ‐4 < x < ‐1 9. ‐2 < x < 2 < | | | | | | | | | | > < | | | | | | | | | | > Part 3: Solve and plot the solution to the following inequalities: a) 3x –6 > 12 b) 16 ≤ –4x – 12 c) x
10 – ≥ 11 3
< | | | | | | | | | | > < | | | | | | | | | | > < | | | | | | | | | | > a) 6x – 4x + 2 ≤ 7x – 3 – 4x + 5 b) 3 + 4x – 7 > 9 – 5x + 5 – 7x c) 8 – 5x < 7 –3x + 9 – 7x < | | | | | | | | | | > < | | | | | | | | | | > < | | | | | | | | | | > d) 4x – 3(x – 4) ≥ 2(x – 6) e) 3(x + 2) – 2(x – 3) < 5(x + 1) f) –4(x – 3) ≤ –3(x + 7) + 6x < | | | | | | | | | | > < | | | | | | | | | | > < | | | | | | | | | | >