Download Factoring and Solving equations Review

Factoring and Solving equations Review
1. Common Factor the following questions:
a) 14f + f2
b) 20m + 12n
c) 16ab - 12a2
f(14 + f)
4(5m + 3n)
4a(4b – 3a)
2. Factor the following trinomials:
a) c2 + 2c - 8
b) x2 – 13x + 30
(c + 4)( c – 2)
(x – 10)(x – 3)
ANSWER KEY
Math 9
d) 14ab + 12ab2 – 6a2b
2ab(7 + 6b – 3a)
c) y2 – 49
(y – 7)(y + 7)
d) e2 + 10e + 16
(e + 2)(e + 8)
3. Write the expression for the following statements:
a) 5 times a number b) twice a number less 6
c) 2 consecutive numbers
5n
2n – 6
n + n + 1 OR 2n + 1
d) half his height plus four
n + 4
2
4. Solve the following equations and “check” them:
a)
3a – 4 = 17
b) 6x + 8 = 3x + 2
c) 6x – 3 = 5x + 2
d) 5a + 24 = -6
3a – 4 + 4 = 17 + 4
6x – 3x + 8 = 2
6x – 5x – 3 = 2
5a + 24 – 24 = -6 - 24
3a = 21
3x + 8 = 2
x-3=2
5a = -30
a=7
3x + 8 – 8 = 2 - 8
x–3+3=2+3
a = -6
3x = -6
x=5
check: 3(7) – 4 = 17
x = -2
check: 5(-6) + 24 = -6
21 – 4 = 17
check: 6(5) – 3 = 5(5) + 2
-30 + 24 = -6
17 = 17 check: 6(-2) + 8 = 3(-2) + 2
30 – 3 = 25 + 2
-6 = -6
-12 + 8 = -6 + 2
27 = 27
-4 = -4
5. Solve the following equations by simplifying first:
a) 5(b + 2) = 20
b) 5a + 2 – 2a = 7a – 5a + 6
5b + 10 = 20
3a + 2 = 2a + 6
5b + 10 – 10 = 20 - 10
3a – 2a + 2 = 6
5b = 10
a+2=6
b=2
a+2–2=6–2
a =4
d) 3 – 6b + 6 = 2b – 7
9 – 6b = 2b - 7
2b – 7 = 9 – 6b
2b + 6b – 7 = 9
8b – 7 = 9
8b – 7 + 7 = 9 + 7
8b = 16
b=2
e) x = 5
3
cross multiply
x = 15
c) 4 (b – 3) = 0
4b – 12 = 0
4b – 12 + 12 = 0 + 12
4b = 12
b=3
f) c - 1 = 1
3
2
4
multiply all by 12
12 c - 12 = 12
3
2
4
4c – 6 = 3
4c – 6 + 6 = 3 + 6
4c = 9
c = 9/4
g) 2c + 1 = 6
3
3
multiply all by 3
6c + 3 = 18
3
3
2c + 1 = 18
2c + 1 – 1 = 18 -1
2c = 17
c = 8.5
6. Solve the following word problems using algebra
a) Find 2 consecutive numbers that add to 23.
n + n + 1 = 23
2n + 1 = 23
2n = 22
n = 11
numbers are 11,12
b) Find 3 consecutive numbers that add to 117.
n + n + 1 + n + 2 = 117
3n + 3 = 117
n = 38
numbers are 38, 39, 40
3n = 114
c) You buy a coat, boots and gloves. You spend $10 more on the boots than the gloves, and 5 times the amount
of money on the coat as the gloves. If you total is $150 what was the price of each?
Gloves = g
boots = g + 10
coat = 5g
g + g + 10 + 5g = 150
7g + 10 = 150
gloves = $20
7g = 140
boots = $30
g = 20
coat = $100
d) Dan and Fred are brothers and there heights combined equals 10.2 m. If Fred is 0.2m taller than Dan. How
tall is each brother?
Dan = d
Fred = d + 0.2
d + d + 0.2 = 10.2
2d + 0.2 = 10.2
2d = 10 d = 5
Dan is 5 m and Fred is 5.2m
Advanced:
7 a) Sam is twice Jennie’s age. Three years ago the sum of their ages was 45. What are their ages today?
Jennie’s age = j
three years ago j – 3
j – 3 + 2j – 3 = 45
Sam’s age = 2j
2j – 3
3j – 6 = 45
3j = 51
j= 17
TODAY Jennie is 17 and Sam is 34
b) -3 + 4(a-1)= 3(a + 5)
-3 + 4a – 4 = 3a + 15
-7 + 4a = 3a + 15
-7 + 4a – 3a = 15
-7 + a = 15
a = 22
c) The cash box has 61 bills. How many 2 dollar bills and 5 dollar bills are there if the total is $233
number of 2 dollar bills = n
number of 5 dollar bills = 61 – n
2n + 5(61 – n) = 233
2n + 305 – 5n = 233
-3n = -72
n = 24
There are 24 $2 bills
There are 37 $5 bills
d) (a + 2)(-6a – 1) = (3a – 1)(-2a + 3)
-6a2 – 1a – 12a – 2 = -6a2 + 9a + 2a – 3
-6a2 – 13a – 2 = -6a2 + 11a – 3
-6a2 + 6a2 – 13a – 11a – 2 = -3
-24 a - 2 = -3
-24a – 2 + 2 = -3 + 2
-24a = -1
A= 1
24