1. Colegio San Patricio
5th. Period Review WITH ANSWERS
School Year 2009 – 2010
Name ___________________________________________________List No._________8th_________
Teacher_________________________________________________ Date_______________________
Probability
Answer the following. You MUST SHOW process.
1. In a box you have the following candies: 2 gums, 3 lollipops, and 5 chocolates. What’s the
probability of taking a lollipop out of that box?
a) 20% b) 30% c) 40% d) 50%
2 gums
+ 3 lollipops 3/10 = 0.3 * 100 = 30%
5 chocolates
10 candies
2. The probability of going out during vacations is 5/10, meanwhile the probability of staying
home to work is 2/6. What’s the probability of going out and NOT working?
a) 1/6 b) 1/ 3 c) 5/6 d) 7/ 6
2 events: Going out AND Staying home (either working or resting – NOT working)
Going out = 5/10 = ½
Staying Home = WORKING= 2/6 = 1/3 NOT working = 2/3
Going out * NOT working = ½ * 2/3 = 2/6 = 1/3
Solving Linear Systems
3. Determine whether (1,2) is a solution to the following equation:
2x – 5y = -8
-x + 2y = 3 YES, IT’S A SOLUTION
2(1) – 5(2) = -8 -(1) + 2(2) = 3
2-10 = -8 -1+4 = 3
-8 = -8 3=3
Solve the following system of equations:
4. By GRAPHING method.
4x – y = 1
x+y=4
(1,3)
-y = 1 - 4x y= 4 - x
y= -1 + 4x m: -1/1
m: 4/1 b: 4
b: -1
Check: 4(1) – (3) = 1 (1) + (3) = 4
4-3=1 4=4
1=1

2. 5. By SUBSTITUTION method.
x – 2y = 4
-2x + y = 3 (-10/3 , -11/3)
x = 4 + 2y x = 4 + 2y Check: (-10/3) – 2(-11/3) = 4
-2(4 + 2y) + y = 3 = 4 + 2 (-11/3) -10/3 + 22/3 = 4
-8 – 4y + y = 3 = 4 – 22/3 12/3 = 4
-8 – 3y = 3 = 12/3 – 22/3 4=4
-3y = 3 + 8 x = -10/3 -2(-10/3) + (-11/3) = 3
-3y = 11 20/3 - 11/3 = 3
y = - 11/3 9/3 = 3
3=3
6. By ELIMINATION or linear COMBINATION method.
-2x + 3y = 15
-6x + 6y = 18 (6, 9)
(-2x + 3y = 15) -3 = 6x – 9y = -45 -2x + 3y = 15
-6x + 6y = 18 -6x + 6y = 18 -2x + 3(9) = 15
0 – 3y = -27 -2x = 15 -27
y = -27/-3 -2x = -12
y=9 x = -12/-2 = 6
Check: -2(6) + 3(9) = 15 -6(6) + 6(9) = 18
-12+27 = 15 -36 + 54 = 18
15 = 15 18 = 18
Factoring
Factor out the GCF from each polynomial.
7. 5x2 – 15x 8. 7x3 + 21x2 + 35x
5x(x-3) 7x(x2+3x+5)
Factor the following trinomials.
9. 9x² + 54x + 81 10. 4x² - 25
(3x+9)2 (2x + 5)(2x - 5)
Polynomials
Solve the following polynomials.
11. -(-x2 + 8x - 7) + (15x2 - 6x - 3) 12. Subtract (x2 - 2x + 4) from (12x2 – 5x +6)
x2 - 8x + 7+ 15x2 - 6x – 3 (12x2 – 5x +6) - (x2 - 2x + 4)
16x2 - 14x + 4 12x2 – 5x +6 - x2 + 2x - 4
11x2 – 3x + 2
13. (x5)2(3x0 + 4x +2) 14. -8x18 = 2
-12x25 3x7
X10 (3x0 + 4x +2)
X10 (3(1) + 4x +2)
X10 (3 + 4x +2) = X10 (5 + 4x) = 5x10 + 4x11

3. Numerical Sequences
15. From the following numerical sequence 3, 5, 7, 9, …, what is the number on the
8th.position?
a) 11 b) 13 c) 17 d) 19
2n + 1
2(8) + 1 = 17
Counting Techniques
16. A woman wants a salad, a drink, and a side order for dinner. At the snack bar they have
three kinds of salads available, chicken, shrimp and fajitas. The available drinks are diet coke,
water and milk, and side orders are bread sticks and garlic bread.
a) How many possible lunches can the woman have?
Salads (3) * Drinks (3) * Side Orders (2) = 18
b) If the she is on strict diet and can not order shrimp and always orders diet coke. How
many meals can she have?
Salads (2) * Drinks (1) * Side Orders (2) = 4
Angle Relationship
17. From the figure below answer the following:
m<4 = 113°
1 2 m<6= 67°
67° 3 4
5 6
7 8
Volumes
Draw and state the volume of the following figures:
18. A cube which side measures 8cm.
V = Ab *h
V= (8cm*8cm) 8cm = 512 cm3.
19. A triangular pyramid with the following measures:
Base = 6 cm Height = 13 cm
V= Ab * h Ab = bh/2 = 6*13 / 2 = 39cm2
3
V = Ab * 13 = 39cm2(13cm) = 169cm3
3 3
20. A hexagonal prism with the following measures:

4. Base = 3 cm Apothem = 4 cm Heigth = 8 cm
V= Ab *h Ab = Pa /2
P = 6* 3 = 18cm
Ab = 18 (4) /2 = 36cm2
V = 36cm2(8cm) = 288 cm3