Here are the solutions to the exponent problems: 27) 32 = 9 (because 3 x 3 = 9) 28) (y + 3)2 = 25, when y = 2 (2 + 3)2 = (5)2 = 25 29) x2 + 8 = 12, when x = 2 (2)2 + 8 = 4 + 8 = 12 30) x3 = 64, when x = 4 43 = 64 So in summary: 27) 9 28) y = 2 29) x = 2 30) x = 4

1. COLEGIO SAN PATRICIO
ANSWER KEY Math Practice for 4th Period Exam
School Year 2009 – 2010
I.- Simplify the expression:
1) 24 – 6x + 42 = ________ 2) 12x + (6 – x) 4=__________ 3) -9x(6x +18)=__________
- 6x + 42 + 24 12x + (24 - 4x) - 54x² - 162x
- 6x + 66 12x + 24 - 4x
12x - 4x + 24
8x+24
4) (4x-5)(6) +x=________ 5) -4(x – 3)=__________ 6)3x + 2x² - 9 + x + 7 = ______________
24x – 30 +x - 4x + 12 2x²+ 3x + x – 9 + 7
24x + x – 30 2x² + 4x – 2
25x – 30
II.- Solve the equation:
7) 60x = 30x + 60 8) 25b = 135 + 15 9) -3 + n = 0 10) y - 80 = 80 11) x = 4 + 5
6
60x- 30x = 60 25b = 150 n=0 y = 80 + 80 x=9
30x = 60 b = 150 n=3 y = 160 6
x = 60 25 x = (9) (6)
30 b=6 x = 54
x = 20
11) 6x + 4 = 2x + 16 12) 3y – 7 = 4²- 11 13) 8x + 4 = 7x + 11 14)72 + 8 = x + 68
8
6x – 2x = 16 – 4 3y – 7 = 16 – 11 8x – 7x = 11 – 4 80 = x + 68
4x = 12 3y - 7 = 5 x=7 8
x = 12 3y = 5 + 7 80 – 68 = x
4 3y = 12 8
x=3 y = 12 12 = x
3 8
y=4 (12) (8) = x
96 = x
III.- Problem Soving.-
15. The spelling and grammar test was taken by 217 students. Thirty-seven failed.
What percent passed?
c) 83
Information that I have:
Total number of students: 217
Students that failed: 37

2. Students that passed (represented by x): x = 217 – 37
x = 180
Now that you have the amount of students that passed you will look for the percent
that those students represent.
180 is what percent of 217 students ?
You can use the Equation from lesson 11.2 or you can find your answer using
proportions.
Formula:
a=pb
a= 180
p = unknown
b = 217
Let`s substitute:
180 = p (217)
180 = p
217
0.83 = p
Now, since we are looking for a percent, we need to multiply the answer that we
get by 100.
(0.829)(100)= 83 %
If you want to use proportions you should do it as follows:
180 = x
217 100
217 x = (180) (100)
217 x = 18000
x = 18000
217
x = 83 %
16. Last year, the school spent $8,300 for office equipment. This year, it will spend
5 percent less. How much will it spend this year.
a) $7,885
In this problem, you are going to change the percent into a decimal:
5% = 0.05
Then, you are going to multiply the amount spent for office equipment by the
percent (as a decimal):
($8300)(0.05)= $415

3. Now, you will subtract the answer you got ($415) by the amount spent last year
($8300), and you will get the amount that they will spend this year.
$8300 – $415 = $7885
17.- There are 30 students in 7th H, 14 of them play football. What percent of the
students in 7th H play football?
Answer:
14 out of 30 play football, we need to find the percent.
a: pb
a = 14 (students that play football)
p = unknown
b = 30 (total amount of students)
Substitute:
14 = 30p
14 =p
30
0.47 = p
Now, you need to change it to a percent by multiplying by 100, or by moving the
decimal point two spaces to the right.
(0.47)(100) = 47 %
Notice that you can also use proportions on this problem.
19.- In a concert 75% of the attendants were on time. If there were a total
of 560 people. How many were on time? How many were late?
Answer: 420 were on time and 140 were late.
a = pb
a=x
p = 75% (but we need to change it to its decimal) = 0.75
b = 560
a = (0.75)(560)
a = 420 were on time
Now that we know the amount of attendants that were on time, we are going to find out
the amount of attendants that were late. And we will do this by subtracting the total
amount of attendants by the attendants that were on time.
560 – 420 = attendants that were late
140 were late

4. 20.- How many outcomes would you have if you throw three coins to the air?
Answer: 8 outcomes.
H (heads) T (tails)
(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT)
IV.- GEOMETRY.- Draw and find the area of:
21- A triangle which measures are 5cm, 9cm and an angle of 50°.
Remember the steps:
1.- trace a line segment, (any of the 2)
2.- measure the angle,
3.- trace the other line segment,
4.- trace the third line segment to finish the triangle.
5.- measure the height to find the area.
Answer:
To find the area, you need to measure the height on the triangle that you just
did.
Formula:
Area: (base)(height)
2
Area: (9)(3.7)
2
Area: 33.3
2
Area: 16.7 cm² (approx.)

5. 22- A rhombus which diagonals measure 6cm and 4cm.
Answer:
Formula:
Area: (Diagonal)(diagonal)
2
Area: (6)(4)
2
Area: 24
2
Area: 12 cm²
23- Can you trace a triangle which measure are 4cm, 3cm 5cm. If it is possible,
Trace it and find the area.
Answer:YES, because if I add two of its sides I will get a number that is greater than
the third side. (REMEMBER THE RULES FOR TRACING A TRIANGLE)
To find the area, you need to measure the height on the triangle that you just
did.
Formula:
Area: (base)(height)
2

6. 24.- Find the area of a circle that has a diameter of 12 cm:
Answer: To draw the circle open your compass to 6 cm, then trace the circle,
whenever
you finish measure the diameter, to make sure that it measures 12 cm.
Formula =
Area: πr²
Information that I have:
Diameter: 12 cm
I know that the radius is half of the diameter, so radius is 6cm.
Area: πr²
Area: (3.14) (6²)
Area: (3.14) (36)
Area: 113.04 cm²
25.- How much would I need to cover the football field with grass if it measures
20m length and 12m width?
Answer:
Area: (base)(height)
Area: (20m)(12m)
Area: 240m²

7. 26.- Draw a tree diagram to show the possible combinations with the following clothes:
2 pair of jeans, 6 t-shirts, boots, sneakers, and sandals
Answer: To know the possible combinations you need to multiply :
2 x 6 x 3 = 36 possible combinations.

8. V.- EXPONENTS
27. 3²= 9
28. (y + 3)²= 25, when y= 2
29. x² + 8=12, when x=2
30. x³ =64, when x=4