Answer Key Period Exam

COLEGIO SAN PATRICIOANSWER 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 = 2

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 = xIII.- 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: 217Students that failed: 37Students 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= 180p = unknownb = 217

Let`s substitute: 180 = p (217) 180 = p 2170.83 = 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)= $415Now, 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 = unknownb = 30 (total amount of students)

Substitute: 14 = 30p 14 =p30

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 = xp = 75% (but we need to change it to its decimal) = 0.75b = 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 late140 were late

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 2Area: 16.7 cm² (approx.)

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

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

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.

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