COLEGIO SAN PATRICIOANSWER KEY Math Practice for 4th Period Exam

School Year 2010 – 2011

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

Formula: a=pb a= unknownp = 5% = 0.05 b = 8,300

Let`s substitute: a = (0.05) (8300) a = $ 415

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.

18. Yesterday I bought a CD that was on sale at $30. It was 25% its original price. What was its original price? Answer: $120 was the original price of the CD.

a = pb a = 30 (sale price)p = 25% = 0.25b = unknown

Substitute: 30 = 0.25b 30 = b0.25

120 = b

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

12cm.

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. Make a pie graph for each set of data below. Label sections by coloring each section of the graph and creating a key. Give each graph a title.

 Favorite Web Site

Votes Decimal Percent

Degrees

AOL (Homepage)

4 4/35 = 0.11 11 % 0.11 * 360 = 40°

Lycos 3 3/35 = 0.09 9 % 0.09 * 360 = 32°

MSN 7 7/35 = 0.2 20 % 0.2 * 360 = 72°

Napster 13 13/35 = 0.37 37 % 0.37 * 360 = 133°

Yahoo 8 8/35 = 0.23 23 % 0.23 * 360 = 83°

Total 35 1.00 100 % 360

 Title: FAVORITE WEB SITE

 

 Use your protractor to trace the correct angle for each website. Remember to start with 0. Don´t forget to make a key (leyenda) for the circle graph.

V.- EXPONENTS

27. 3² 3*3 = 9

So, the answer is 9

28. (y + 3)², when y= 2

You substitute y for 2: (2+3) ² You follow PEMDAS5 ² 5*5= 25

So, the answer is 25

29. x² + 8, when x=2

You substitute x for 2: 2² + 8 You follow PEMDAS4 + 8 = 12

So, the answer is 12

30. x³ , when x=4 You substitute x for 4: 4³ 4*4*4 = 64

So, the answer is 64

31. En una urna hay 6 bolitas blancas, 3 bolitas amarillas y una bolita roja.

Extraemos al azar una bolita y nos fijamos solamente en su color. ¿Cuál es la

probabilidad de que la bolita extraída sea de color blanco?

a. 6/10

El número de casos posibles son 10, ya que hay 10 posibilidades de sacar una bolita.

Ahora bien de sacar una bolita blanca solo tengo 6 posibilidades de un total de 10.

Por lo tanto casos favorables:6 y casos posibles:10

32. ¿Cuál es la probabilidad de obtener un número mayor que 2 al lanzar un

dado?

a. 4/6

Al lanzar un dado tenemos 6 casos posibles, los cuales son: {1, 2, 3, 4, 5, 6}Y los números mayores que 2 son: {3, 4, 5, 6}