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MATHEMATICS I

GUIDE EXAM

2nd. BIMONTHLY
1.- Solve problems adding and subtracting fractions

a. In a party, Aisha and her friends ate 21/2 of pizzas. After the party, were 1 1/8 of pizzas.

¿How many pizzas did Aisha have at the beginning of the party?
b. Theresa is going to distribute her candy to her brothers. 1/3 to the older, 3/8 for the brother in the middle and the rest to the younger brother. What fraction, of the total amount, is for the younger brother?
c. During a day in the summer, a family has drunk: two bottles of water with 1 ½ lt. each one., 4 bottles of 1/3 lt of juice and 5 lemonades of 1/4 lt. ¿How many liters of liquid has the family drunk?
d. ¿How many 1/3 lt are there in 4 l?
e. A marshmallows box contains 60 pieces. Eva ate 1/5 of them and Ana ½ of them. What fraction of the box did they eat? And How many pieces did they eat?
f.- 2/5 of the income in a community are used to fuel, 1/8 is used to electricity, 1/12 is used to clean the town, 1/4 is used to building maintenance and the rest is used to provide water. What fraction of the total income is used to provide water? Express as a decimal.
g. Alicia has 300 € for shopping. On Thursday, she spent 2/5 of the total and on Saturday 1/4 . What fraction of the total money did she spend? And What is the fraction of the money that remains? Express the factions into decimals, too.
h.- A tank was full of water. First, 5/8 of the that water were used, after 1/6 was used. Find:

a) The fraction of water left in the tank after 5/8 of water were used..

b) The fraction of water left in the tank after 1/6 was used

.

i.- A farm has an area of 2.016 m2. 16/63 of the farm are used to plant wheat, 35/48 of it are planted of barley and the rest is unplanted. Find:

a) The fraction of area that is planted

b) The fraction of area that is unplanted.

2.- Angles

Measure and classify the following angles:

_______________________ _______________________ _____________________

_______________________ ______________________

3.- Polygons

a) Classify the following triangles by sides and by angles

_______________________ __________________________ ________________________

__________________________ ____________________________

b) Tracing polygons and lines in a triangle (using compass or /and geometry set)

a.- Trace a square 6cm by side

b- Trace an equilateral triangle 5 cm by side

c.- Trace an scalene obtuse triangle (measures you want) and trace the medians and find the barycenter

d.- Trace the angle bisectors and the inscribed circumference in an isosceles right triangle

e.- Trace the altitudes and find the orthocenter in an scalene obtuse triangle

c) Choose from the box the correct word and write on the line to complete the sentence

perpendicular bisector angle bisector median altitude orthocenter incenter

barycenter circumcenter circumscribed inscribed inside outside

a.- The line that goes from the midpoint of a segment to its opposite vertex is the ____________________

b.- The center of mass, in a triangle, is the point where the medians intersect each other, is called _________

c.- The perpendicular line that goes from a vertex to its opposite side is __________________

d.- The point where the angle bisectors intersect each other and is always located inside the triangle is called __________

e.- The perpendicular line that goes from the midpoint to a segment and divides it into two equal parts is named _____________________________

f.- In an obtuse triangle, the orthocenter is located ______________ the triangle

g.- Finding the incenter, you can trace a _______________circumference.

h.- The point where the perpendicular bisectors intersect each other is called _________________

i.- In an acute triangle, the orthocenter is located _____________ the triangle

j.- The point where the altitudes intersect each other is called _________________

k.- The line that divides the angle into two equal angles is called ________________

l.- The circumcenter is the center of a ____________________________ circumference.

Areas and perimeters

1.- Find the area and perimeter of each polygon:





8,7 cm heigth

4.- Prime and compound numbers
a.- How many factors does a prime number have? ______________________

b.- Write the prime numbers in a sequence from 1 to 100 __________________________________________

c.- What is a multiple? ____________________________________

d.- The numbers end in _____________________are divisible by 2

e.- How do you identify a number divisible by 3? _______________________________________

f.- The number divisible by 6 must be divisible by _____ and _____, too

g.- The numbers end in ____________ and __________ are divisible by 5

h.- The numbers end in 0 are divisible by ______, ________, and _______

g.- What are the compound numbers?

i.- A number is divisible by 9 when ______________________________________
5.- Greatest common factor and Least common multiple (GCF and LCM)
Find the LCM of each set of numbers

{3, 7, 15, 25} LCM = _____________________ {7, 2} LCM = ______________________

{4, 6, 8} LCM = _____________________ {3, 15, 225} LCM = __________________

Find the GCF of each set of numbers :

{12,18} GCF = ____________________ {28, 42, 70} GCF = ________________

{36, 54, 90, 180} GCF = ___________________ { 16, 25, 75, 136} GCF = ______________

Solve problems

a.- Martin is pasting pieces of square coloured paper of equal size onto a board measuring 72 cm by 90 cm. If only whole square pieces are used, and the board is to be completely covered, find the largest possible length of the side of each square coloured paper.

b.- On a track for remote-controlled racing cars, racing car A completes the track in 28 seconds, while racing car B completes it in 24 seconds. If they both start at the same time, after how many seconds will they be side by side again? 

c.- Tim has a bag of 36 orange-flavoured sweets and Peter has a bag of 44 grape-flavoured sweets. They have to divide up the sweets into small trays with equal number of sweets; each tray containing either orange-flavoured or grape-flavoured sweets only. If there is no remainder, find the largest possible number of sweets in each tray. 
d.- Two wires with lengths of 448 cm and 616 cm are to be cut into pieces of all the same length without remainder. Find the greatest possible length of the pieces. 


e.- Janice and Jasmine were each given a piece of ribbon of equal length. Janice cuts her ribbons into equal lengths of 2 m, while Jasmine cuts her ribbons into equal lengths of 5 m. If there was no remainder in both cases, find the shortest possible length of ribbon given to them
f.- Mr. Brackett works in factory with his two sons. He is allowed to take a break every 140 minutes while his two sons are allowed to take breaks in 210 minutes and 280 minutes. How many minutes will they have to wait after their first break together to get together again?

g.- John, who is only 7, wants to be an architect when he grows up so his parents have built him a little shed in the backyard. Today he has some bricks with which he is planning to make his masterpiece! If his bricks have dimensions 10cm, 20cm and 25cm, what's the volume of the smallest cube (in cm3) he could build using these bricks?

i.- Mrs.Bell owns a small grocery store. She has just received 3 sacks of sugar weighing 27kg, 36kg and 72kg and she wants to put them in equal-sized bags before she sells them. What's the least number of bags she would need if she doesn't want any sugar to be left without a bag?

j.- Mrs.Flynn has baked 84 raisin cookies, 106 muffins and 128 chocolate chip cookies, which all smell delicious! They smell so good she would like to keep 4 raisin cookies, 6 muffins and 8 chocolate chip cookies for herself though she know she has to cut down on sweets. She'll then put the rest into boxes with equal numbers of each type. What would be the largest number of cookies or muffins in each box?

j.- Ms.Pearl is shopping at a supermarket. She is getting things for the sandwiches she is going to prepare for next Sunday's picnic. She sees that hamburger buns come in packs of 8 but the hamburgers themselves are in packages of 10. What's the least number of packets she should get of each so that there are no leftovers?

6.- Sequences:

a.- Find the following 8 terms to the following sequence:

2,6, 10, ____, ____, ______, _____, _____, _____, _____, _______

5, 15, 25, _____, _____, _____, _____, _____, _____, _____, _____

b.- Check the following sequence and answer the questions:

Draw the next two terms;

How many shaded ovals does the 8th. position have?

c.- Check if the sequence is arithmetical or geometric

2,4,6,8,10,……… ________________________

7,10,13,16,19, ……….. _____________________

1,3,9,27,81,……… _______________________

26, 21, 16, 11, 6,….. ______________________

64, 16, 4, 1 ……. _________________________

d.- Find the rule to each sequence:

3, 5, 7, 9, 11, ……… _____________________

45, 40, 35, 30, 25, ….. _______________________

16, 19, 22, 25, 28, ….. ______________________

2, 10, 18, 26, 34, …… _____________________

99, 89, 79, 69, 59, …..________________________

MATHEMATICS II

GUIDE EXAM

2ND. BIMONTHLY
1.- Solve multiplications

a) (9)(-5)(3) = _____________________

b) 17(-5)(-2)(-1) = _____________________

c) (1/2)(-1/5)(-2)(-1/3)(3/8) = ____________

d) (-7/10)(-2/7) = _____________________

e) 0.147(1.05)(-3.2) = ________________

2.- Solve divisions

a) -126/-3 = _____________________

b) 1275/-5 = _____________________

c) (-5/8) ÷ (-5/9) = _____________________

d) (-9/12) ÷ (-2/5) = _____________________

e) (- 2/10) ÷ (6/12) = ________________
3.- Express the multiplications or power in an extended form

a) 48 = _____________________

b) 198 = ______________________

c) (-5)2 = _____________________

d) k5n = _____________________

e) 5(14) = ____________________

4.- Solve operations using power rules

a) h8h3h25 = ______________________

b) m2q5 (m2q7) = ___________________

c) (-k)3 (-k)5 (-k)9 = ______________________

d) x5 y4 z2 / x3 y = _____________________

e) 4x3 y5 / -2xy = ____________________

f) -9m5n3 / -3m5n4 = ______________________

g) 40x16 / -10x16 = ___________________
5.- Solve problems using percentages

a) What is the 16% of 149?
b) Find the percentage represented by 52 in 2175
c) 20% of a number is 276, What is the number?
d) A dress costs with discount $ 1 325, if the discount was 18%, What was the real price of the dress?
e) A store offers 20% off in all items. How much money does a LCD TV cost, if its original price is $ 42,720?
f) A dancing school will send 15% of its students to a contest. If the school has 50 students, How many students will go?
g) Ruben is a football player, who has scored 20% of his shots on goal, if he has scored 8 goals until now, How many shots on goal did he do?
h) You buy a book with a 15% sales tax. You pay $ 9.95 in tax. What is the price of the book?
6.- Angles

a) Classify the pairs of angles as: corresponding, alternate interior, alternate exterior, collateral interior, collateral exterior, supplementary, verticals, or neither.
a-d = _______________________

a b d-h = _______________________

c d c-f = ________________________

b-g = ________________________

e f d-g = _________________________

g h a-g = ________________________

d-f = _________________________

h-f = _________________________


b) Find the measure to each angle in each angle system: Use 5x, 13x, etc, as degrees.
http://www.reocities.com/siliconvalley/lab/5648/imagenes/angulos1.jpg

7. Statistisc

Measures of central tendency:Mean, Mode and Median

Find the mean, mode and median to each problem

a) The following data correspond to a library and represent the number of books sold in a month

47- 22- 15- 13- 28- 39- 41- 43- 36- 24- 23- 17- 19- 21- 31- 35- 37- 41- 43- 47- 5- 12- 19

b) The number of goals for a football team during 26 games are: 2, 4, 6, 6, 4, 4, 5, 5, 4, 7, 3, 5, 4, 3, 3, 5, 6, 3, 4, 3, 4, 3, 4, 3, 2, 4.

c) The weight, in Kg,.of 20 students of a junior high school are: 51,47, 55, 53, 49, 47, 48, 50, 43, 60, 45, 54, 62, 57, 46, 49, 52, 42, 38, 61.

8.- Experimental Probability

a) There are 100 balls numbered from 0 to 99 in a box. A ball is picked up at random, find the probability that 7 is between its numbers.
b) There are 2 red balls, 4 green balls and 4 blue balls in a bag. A ball is picked up at random, what is the probability that the ball is not green.

c) Clarise did an experiment to find the probability to score a shot in a basketball game. Clarise scored 40 of 100 shots. What is the probability to score a shot?

d) If a card is tossed 40 times and 24 times a figure is upwards. What is the probability a figure is upwards?

e) Celia has a bag with 10 marbles. Some of them are blue and some are yellow. She picked a marble up 100 times, replacing the marble each time. If she picked a blue marble up 78 of 100 times, How many blue marbles are there the bag?

9.- Theoretical probability

a) In a class, there are 12 boys and 16 girls, is going to choose one to represent the students. What is the probability to choose a girl?

b) What is the probability to get a number greater than 3 when you rolling a dice?

c) What is the probability to get a red marble from a bag with 3 black marbles, 5 yellow and 2 red marbles?

10.- Areas and perimeters of compound figures

Find the area and perimeter of the following figures:






















5.-
13 cm


9 cm 5 cm

13 cm

7 cm

11.- Volumes prisms and pyramids

a) Find the weight of a cubic concrete block of 1.9 m by side. (a cubic meter of concrete weights 2350 kg)

b) How many small or medium sized fish can be introduce in an aquarium 88 long x 65 wide x 70 height cm? (It is recommended to introduce a fish by four liters of water)

c) The base of a prism is a regular hexagon 1.7 cm by side and its apothem is 1.5 cm. Find the volumen knowing the height is 3.9 cm.

d) The base of a pyramid is a regular pentagon 1.3 cm by side and its apothem is 0.9 cm. Find the volumen when its height is 2.7 cm.

e) The Pyramid of Giza, is 137 m height and its squared base is 230 m long. What is its volumen?

f) Find the weight of a silver bar of 19x4x3 cm. Density of the silver is 10,5 g/cm3.

g) A swimming pool is a rectangular prism 25m x 15m x 3m. How many liters of water are requiered to fill 4/5 of its total volume?

h) Find the height of regular hexagonal pyramid of 20 cm by side, apothem of 17.3cms and a volume of 7,266 cm3.

i) A triangular prism has a volume of 526.5 cm3, its height is 15 cm. Find the measures of its base that is an equilateral triangle 7.8 cm height.

MATEMATICAS II

GUIA EXAMEN

SEGUNDO BIMESTRE
1.- Resolver las multiplicaciones

a) (9)(-5)(3) = _____________________

b) 17(-5)(-2)(-1) = _____________________

c) (1/2)(-1/5)(-2)(-1/3)(3/8) = ____________

d) (-7/10)(-2/7) = _____________________

e) 0.147(1.05)(-3.2) = ________________

2.- Resolver las divisiones

a) -126/-3 = _____________________

b) 1275/-5 = _____________________

c) (-5/8) ÷ (-5/9) = _____________________

d) (-9/12) ÷ (-2/5) = _____________________

e) (- 2/10) ÷ (6/12) = ________________
3.- Expresar las multiplicaciones y potencias en forma extendida

a) 48 = _____________________

b) 198 = ______________________

c) (-5)2 = _____________________

d) k5n = _____________________

e) 5(14) = ___________________

4.- Resolver las operaciones utilizando las reglas de los exponentes

a) h8h3h25 = ______________________

b) m2q5 (m2q7) = ___________________

c) (-k)3 (-k)5 (-k)9 = ______________________

d) x5 y4 z2 / x3 y = _____________________

e) 4x3 y5 / -2xy = ____________________

f) -9m5n3 / -3m5n4 = ______________________

g) 40x16 / -10x16 = ___________________

5.- Resolver los problemas de porcentaje
a) Cuál es el 16% de 149?
b) Encontrar el porcentaje representado por 52 en 2175
c) El 20% de un número es 276, Cuál es ese número?
d) Un vestido cuesta con descuento $ 1 325, si el descuento fue del 18%, Cuál es el precio real del vestido?
e) Una tienda ofrece el 20% de descuento en todos sus artículos. Cuánto costará una Tv LCD, si su precio original es de $ 42,720?
f) Una escuela de danza enviará el15% de sus alumnos a un concurso. Si la escuela tiene 50 alumnos, A Cuántos alumnos enviará al concurso?
g) Rubén es un jugador de futbol, quien ha anotado el 20% de sus tiros a gol, si ha anotado 8 goles hasta hoy, Cuántos tiros a gol habrá hecho?
h) Compras un libro con 15% de impuesto sobre ventas. Si pagas $ 9.95 de impuesto. Cuál es el precio del libro?

6.- Angulos

a) Clasificar los pares de ángulos como: correspondientes, alternos internos, alternos externos, colaterales internos, colaterales externos, suplementarios, opuestos por el vértice o ninguno.
a-d = _______________________

a b d-h = _______________________

c d c-f = ________________________

b-g = ________________________

e f d-g = _________________________

g h a-g = ________________________

d-f = _________________________

h-f = _________________________


b) Encontrar la medida de cada ángulo en cada sistema de ángulos: Usar 5x, 13x, etc, como medidas en grados.
http://www.reocities.com/siliconvalley/lab/5648/imagenes/angulos1.jpg

7. Estadística

Medidas de tendencia central :Media, Moda y mediana

Encuentra la media, moda y mediana en cada problema

a) Los siguientes datos corresponden a una librería y representan el número de libros vendidos en un mes

47- 22- 15- 13- 28- 39- 41- 43- 36- 24- 23- 17- 19- 21- 31- 35- 37- 41- 43- 47- 5- 12- 19

b) El número de goles anotados por un equipo de futbol durante 26 juegos son: 2, 4, 6, 6, 4, 4, 5, 5, 4, 7, 3, 5, 4, 3, 3, 5, 6, 3, 4, 3, 4, 3, 4, 3, 2, 4.

c) El peso, in Kg,.de 20 estudiantes de secundaria son: 51,47, 55, 53, 49, 47, 48, 50, 43, 60, 45, 54, 62, 57, 46, 49, 52, 42, 38, 61.

8.- Probabilidad Experimental

a) Hay 100 bolas numeradas del 0 al 99 en una caja. Se saca una bola de manera aleatoris, encontrar la probabilidad que el 7 esté entre sus cifras.
b) Hay 2 bolas rojas, 4 bolas verdes y 4 bolas azules en una bolsa. Se saca una bola al azar, Cuál es la probabilidad que la bola No sea verde?

c) Clarise hizo un experimenmto para encontrar la probabilidad de anotar un tiro en un juego de basquetbol. Clarise anotó 40 de 100 tiros. Cuál es la probabilidad de anotar un tiro?

d) Si una carta de la baraja es lanzada 40 veces y 24 veces cae una figura hacia arriba. Cuál es la probabilidad de que una figura caiga hacia arriba al lanzar una carta?

e) Celia tiene una bolsa con 10 canicas.Algunas son azules y otras son amarillas. Si saca una canica 100 veces, volviéndola a regresar a la bolsa y saca una canica azul 78 of 100 times, Cuántas canicas azules habrá en la bolsa?

9.- Probabilidad Teorica

a) En unac clase hay 12 niños y 16 niñas, se va a escoger uno para representar a los estudiantes. Cuál es la probabilidad de que sea niñal?

b) Cuál es la probabilidad de sacar un número mayor a 3 cuando lanzas unn dado?

c) Cuál es la probabilidad de sacar una canica roja de una bolsa con 3 canicas negras, 5 amarillas y 2 rojas?

10.- Areas y perímetros de figures compuestas

Find the area and perimeter of the following figures:



a)

b)






c)

d)

e)
13 cm


9 cm 5 cm

13 cm

7 cm

11.- Volumenes de prismas y pirámides

a) Encontrar el peso de un bloque cúbico de concreto de1.9 m de lado. (un metro cúbico de concreto pesa 2350 kg)

b) Cuántos peces pequeños y medianos pueden ser depositados en una pecera de 88 largo x 65 ancho x 70 alto cm? (se recomienda introducir un pez por cada 4 lt de agua)

c) La base de un prisma es un hexágono regular de 1.7 cm de lado y apotema de 1.5 cm. Encontrar el volumen sabiendo que su altura es de 3.9 cm.

d) La base de una pirámide es un pentagon regular de 1.3 cm de lado y apotema de 0.9 cm. Encontrar el volumen cuando la altura de la pirámide es de 2.7 cm.

e) La Pirámide de Giza, tiene 137 m de altura y su base cuadrada mide 230 m de largo. Cuál es su volumen?

f) Encontrar el peso de un lingote de plata de 19x4x3 cm. La densidad de la plata es de 10,5 g/cm3.

g)Una alberca es un prisma rectangular de 25m x 15m x 3m. Cuántos litros de agua se necesitan para llenar 4/5 de su volumen total?

h) Encontrar la altura de una pirámide hexagonal de 20 cm de lado y apotema de 17.3cms si su volumen es de 7,266 cm3.

i) Un prisma triangular tiene un volumen de 526.5 cm3, su altura es de 15 cm. Encontrar las medidas de la base, si se trata de un triángulo equilátero con altura de 7.8 cm .

MATHEMATICS III

GUIDE EXAM

2nd. BIMONTHLY
1.- For each binomial , classify and find the product ( square binomial, common term binomial, conjugated binomial or neither)

1. (2x -3)2
2. (5x -4)2
3. (7x +5)2
4. (6x +3)2
5. (30x -1)2
6. (3x+ 4b) (3x - 4b)
7. (8x2 + 7) (8x2 - 7)
8. (9x9 - 10b6) (9x9 + 10b6)
9. (20x25 - 12b30) (20x25+ 12b30)
10. (0,5x2 +0,2 b2) (0,5x2 - 0,2b2)
11. (2x + 2) (2x + 3)
12. (3x + 9) (3x + 2)
13. (4x2 - 9) (4x2 - 6 )
14. (8x2 - 3) (8x2 - 7)
15. (5x3 + 12) (5x3 - 10)
16. (x − 2)(x + 2)

17. (a + 3)(a − 3)

18. (2x −5)(2x +5)

19. (3x + 2)2

20. (a +1)2

21. (6x −5y)2

22. (2a − 3)(a + 3)

23. (4x + 2)(x −5)

24 (5x − 2)(5x − 2)

25. (2x2 - 1)(3x2 - 3)

26. (7m2 - n )(3m – 2n )

2. Factoring

a) Find the factors of each product: First, identify the product as: difference of squares, perfect square trinomial, trinomial, polynomial with common term. Then factor the product.

1) x5 + 10x4 - 15x3;  

2)   y3 + 4y2 - y + 2

3)  x8 - 4x3

4)   ay3 + 2a4y2 - y + a

5)  16x6 - 4x3 + 12x2

6)   24a6y3 + 4a4y2 - 12a3y

7)   x2 + 2x – 15

8)  x2 - 4x + 3

9)   z2 + 2z – 4

10) x2 – 25

11)  y4 – 4

12)  4x2 – 9

13)  121 - 16z4

14)  x2 - 6x + 8

15)   y2 - 5y 

16) 81a2 – 225b4 

17) 121p4 – 144q8 

18) x2 + 14x +49 = 
19) x2 + 8x + 16 = 
20) x2 -22x +121= 
21) a6 – b6 = 
22) 16m4 – 25m2 + 9 = 
23) x5 – 40x3 + 144x = 


3.- Solve quadratic equations

a) Factoring and then solve and find the solutions (values of the variable or roots)

1) r2 – 5r + 6 = 0.

2) 5b2 + 4 = -12b

3) 2m2 + 10m = 48

4)   x2 + 2x – 15

5)  x2 - 4x + 3

6) x2 – 25

7)  y4 – 4

8)  4x2 – 9

9)  121 - 16z4

10)  x2 - 6x + 8

11) 81a2 – 225b4 

12) x2 + 14x +49

13) x2 + 8x + 16

14) x2 -22x +121

15) 1 – 2a2 + a4 

16) 16m4 – 25m2 + 9

17) x2+7x+10

18) x2-3x-40

4.- Solve problems using similarity of triangles

a) A man is 1.75 m tall and casts a shadow of 3.50 m, Find the measure of the shadow of a pole 8.25 m height?

b) A building 95 m height casts a shadow of 650 m, a man casts a shadow of 11.60 m long, find his heigh.

c) An antenna casts a shadow 50.4 m long and a pole 2.54 m height casts a shadow 4.21 m long. Find the antenna’s height

e) A tower casts a shadow 79.42 m long and a pole 3.05 m height casts a shadow 5.62 m long. How many meters is the tower height?

f) An antenna is 1.20 m height, another one, similar of it, is 5 times of the original. What is the measure of the bigger antenna?

5.- Similarity and congruence

a) Mention the three criteria of congruence

b) Mention the four criteria of similarity

c) What is the meaning of criteria of congruence?

d) Trace the triangles with the following information:

Angle A 56° -- side 8 cm -- angle B 87°. find the other measures and write what criteria of congruence is used

side A 7.5 cm – angle 65° -- side B 10.5. find the other measures and write what criteria of congruence is used

6.- Proportions and linear equations

a) Graph each equation, find three solutions for each one

1) y= 4x -5

2) y = 2/3x + 2

b) On which of the following lines does each point lie? A point may lie on more than one line. Match the point and the line(s)

Points Line

(0,0) y = x + 6

(3,9) y = x – 6

(-2,-1) y = 2x + 3

c) The table shows the relationship between the length of a rectangle (x) and its area (y), considering the width of the rectangle is always 3 cm. Complete the table and then draw the corresponding graph to represents the proportionality

Length (x) (cm)

Area (y) (cm2)

0

0

1

3

2

6

3




4




5




6




7.- Probability

a) The table below shows the City Cinema´s menu. You order popcorn and lemonade. Draw a tree diagram to show the sample space.

Popcorn

$

Lemonade

$

Small

3.00

Small

2.75

Medium

4.00

Medium

3.00

Large

5.00

Large

3.25







Jumbo

3.75



b) A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either 7 or 11?

c) A pair of dice is rolled. What is the probability that the sum of the numbers rolled is either an even number or a multiple of 3?

d) The probability that a student passes Mathematics is 2/3​​ and the probability that he passes English is 4/9 . If the probability that he will pass at least one subject is 4/5​​ , what is the probability that he will pass both subjects?

e) A box contains 100 items of which 4 are defective. Two items are chosen at random from the box. What is the probability of selecting

P( 2 defectives if the first item is not replaced)

P( 2 defectives if the first item is put back before choosing the second item)

P(1 defective and 1 non-defective if the first item is not replaced)

f) A deck of card contains 52 cards, if you select a card, find the following probabilities:

P( king and hearts)

P( queen and king)

P( black and 10)

P( hearts and black)

P(queen or 2’s)

P( red or any number)

8.- Pythagorean Theorem

a) The following measures correspond to four different triangles, classify them as ; acute, obtuse or right:

a) 22 b) 17 c) 10

a) 37 b) 35 c) 12

a) 61 b) 60 c) 11

a) 42 b) 31 c) 30
b) A wooden pole is 8m height, three steel wires are located from its top to the floor, 3m from the base of the pole. How many meters of steel wire are required?
c) A ladder 10 m long, is leaning against the wall. The bottom of the ladder is 6 m from its base of the wall. What is the altitude of the ladder over the wall?
d) Find the side of an equilateral triangle with a perimeter equal to a square 12 cm by side. Are the areas equal?
e) Find the area of an inscribed equilateral triangle in a circumference 6 cm of the radius.
f) Determine the area of an inscribed square in a circumference that is 18.84 m. long
g) The perimeter of an isosceles trapezoid is 110 m, the bases are 40 y 30 m. Find the measures of not parallel sides y its area.
h) A carpenter does rectangular wooden frames for windows, to avoid deformations, he adds a diagonal, in the back of the frame, 2m long and the frame is 1.2m height. What is the width of the frame?
i) A balloon is attached to the floor by a rope.Yesterday, without wind, the balloon was 50m from the floor. Today, a windy day, the balloon attached to the floor, yet, has moved 30m in the air, from the place where is attached. What is the altitude of the balloon today?



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