TAREAS DE VERANO

MATERIA Y OPCIÓN: MATEMÁTICAS 2º ESO BILINGÜE

NOMBRE DEL ALUMNO:CURSO:

LA REALIZACIÓN DE ESTAS TAREAS ES OBLIGATORIA.SI NO SE ENTREGAN EN LA FECHA DE LA PRUEBA O SU CALIFICACIÓN

ES INSUFICIENTE LA EVALUACIÓN EXTRAORDINARIA DE SEPTIEMBRE SE CONSIDERARÁ ABANDONADA.

Unit 1: Integers1. Calculate:

a) 10 – 3 + 5 =

b) 5 – 8 + 6 =

c) 2 – 9 + 1=

d) 7 – 15 + 2 =

e) 16 – 4 – 6 =

f) 9 – 8 – 7 =

g) 15 – 12 + 6 =

h) – 3 + 10 – 1 =

i) – 8 + 2 – 3 =

j) – 5 + 6 + 4 =

k) – 18 + 3 + 6 =

l) – 2 – 13 – 5 =

2. Calculate

a) 3 – 7 + 2 – 5 =

b) 2 – 6 + 9 – 3 + 4 =

c) 7 – 10 – 5 + 4 + 6 – 1 =

d) – 6 + 4 – 3 – 2 – 8 + 5 =

e) 12 + 5 – 17 – 11 + 20 – 13 =

f) 16 – 22 + 24 – 31 + 12 – 15 =

3. Take out brakets and y calculate

a) (–3) – (+4) – (–8) =

b) (+8) – (+6) + (–7) – (–4) =

4. Calculate

a) 9 – (20 – 6) =

b) 15 – (6 – 19 + 5) =

c) 21 – (3 – 10 + 11 – 6) =

5. Calculate

a) 7 – [1 + (9 – 13)] =

b) – 9 – [8 – (13 – 4)] + 9 =

c) 2 + [6 – (4 – 2 + 9)] =

d) 15 – [9 – (5 – 11 + 7) =

e) (2 – 9) – [5 + (8 – 12) – 7] =

f) 13 – [15 – (6 – 8) + (5 – 9) =

g) [4 + (6 – 9 – 13)] – [5 – (8 + 2 –

18)] =

6. Calculate

a) 6 – 10 : 2 – 14 : 7 =

b) 7 · 3 – 5 · 4 + 18 : 6 =

c) 5 · (– 8) – (+ 9) · 4 =

d) 32 : (– 8) – (– 20) : 5 =

e) (– 2) · (– 9) + (– 5) · (+4) =

f) (+ 6) · (– 7) + (– 50) : (–2) =

2

g) 18 – 5 · (3 – 8) =

h) 11 – 40 : (–8) =

i) 4 · (8 – 11) – 6 · (7 – 9) =

j) (4 – 5) · (–3) – (8 – 2) : (–3) =

7. Calculate

a) 15 + 2 · [8 – 3 · 5] =

b) (–3) · (+5) – 3 · [11 + 3 · (5 – 11)] =

c) 28 : (–7) – (–6) · [23 – 5 · (9 – 4)] =

d) (–2) · (7 – 11) – [12 – (6 – 8)] : (–7) =

8. Calculate as a power

a) 152 · 153 =

b) 122 ·123 · 122 =

c) 66 · 62 =

d) 92 · 94 · 9 =

e) 66 · 46 =

f) 94 : 93 =

g) 274 : 94 =

h) 127 : 124 =

i) (32)2 =

j) (82)3 =

k) (3 · 5)2 =

l) (3 · 2 · 1)3 =

9. Calculate as a power

a) (–3)2 =

b) (–6)3 =

c) (–53)2 =

d) (–52)4 =

e) (–3)4 · (–3)3 =

f) (–8)3 : (–8)2 =

g) (–5)2 · (–5)4 =

h)

i)

10. Calculate

a)

b)

4

c) Unit 2 Fractions

1. Check if the following fractions are equivalent.

(Note: If you get the simplest form of a fraction, maybe all the operations will be easier.)

a. y b. y

2. Sort the following fractions, use the signs <, > o =.

, , , , ,

3. Write an equivalent fraction of whose denominator is 20.

4. Calculate:

a.

b.

c.

d.

e.

f.

g.

h.

i.

5. Write the following powers as a fraction

6. A group of students went to a fast food restaurant. of them bought a beef burger and of

them bought a chicken burger. The rest of them just bought drinks. What fraction of the

group bought drinks?

7. Joan earns £1800 a month. She spends of her salary every month. She gives her parents

of the remainder and saves the rest. How much money does she save every month?

8. In a cafetería, in the morning, it has been sold half of the prepared sandwiches and in the

afternoon, one-third of the remaining snacks. If at the end of the day there were four

sandwiches.

a.How many sandwiches have been prepared?

b.How many sandwiches have been sold in the morning? And in the afternoon?

6

Unit 3: Decimal numbers

1. Write each of the following as a decimal

a.

b.

c.

d.

2. Write each of the following as a fraction

a. 23,45 =

b. 98,003 =

c. 0,04 =

d. 0,00233 =

3. Round 8,9463 kilograms to:

a. one decimal place

b. two decimal places

c. three decimal places

d. the nearest gram

4. Classify the following decimal numbers without doing the division

a.

b.

c.

d.

e.

f.

5. Classify the following decimal numbers

a) 0,831313131…….

b)

c)

d) 0,25

e) 0,2525

f) 4,0404444444……

6. Roberto goes to the market with 62.81€ and buys 2.6kg grapes at 1.80€ each kg. 0.58Kg

bananas at 2.15€ per kg, a hake (merluza) that weighs 850g and costs 11.45€ each Kg, and a

chicken of 1.25Kg, that costs 5.95€ per Kg.

How much has he spent? How much does he have left?

7. Complete. Write all the operations

a. 15% of 125 = ___ b. ___% of 240 = 108 c. 32% of ____ = 450

8. Work out in one operation:

a. Decrease 246 by 20 % b. Increase £1,270 by 25 %

9. Calculate the percentage increase/decrease in each of the following cases:

a. A bus fare of 40p is now 50p. b. A train fare of 60p is now 42p.

10. In a town of 60,000 people, 65% own terrace houses. How many people own terrace houses?

11. Mr. Smith bought a basket of 30 plants. 12 of the plants were spoilt. What percentage of the

plants were not spoilt?

12. Mrs. Warren spends 12% of its salary on petrol, that is 135€ . How much does she earn in a

month?

13. In a class of 40 pupils, 4 failed the physical fitness test. What percentage of the class failed

the test?

14. An alloy consists of 2.5 kg of zinc and 4 kg of tin. What percentage of the alloy is made of

tin?

15. A watch is priced in a catalogue at £ 198 but the dealer offers a 15% discount to the

purchaser. Find the actual amount of money paid

16. The cost of some building materials is £ 64.80 plus VAT. VAT is charged at 21%. What is

the total cost?

17. Ten years ago, a town had a population of 12,250. Now, the population of the town is

13,965. Find the percentage increase in the population of the town.

18. A second-hand car dealer bought a second-hand car and spent £650 on repairs. He sold the

car for £18,650, gaining 20% on the purchase price. For how much did he buy it?

19. By selling a particular set of books for £408, a bookseller suffers a loss of 4%. Find the cost

price of the books. What is the percentage gain or loss if the books are sold for £ 510?

20. A television has a sale price of £180. This is a saving of 25% on the original price. What was

the original price?

Unit 5: Algebra

1. Use an algebraic expresión for the following sentences.

a. The double of a number is__________________________________________________

b. The half of a number is____________________________________________________

c. The sum of two different numbers is_________________________________________

d. The square of a number is__________________________________________________

e. The square of a number, decremented by 25 is__________________________________

f. The following number of p_________________________________________________

g. The square of a number plus the square of another number________________________

h. Twice of x minus y plus 1__________________________________________________

i. Fifty divided by two times a number_________________________________________

j. seven times y squared_____________________________________________________

2. Complete the table

a b Algebraic expresion Value2 3-1 53 -4-4 2

3. Try to write an algebraic expresion that describes the following real situation

a. Imagine you work as a ticket saler in a cinema, you boss has told you that each ticket cost

4€. Write an algebraic expresion to show the cost of some amount of tickets.

b. In your electricity bill you will fin that the bill is divided in two parts. A fix amount that

doesn´t depend on the amount of electricity you spend and another part that depends in the

kilowatts you use. The fixed part is 12€ and one kilowatts is 0,35€. Write an algebraic

expresion to describe all the electricity bills.

Monomios

4. Complete the table

Monomial Coeficient Literal Part Grade

5. Calculate:

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.

l.

m.

n.

o.

6. Calculate

a.

b.

c.

d.

e.

f.

7. Expand the brackets

a.

b.

c.

d.

Unit 6: Equations

1. For the following equation . Which of the following values is a solution?

e. x = - 3

f. x = 0

g. None of the above

h. x = 18

2. Which of the following algebraic expressions is an equation and what is an identity?

a. b.

c. d.

3. Solve

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

4. Solve

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

5. Sari and her friends are going to play miniature golf. There are p people in the group. Each

person pays €5 for a round of golf and together they spend €9 on snacks. Write an

expression that represents the total amount that Sari and her friends spent.

6. At the Beltway Outlet store, you buy x computer games for $13 each and a magazine for

$4. Write an expression in simplest form that represents the total amount of money you

spend.

7. There are 31 people in a café. There are 5 more men than women. How many men and how

many women are there?

8. On a farm, the horns (cuernos) and legs of the cows add up to 30. How many cows are

there on the farm?

9. Juana bought two pens and a marker for a total of €5. What was the price of each item if a

marker costs fifty cents more than a pen?

10. The base of a rectangle is three centimetres longer than its height. Its perimeter is 38 cm.

What are the dimensions of the rectangle?

11. Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did

each pencil cost?

12. Sumalee won 40 super bouncy balls playing horseshoes at her school's game night. Later,

she gave two to each of her friends. She only has 8 remaining. How many friends does she

have?

13. Solve the following quadratic equation

k.

l.

m.

n.

o.

Unit 7: System of Equations

1. For the following system of equations . Which of the following values is a

solution?

i. x = - 3, y = 0

j. x = 5, y= -6

k. None of the above

l. x = 2, y=- 2

2. Fill, so the solution is x=3, y=-2

3. Calculate

a.

b.

c.

d.

e.

f.

4. A hotel has double rooms and single rooms. In total there are 90 rooms and 165 beds. How

many rooms are of each type?

5. A school canteen has tables that seat 6 people and tables that seat 4 people. There are 20

tables in total, and together they offer enough seating for 104 students. How many tables of

each type are there?

6. The sum of two numbers is 30. Three times the first number added to twice the second

number is 64. Find the numbers.

Unit 8: Functions

1. Write down the coordinates of each place on the map of the island

2. In the chart bellow you can see the height of a small plane during its three hours flight.

a. How long does it remain stable? At what height?

b. How long does it take to stabilize the height?

c. When does it reach its maximum? How high is it?

d. Make a brief summary of the evolution of the height of the plane since it takes off

until its landing.

3. The relationship can be used to convert temperatures in degrees Celsius,

ºC, to temperatures in degrees Fahrenheit, ºF.

a. Complete the table below:

Temperature in ºCelsius 0 20 100Temperature in ºFahrenheit

b. Use the information in the table to draw a graph of .

c. The recommended temperature for a greenhouse is 80ºF. Use your graph to

convert this to ºCelsius.

4. For the following functions, construct a table of values, a graph, express them using a

sentence:

a.

b.

5. Say if they are a function and explain why:

6. Which of the following pairs of variables are a function

a. The weight of a person and their height

b. The weight of a barrel and the amount of liquid it contains.

c. The length of the side of a regular polygon and its perimeter.

d. The grade in a test and the number of hours used in your study.

e. The number of workers and the time it takes to finish a job.

7. Indicates which of these functions should be represented by a continuous graph and which

one by a discontinuous graph:

a. Cost of the car park based on the time that has remained in it.

b. Space traveled as a function of time.

c. Temperature as a function of time of day.

d. Height of a person according to his age.

8. Write the characteristics of this function:

Unit 9: Linear Functions

14. Complete the following pairs of coordinates using the relationship .

a.

b. Plot the points on a set of axes.

c. Draw a straight line through these points.

15. Complete the following pairs of coordinates using the relationship .

a.

b. Plot the points on a set of axes.

c. Draw a straight line through these points.

16. Calculate the intercept points of the function

17. Calculate the intercept points of the function

18. Which of the following functions are linear and which not?

a.

b.

c.

d.

19. Which of the following lines have a posittive slope and which have a negativa slope?

Calculate the slope of each of these lines

20. Draw the graph of

a.

b.

c.

d.

21. Get the equation of the functions from the following graph

22. Determinate the equation of the function from the following table

x y-2 -1-1 10 31 52 7

23. Complete the following table

Equation Slope Intercept

8

7· 2

24. We can buy three pounds of squid at the market for 18€. Determine the equation and

represent the function that defines the cost of squid based on weight.A.

25. A car rental charge is 100€ deposit and 0,30€ per mile travelled. Determine the equation

of the line that represents the cost by the number of miles travelled and graph it. If a total

of 300 miles was travelled, how much is the rental company going to receive as payment?

Unit 10: Geometry

1. Find the perimeter of each shape below:

2. Louise does a sponsored bicycle ride. Each wheel of her bike is of radios 25 cm.

a. Calculate the circumference of one of the wheels.

b. She cycles 50 km. How many revolutions does a wheel make during the sponsored

ride?

3. Find the area of each shape:

4. You have a small marble statue of Wolfgang Mozart that is 4 dm tall. The original statue

in Vienna is 2 m tall.

a. What is the similarity ratio?

b. The width of your statue is 40 cm, what is the real width?

c. What is the surface ratio between the two statues?

d. Your statue has a volume of 2.4 dm3. Estimate the volume of the original statue.

5. A map has a scale of 1:80 000 000. What real distances are represented by 1 cm on the

map? And by 4.8 cm? What is the real surface of a 1cm2 square?

6. In a right triangle with hypotenuse c and legs a and b,

a) Find c if a=5 and b=12

b) Find a if b=8 and c=12

c)

7. A rectangle has base 6 and height 10. What is the length of the diagonal?

8. The diagonals of a rhombus have lengths 6 and 8. Find the length of one side of the

rhombus.

9. There is a building with a 12 ft high window. You want to use a ladder to go up to the

window, and you decide to keep the ladder 5 ft away from the building to have a good

slant. How long should the ladder be?

10. Work out the height of an equilateral triangle whose sides are 6cm long.