Download Number of letters 1 2 3 4 5 6 7 8 9 10 11 12 13

Holiday homework 3rd year
1)
Write those expressions as a power (as simple as possible):
(72)5=
75:72=
60·24·8·4=
32·27·3·33=
72·73·70·75=
53·25·52·125=
(82)3=
(-81)3:93=
(-27)2:(-9)2=
2)
In a farm 16 rabbits are fed for 12 days with 100 kg carrots. For how many days can 6 rabbits be fed
with 100 kg carrots?
3)
Multiply
x
5

 x 3  x 2  6x  7  x 2  2

4)
A storm breaks a tree 12 m high. The top of the tree touches floor 8 m far from its bottom. Find out the
height at which the tree broke.
5)
A medicine is to be taken at a reason of 0.25 g per kg of the patient’s weight till a maximum of 15 g.
Plot the graph of the function that relates the “patient’s weight” and the “dose” making a table of values before.
6)
At a road speed control the following data were obtained:
Speed
number of cars
60-70
5
70-80
15
80-90
27
90-100
38
100-110
23
110-120
17
Make a table of frequency defining a central value for each class; then, calculate all the measures of central
tendency and all the measures of spread you have studied. Finally, answer the following question: what is the
percenteage of cars run faster than 90 km per hour?
7)
A tobacco shop, after having sold 3/8 of the whole stock of cigarettes, has got 5 555 packets of
cigarettes left. How many packets of cigarettes had the shop at the beginning?
8)
Calculate:
110% of 2980
8,5% of 250
9)
Write the number 133 as a sum of two quantities such that one of them divided by the other one gives 4
as quotient and 8 as remainder.
10)
Draw the following parabolas on a cartesian coordinate system and study their curvature, intercept
points and vertices:
y  x 2  6x  5
y  2 x 2  10 x  8
(-0’15)2=
(0’01)4=
11)
Calculate these powers changing their bases into fractions first:
12)
If 15 litres of water become 16 litres ice, how much volume will 2 m3 water have once it is frozen?
13)
Do the following divisions and then check the results:
a) ( x 3 + 4x2 + 6 ) :(x - 4 )
b) (6x4–x3–5x2+3x–4) :(2x2–x–5)
14)
Tell if these triangles are right angled according to the length of their sides, and calculate their area:
49 m, 18 m and 52 m.
44 cm, 17 cm and 39 cm.
Page 1 of 6
Holiday homework 3rd year
15)
Complete the table that relates the legth of the basis (x) and the height (y) of rectangles whose surface is
2
24 cm . Express this function by means of a formula.
16)
These data are the weekly time a group of students usually spent studying (in hours):
14
9
9
20
18
12
14
6
14
8
15
10
18
20
7
18
8
12
10
20
16
18
15
24
10
12
25
24
10
4
8
20
10
12
16
5
4
13
Put these data into intervals: 1.5-6.5
6.5-11.5
11.5-16.5
16.5-21.5
21.5-26.5
Make a table of frequency.
Calculate the mean and the standard deviation.
2
17
17)
It takes 3 hours to a couple of men to finish a work. If it would take 4 hours to the first man to do the job
by himself, how many hours would it take to the second man?
18)
Calculate the percenteage that represents:
96 in 480
16 in 320
19)
 x  3 y  2
Solve using algebra and plot the lines of these pair of simultaneous equations : 
 2 x  y  29
20)
Find two consecutive numbers such that if the bigger one is added to the half part of the smaller one, the
outcome is 13 units greater than the sum of the fifth part of the smaller one and the eleventh part of the bigger
one.
21)
Change into fractions:

5,3
5,32
0,051
327,41331
22)
A tap that pours 5 litres per minute fills a tank in 30 minutes. Calculate the flow of another tap that fills
the same tank in 40 minutes.
23)
Simplify this expression:
Simplify this expression:
Simplify this expression:
24)
Calculate:
(3x–1)2
(x+4)2
(3x+1)(3x–1)
a) The sides of a square whose diagonal is known to be 24 cm long
b) The length of the diagonal of a rectangle whose sides are 4 cm and 5 cm long
25)
A spring 4 dm long hangs from the ceiling. If we put some weight on it, the spring gets longer
proportionally to the amount of the hunged weight. A 2 kg weight makes the spring get 3 dm longer, reaching 7
dm long. Write an equation for the function “hunged weight spring’s lenght” and represent its graph.
26)
The number of letters that each word from a article has were counted. The article had 128 words.
Calculate the mean and the standard deviation; now answer: how many words have a number of letters between
x   and x   ? What percenteage of the total number of words are they?
Number of letters 1 2
3
4
5
6
7
8
9
10
11
12
13
Number of words 4 36
14
9
15
7
6
9
7
8
6
4
3
27)
Tell the integer numbers, the natural numbers, and numbers that are none integer none natural

3
-7
-20
2
1/5
4/2
0’56 13
'
16
5
28)
There was 340 hl water in a reservoir. This summer, the amount of water decreased a 43 %. How much
water is there in the reservoir now?
Page 2 of 6
Holiday homework 3rd year
29)
Solve the following pair of simultaneous equations (find the value of the unknowns “x” and “y”, and use
 x  y 1

all the three methods you have studied) (a substitution, an elimination and “equalization”):
 2x  3y  5
 5
4
30)
In the right-angled triangles below, the hypothenuse and a short side are known. Calculate the other
short side:
37 cm and 45 cm
15 cm and 39 cm.
31)
Do these operations without a calculator:
2 :1 (-2 · 454)0 + 2  : 41 =
4 - 8 : (-2 · 4)3 + 2  : 4-1 =
32)
While building a highway, 20 trucks that work 8 hours a day can dump 4 dam3 soil a day. How much
soil a day can 12 trucks dump if they work 10 hours a day?
33)
Write as a product of factors: x 3  4 x 2  4 x  16
3
2
Write as a product of factors: x  6 x  9 x  54
34)
Calculate the area and the perimeter of:
A rectangle with a basis 5 m length and a diagonal 17 m length
A romboid with a short side 15 m length, long side 24 m length and projection of the first over the
second 12 m length
35)
Draw the graph correspondent to the following data:
a) When x=0, y=10
b) The function is increasing from x=0 to x=6
c) The function has a local minimum at point (6,3)
d) The function is increasing from x=6 to x=8
e) When x=8, y=7
f) The function is constant from x=8 to x=12, being y=7
g) The function is decreasing from x=12 to x=15
h) When x=15, y=0
36)
The monthly expenses of company “A” have a mean of 60 000 € and a standard deviation of 7 500 €
The expenses of company “B” have a mean of 9 000 and a standard deviation of 1 500 €.

Calculate the coefficient of variation
of both companies to decide which of them has a major relative
x
variability.
37)
Solve without using a calculator:
2
 a  b 2   a 2  b1 

3
a 2  b 3

 
 b2  a 2
2
 3  2  3 
   :   
 2   4 
x
 0'1   
 9 7  1  1  2 
 5 4 1  2  1  3 
:


   

    :  
 7 9   7  
 2 3 6   2  
5
3
8 7 
 3
1  1:    :   3 
 4
5 2 
1

3
2 3
2
 y3
   x  y : x
1
2
1
2
2
3 
  3   
5
4 
2
2
 
3
  2 33 

 
9


2
2:
2 
1 
  1    1
3 
5 
1
5
y

3

2

1
1
 1 2 
    1  
 3 5 
2
3

Page 3 of 6
Holiday homework 3rd year
38)
A sort of shares were 7,85 € worth at the beginning of this year, but their value was increased in a 120%
How much are they worth now?
39)
Today, a son’s age is the fifth part of his father’s age. In a 7 year’s time, the father’s age will be three
times his son’s age. Calculate both ages at present time.
40)
A pond contains 28 600 litres water for irrigation. The sink and a tap are open at the same time. The sink
pours off 360 l/min and the tap pours in 140 l/min. How much does it take to empty the pond?
41)
Do these operations without a calculator. The outcome must be an integer number or a fraction:
3
1
  
5
2
 
3
2

 3
 
 4
2
 32 

2
4
 3
  
 2
 1
  
 3
 1
 
 2
1

 21 
42)
Three partners invested respectively 2, 3 and 6 million euros to create a company. Which part of the
profit should each partner get? If the first year’s profit was 75 900 €, how much money corresponds to each
one?
43)
Solve this equation: x–4 = 1–4x
44)
Mark owns a field of rectangular shape, 280 m long.and 210 m. width. He has risen a fence along the
field diagonal. How many metres of fence did Mark need?
45)
Plot the graphs:
5
y x
yx
3
y  3x  2
y
y  3  2x
2
x5
3
y  2
46)
How much does a 100 000 € capital become when put to a 0,3% monthly interest for 3 years long
(compound interest)?
47)
Calculate the value of the following expression without a calculator. The outcome must be an integer
number or a fraction:
4
 3
2 
2
  8 1

 2  4  : 1  3   2   1  3  1  5 
 


 



2
 3  2  3 
   :  
 2   4 
3
5
48)
After the delivery of 27% of the boxes a store has inside, 38690 boxes still remained there How many
boxes there were at first?
49)
Express as a single decimal number of degrees the following angles :
a) 30º 21´50”
b) 15º 10’ 5”
50)
A cooperative has at its disposal three silos where to store wheat. The first silo contains 1/5 of the total
wheat, the second one contains 2/5 of the total and the third one contains 52 000 kg. Calculate how many kg
does each silo contain and the total amount of stored wheat.
51)
Solve without a calculator. The outcome must be written as an integer number or a fraction:
2
2
5 3
  
8 4
 4 :  4
5
5
3
1 1 1 1
       
2 2 2 2
3




2
3
2
1
 3 5
     
2
 2  3
3
2
7 7
  :  
5 5
 1 
 3 
 1  3  6 

     5 
 3   5 

3 2
4 3

4

Page 4 of 6
Holiday homework 3rd year
52)
Share out 17 camels proportionally to 1/2, 1/3 e 1/9
53)
Solve this equation (find the value of “x”): 3(2x – 6) – x – (3x – 8) + 1=2 – (3 – 2x)
54)
A table in the shape of a rectangle is 0,8 m wide and 1,2 m long. What is its area? How much does it
cost to varnish the table if the product price is 45 € per m2?
55)
Say how much is the slope of each one of the lines below:
y  2x  5
y  x  5
y5
56)
Operate the following surds:
57)
Simplify the surds by writing the rooted as a product of factors if necessary:
3
8
3
1000
2x  y  1  0
2
3
5
192


 63 
15 14 48
9
4
16
81  a 6  b5  c8
27a 6
58)
A tradesman increases the price of his products in a 40% and afterwards, trying to bring them back to
the original price, he decreases the prices in a 40%. Write the price of a jacket that was initially worth 100 € at
each stage of the process. How much is the percenteage change of any product with respect to its original price?
59) Express in degrees, minutes and seconds the following angles:
a) 42,41º
b) 37,111º
60)
Find out the hypothenuse in the following right-angled triangles (the short sides are giver):
37 cm and 45 cm
16 cm and 30 cm
61)
Operate without a calculator. Leave the outcome as an integer number or a fraction:
8 2 4 4 7 3 2
3 2 2 5 1 3
 :   :  
 : 
 : 4
5 5 5 3 3 4 7
5 3 5 21 5 4
62)
If you mix 12 kg coffee worth 12,40 €/kg and 8 kg coffee worth 7,40€/kg How much is a kg of mixture
worth?
2 x  5 52 x  3 35 x  2
5


63)
Solve this equation(find out the value of “x”):
4
3
2
64)
Calculate the area of a circle bordered by a circumference 230 cm long.
65)
Write the equation of the line that goes throug point P(5 , –2) with a slope of m = – 4
67)
Calculate the following root without using a calculator, using factoring and fractions:
0'0009:081
'
6'25:0'01
68)
A 28 000 € capital is put under an interest of 10% per year. How much will it become after 3 years
(simple interest)?
69)
Given the angles : Â = 80º 27´ 50” and B̂ = 42º 56”, find out its sum, its difference and also 2 Â –3 B̂
70)
Write the equation of a line that intercepts points P(4 , –2) and Q(6 , –3)
Page 5 of 6
71)
Holiday homework 3rd year
Solve without a calculator. The result must be an integer number or a fraction:
1 1  1 1 
35 1 4  3 1
 1 1 
3  4       3 :  :  
     
8  3 2  11  4 5 
 3 2 
3 2  4 5 
 1 1  1 1     3 
 1 1  1 1 
 3 
      5  3 4 :  1 
 3  2  2  4   5  34 :  5  1 
 3 2  2 4 
 5 

   


1 2 2 
  3 
3  4 3 
4 
 
3 

2   1  1 4 2 
 :
   3
5   2 4 3 4 
72)
A barrel contains 1 hl of wine with high-alcohol content, worth 3.60 €/l. Then, 20 l of water are added to
it in order to low down its alcohol content. How much is the price of the wine now?
73)
Solve this equation: 14 x 2  5 x 
3
0
7
74)
Calculate the area of an isosceles triangle with a basis 6 cm long (not equal side) and the two equal sides
4 cm long.
75)
Calculate the slopes of the lines that pass through these pairs of points:
a) (3 , 1) and (7 , 5)
b) (3 , 5) and (7 , - 2)
76)
Solve this equation: 24x + 9 = –16x2
77)
Find the following surds’ value:
1  6  5  16
2  5 4  64
78)
How much does a 100 000 € capital become if it is put to a 3.6% yearly interest for 3 years long
(compound interest)?
79)
Complete the table:
ANGLE
COMPLEMENTARY ANGLE
SUPLEMENTARY ANGLE
40º 15’ 18”
36º 10’
120º 42’ 30”
80)
A car moves at a speed of 120 km/h and a truck moves at a speed of 90 km/h. If the car is 75 km far
from the truck and runs after it, how long will it take to the car to catch the truck? If they are separated by a
distance of 504 km and move one towards the other, how long will it take them to meet?
81)
Calculate the value of the expression below without using a calculator. Leave the result as an integer
number or a fraction:
 2 7   2 1  2
2
1 
 5    1
 3  4  :  7  5   9
5
 


2 


5
13
2
4
Page 6 of 6