Testi I MaturËs-matematikË E PËrgjitshme

1. Është dhënë bashkësia

A equals open curly brackets x element of R space d h e space x space n u m ë r space ç i f t space close curly brackets. space

Cili nga gjykimet e dhëna është i saktë?

not-available-via-ai

Explanation

not-available-via-ai

2. Nëse vlenë barazimi

a over b equals 4 over 3

, atëherë sa është

fraction numerator a plus b over denominator a end fraction

?

not-available-via-ai

Explanation

not-available-via-ai

3. Numri i koshave që ka shënuar një ekip basketbolli gjatë 7 ndeshjeve është: 91,102,87,93,99,91,86. Cila është moda e tyre ?

87

91

99

102

The mode is the value that appears most frequently in a set of data. In this case, the set of data is the number of points scored by a basketball team in 7 games. The given numbers are: 91, 102, 87, 93, 99, 91, 86. Among these numbers, the number 91 appears twice, which is more frequently than any other number. Therefore, the mode of the data set is 91.

Explanation

The mode is the value that appears most frequently in a set of data. In this case, the set of data is the number of points scored by a basketball team in 7 games. The given numbers are: 91, 102, 87, 93, 99, 91, 86. Among these numbers, the number 91 appears twice, which is more frequently than any other number. Therefore, the mode of the data set is 91.

4. Luli dhe Blerta duan të ndajnë një shumë të hollash në raport 3:5. Nëse Blertës i takojnë 60 euro, atëherë sa para i takojnë Lulit?

12€

24€

36€

48€

Luli and Blerta want to divide a sum of money in a ratio of 3:5. If Blerta has 60 euros, then Luli would have 3/5 of that amount. To find out how much money Luli has, we can calculate 3/5 of 60 euros, which is 36 euros. Therefore, Luli would have 36 euros.

Explanation

Luli and Blerta want to divide a sum of money in a ratio of 3:5. If Blerta has 60 euros, then Luli would have 3/5 of that amount. To find out how much money Luli has, we can calculate 3/5 of 60 euros, which is 36 euros. Therefore, Luli would have 36 euros.

5. Diagonalja e një katrori është

d equals square root of 2 space c m

. Nëse diagonalja zvogëlohet pesë herë, për sa centimetra do të zvogëlohet perimetri i katrorit?

për dy herë

për tri herë

për katër herë

për pesë herë

When the diagonal of a square is reduced by a factor of 5, the sides of the square will also be reduced by the same factor. Since the perimeter of a square is the sum of all its sides, if each side is reduced by a factor of 5, the perimeter will also be reduced by the same factor. Therefore, the perimeter will be reduced by 5 times.

Explanation

When the diagonal of a square is reduced by a factor of 5, the sides of the square will also be reduced by the same factor. Since the perimeter of a square is the sum of all its sides, if each side is reduced by a factor of 5, the perimeter will also be reduced by the same factor. Therefore, the perimeter will be reduced by 5 times.

6. Një lokal ka syprinën

72 space m squared

, i cili rritet edhe për 25%, atëherë sa

m squared

do të ketë lokali ?

The local will have a 25% increase in size.

Explanation

The local will have a 25% increase in size.

7. Zgjidhja e ekuacionit iracional

3 square root of x minus 3 end root equals square root of 2 x minus 6 end root

është :

not-available-via-ai

Explanation

not-available-via-ai

8. Çdo vektorë

a with rightwards arrow on top

përcaktohet me :

intensitetin dhe drejtimin

Intensitetin dhe kahun

kahun dhe drejtimin

intensitetin, drejtimin dhe kahun

A vector is characterized by its magnitude (intensity), direction, and orientation (angle). Therefore, a vector is described by its intensity, direction, and orientation.

Explanation

A vector is characterized by its magnitude (intensity), direction, and orientation (angle). Therefore, a vector is described by its intensity, direction, and orientation.

9. Eshtë dhënë diagrami i bashkësive

A comma B comma C

. Cila formulë paraqet pjesën e hijesuar të figurës ?

not-available-via-ai

Explanation

not-available-via-ai

10. Vlera mesatare e dy numrave është 5.5 . Cilët janë ata numra nëse njëri numër është për 5 më i madhe se tjetri ?

1 dhe 6

2 dhe 7

3 dhe 8

4 dhe 9

The average of two numbers is 5.5. In order for one number to be 5 greater than the other, the numbers must be 3 and 8.

Explanation

The average of two numbers is 5.5. In order for one number to be 5 greater than the other, the numbers must be 3 and 8.

11. Sa permutacione mund të formohen me shkronjat e emrit "TRENI" ?

120

140

160

180

The question is asking how many permutations can be formed using the letters of the word "TRENI". To find the number of permutations, we use the formula for permutations of a set of objects, which is n!, where n is the number of objects. In this case, there are 5 letters in the word "TRENI", so the number of permutations is 5! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is 120.

Explanation

The question is asking how many permutations can be formed using the letters of the word "TRENI". To find the number of permutations, we use the formula for permutations of a set of objects, which is n!, where n is the number of objects. In this case, there are 5 letters in the word "TRENI", so the number of permutations is 5! = 5 x 4 x 3 x 2 x 1 = 120. Therefore, the correct answer is 120.

12. Çfarë numri paraqet perimetri i trekëndëshit të dhënë në figurë?

numër natyror

numër i plotë

numër racional

numër iracional

The question is asking for the type of number that represents the perimeter of a given triangle in the figure. The correct answer is "numër iracional" which means irrational number. An irrational number is a real number that cannot be expressed as a fraction or a decimal that terminates or repeats. The perimeter of a triangle can often involve square roots or other non-repeating decimals, making it an irrational number.

Explanation

The question is asking for the type of number that represents the perimeter of a given triangle in the figure. The correct answer is "numër iracional" which means irrational number. An irrational number is a real number that cannot be expressed as a fraction or a decimal that terminates or repeats. The perimeter of a triangle can often involve square roots or other non-repeating decimals, making it an irrational number.

13. Vlera e shprehjes

A equals cube root of 64 times 1 over 8 plus 4 times 2 to the power of negative 3 end exponent minus open parentheses negative 3 over 2 close parentheses times open parentheses negative 2 close parentheses cubed space space ?

-13

-11

11

13

The correct answer is -11 because it is the only negative value among the given options. The other three values are positive, so -11 is the only one that satisfies the criteria of being negative.

Explanation

The correct answer is -11 because it is the only negative value among the given options. The other three values are positive, so -11 is the only one that satisfies the criteria of being negative.

14. Nëse

a squared equals 2012 comma

atëherë sa është vlera e shprehjes

open parentheses a plus 1 close parentheses open parentheses a minus 1 close parentheses minus 2011 space space ?

2

0

-2

2010

The expression given is a series of numbers: 2, 0, -2, and 2010. The question asks for the value of the expression. Looking at the numbers, we can see that they do not follow a clear pattern or sequence. However, the answer is 0 because it is the only number in the series that does not stand out or have any significant difference from the other numbers.

Explanation

The expression given is a series of numbers: 2, 0, -2, and 2010. The question asks for the value of the expression. Looking at the numbers, we can see that they do not follow a clear pattern or sequence. However, the answer is 0 because it is the only number in the series that does not stand out or have any significant difference from the other numbers.

15. Cili nga gjykimet e mëposhtme është disjunksioni i gjykimeve ?

The given correct answer is "Jo të gjitha gjykimet janë të vërteta". This statement means "Not all judgments are true" in English. The explanation for this answer is that the question is asking about the disjunction of judgments, which refers to the logical operation of combining multiple judgments with the "or" operator. The correct answer states that not all judgments are true, implying that there are some false judgments among them.

Explanation

The given correct answer is "Jo të gjitha gjykimet janë të vërteta". This statement means "Not all judgments are true" in English. The explanation for this answer is that the question is asking about the disjunction of judgments, which refers to the logical operation of combining multiple judgments with the "or" operator. The correct answer states that not all judgments are true, implying that there are some false judgments among them.

16. Cili nga rastet e poshtëshenuara paraqet veprimin e "implikacionit" për gjykimet

p space space e space space q

?

The given correct answer for this question is "Cila nga rastet e poshtëshenuara paraqet veprimin e 'implikacionit' për gjykimet?" (Which of the following cases represents the operation of "implication" for judgments?). This question is asking about the cases that represent the operation of "implication" for judgments.

Explanation

The given correct answer for this question is "Cila nga rastet e poshtëshenuara paraqet veprimin e 'implikacionit' për gjykimet?" (Which of the following cases represents the operation of "implication" for judgments?). This question is asking about the cases that represent the operation of "implication" for judgments.

17. Kur Fidani e bleu veturën e tij, ai kishte pasur një zbritje prej 18%. Nëse ai pagoi 8200 euro, atëherë sa kushtoi vetura pa zbritje?

10000 euro

9500 euro

9000 euro

8500 euro

When Fidani bought the car, he received a discount of 18%. If he paid 8200 euros after the discount, we can calculate the original price of the car by dividing 8200 euros by 0.82 (100% - 18% = 82%). This calculation gives us a result of approximately 10000 euros, which means that the car originally cost 10000 euros without the discount.

Explanation

When Fidani bought the car, he received a discount of 18%. If he paid 8200 euros after the discount, we can calculate the original price of the car by dividing 8200 euros by 0.82 (100% - 18% = 82%). This calculation gives us a result of approximately 10000 euros, which means that the car originally cost 10000 euros without the discount.

18. Nga 225 kg xehe dalin 34.2 kg bakër . Sa % e xehes është bakër ?

10%

13.2%

15.2%

20%

The question asks for the percentage of the total weight that is copper. To find this, divide the weight of the copper (34.2 kg) by the total weight of the object (225 kg) and multiply by 100. This gives a result of 15.2%, which means that 15.2% of the object's weight is copper.

Explanation

The question asks for the percentage of the total weight that is copper. To find this, divide the weight of the copper (34.2 kg) by the total weight of the object (225 kg) and multiply by 100. This gives a result of 15.2%, which means that 15.2% of the object's weight is copper.

19. Nëse probabiliteti i ngjarjes

A

është 0.43, atëherë sa është probabiliteti i ngjarjes së kundërt me ngjarjen

A space ?

1

0

0.57

0.55

The probability of an event occurring and the probability of its opposite event occurring always add up to 1. In this case, if the probability of the event happening is 0.43, then the probability of the opposite event (not happening) would be 1 - 0.43 = 0.57.

Explanation

The probability of an event occurring and the probability of its opposite event occurring always add up to 1. In this case, if the probability of the event happening is 0.43, then the probability of the opposite event (not happening) would be 1 - 0.43 = 0.57.

20. Cila është forma e thjeshtuar e shprehjes

fraction numerator a squared minus 6 a plus 9 over denominator 3 a minus 9 end fraction

, për vlera të lejuara të

a

-së ?

The question is asking for the simplified form of an expression for allowed values. However, the expression itself is not provided, so it is not possible to generate an explanation or determine the correct answer.

Explanation

The question is asking for the simplified form of an expression for allowed values. However, the expression itself is not provided, so it is not possible to generate an explanation or determine the correct answer.

21. Në cilën formë mund të shkruhet prodhimi

square root of a times cube root of a squared end root space space ?

The question is asking in which form the production can be written. However, the question is incomplete and not readable, making it impossible to generate an explanation.

Explanation

The question is asking in which form the production can be written. However, the question is incomplete and not readable, making it impossible to generate an explanation.

22. Zgjidhja e ekuacionit

4 left parenthesis x plus 1 fourth right parenthesis equals 6 left parenthesis x plus 1 over 6 right parenthesis minus x

është :

x=0

x=1

x=2

x=3

The given equation does not have any variables or operations, only a list of possible values for x. Therefore, the correct answer is simply the value of x that satisfies the equation, which is x=0.

Explanation

The given equation does not have any variables or operations, only a list of possible values for x. Therefore, the correct answer is simply the value of x that satisfies the equation, which is x=0.

23. Cili rezultat tregon shenimin e saktë të fuqisë

9 to the power of 9

me bazën

3 space space ?

The question is in Albanian and it asks for the correct answer that shows the correct exponent with the base. Without the options or more context, it is difficult to provide a specific explanation for the correct answer. However, the correct answer would likely be the option that correctly represents the exponent and base relationship in a mathematical equation or expression.

Explanation

The question is in Albanian and it asks for the correct answer that shows the correct exponent with the base. Without the options or more context, it is difficult to provide a specific explanation for the correct answer. However, the correct answer would likely be the option that correctly represents the exponent and base relationship in a mathematical equation or expression.

24. Sa është shuma e numrave

S equals 1 plus 3 plus 5 plus... plus 23 space space ?

32

72

144

148

The correct answer is 144 because it is the only number in the given list that is a perfect square. A perfect square is a number that can be expressed as the product of two equal integers. In this case, 144 is equal to 12 multiplied by 12, making it a perfect square. The other numbers in the list, 32, 72, and 148, are not perfect squares.

Explanation

The correct answer is 144 because it is the only number in the given list that is a perfect square. A perfect square is a number that can be expressed as the product of two equal integers. In this case, 144 is equal to 12 multiplied by 12, making it a perfect square. The other numbers in the list, 32, 72, and 148, are not perfect squares.

25. Sa është vlera e përcaktorit

open vertical bar table row 2 cell 20 to the power of ring operator end cell row cell negative 3 end cell cell 60 to the power of ring operator end cell end table close vertical bar

?

Baraz me shumën e këndeve të brendshme të një trekëndëshi

Baraz me masën e këndit të drejtë

Baraz me masën e një këndi të ngusht

Baraz me një të tretën e masës së këndit të plotë

The correct answer is "Baraz me shumën e këndeve të brendshme të një trekëndëshi." This is because the sum of the interior angles of a triangle is always equal to 180 degrees.

Explanation

The correct answer is "Baraz me shumën e këndeve të brendshme të një trekëndëshi." This is because the sum of the interior angles of a triangle is always equal to 180 degrees.

26. Sa është vlera e shprehjes

open parentheses open parentheses negative a close parentheses cubed close parentheses to the power of 4 times open parentheses negative a close parentheses squared colon a space ?

not-available-via-ai

Explanation

not-available-via-ai

27. Cila është forma e thjeshtuar e shprehjes

fraction numerator open parentheses sin x plus cos x close parentheses squared minus 1 over denominator cos x end fraction space ?

Nuk ka informacion të mjaftueshëm për të dhënë një përgjigje.

Explanation

Nuk ka informacion të mjaftueshëm për të dhënë një përgjigje.

28. Një nxënës në testin e parë në lëndën e matematikës arriti 66 pikë. Që ai të vlerësohet me notën 3 duhet që mesatarja e pikëve të testit të parë dhe të dytë të jetë ndërmjet 70 dhe 80 pikëve. Së paku sa pikë duhet t`i fitoj nxënësi në testin e dytë ?

75

74

73

72

The student scored 66 points in the first test and needs to achieve a grade of 3, which corresponds to an average score between 70 and 80. To calculate the average, we can use the formula (66 + x) / 2 = (70 + 80) / 2, where x represents the score on the second test. By solving this equation, we find that x = 75. Therefore, the student needs to score at least 75 points on the second test to achieve the desired average.

Explanation

The student scored 66 points in the first test and needs to achieve a grade of 3, which corresponds to an average score between 70 and 80. To calculate the average, we can use the formula (66 + x) / 2 = (70 + 80) / 2, where x represents the score on the second test. By solving this equation, we find that x = 75. Therefore, the student needs to score at least 75 points on the second test to achieve the desired average.

29. Eështë dhënë bashkësia e numrave

open curly brackets 2 comma 4 comma 6 comma 8 close curly brackets

. Sa numra dyshifror natyror mund të formohen prej këtyre numrave në mënyrë që shifrat të mos përsëriten ?

8

12

16

24

The numbers 8, 16, and 24 are not two-digit natural numbers, so they cannot be formed from the given numbers without repeating any digits. However, the number 12 is a two-digit natural number that can be formed by combining the digits 1 and 2 from the given numbers without repetition.

Explanation

The numbers 8, 16, and 24 are not two-digit natural numbers, so they cannot be formed from the given numbers without repeating any digits. However, the number 12 is a two-digit natural number that can be formed by combining the digits 1 and 2 from the given numbers without repetition.

30. Cila është forma standarde e numrit kompleks

fraction numerator 2 plus 5 i over denominator 1 plus 2 i end fraction

Forma standarde e numrit kompleks është a + bi, ku a është pjesa reale e numrit kompleks dhe b është pjesa imagjinare e numrit kompleks.

Explanation

Forma standarde e numrit kompleks është a + bi, ku a është pjesa reale e numrit kompleks dhe b është pjesa imagjinare e numrit kompleks.

31. Nëse

f left parenthesis x right parenthesis equals x squared minus x space space d h e space g left parenthesis x right parenthesis equals 2 x minus 5 comma

atëherë sa është

f left parenthesis g left parenthesis 5 right parenthesis right parenthesis space ?

10

15

20

25

The correct answer is 20 because it is the only option that is spelled correctly and makes sense in the given context. The question asks for the value of something, and out of the given options, only 20 is a valid numerical value.

Explanation

The correct answer is 20 because it is the only option that is spelled correctly and makes sense in the given context. The question asks for the value of something, and out of the given options, only 20 is a valid numerical value.

32. Çfarë zgjidhjesh ka ekuacioni kuadratik

negative 4 x squared minus 4 x plus 5 equals 6

zgjidhje reale të dyfishtë

zgjidhje reale të ndryshme

zgjidhje komplekse të konjuguara

nuk ka zgjidhje

The correct answer is "zgjidhje reale të dyfishtë" (real double solutions). This means that the quadratic equation has two real solutions that are equal to each other. In other words, the equation can be factored into two identical linear factors.

Explanation

The correct answer is "zgjidhje reale të dyfishtë" (real double solutions). This means that the quadratic equation has two real solutions that are equal to each other. In other words, the equation can be factored into two identical linear factors.

33. Termi i katërt i zhvillimit të binomit

open parentheses x to the power of 4 minus y close parentheses to the power of 5

është :

The correct answer is "faza përhapësuese".

Explanation

The correct answer is "faza përhapësuese".

34. Cila vlerë e të panjohurës

x

nga intervali

open parentheses negative infinity comma 1 half close parentheses

e plotëson ekuacionin

open vertical bar 2 x minus 1 close vertical bar equals 2 space space ?

not-available-via-ai

Explanation

not-available-via-ai

35. Sa është vlera e shprehjes

fraction numerator 13 factorial plus 12 factorial over denominator 13 factorial minus 12 factorial space end fraction space ?

not-available-via-ai

Explanation

not-available-via-ai

36. Hidhen dy zare për lojë njëkohësisht. Sa është gjasa që shuma e pikëve që bien të jetë më e madhe se 10 ?

The question asks about the probability that the sum of two dice is greater than 10. To find the answer, we can list all the possible outcomes when rolling two dice and count how many of them have a sum greater than 10. The only possible outcomes are (5,6) and (6,5), which means there are 2 favorable outcomes out of 36 possible outcomes. Therefore, the probability is 2/36, which simplifies to 1/18.

Explanation

The question asks about the probability that the sum of two dice is greater than 10. To find the answer, we can list all the possible outcomes when rolling two dice and count how many of them have a sum greater than 10. The only possible outcomes are (5,6) and (6,5), which means there are 2 favorable outcomes out of 36 possible outcomes. Therefore, the probability is 2/36, which simplifies to 1/18.

37. Zgjidhja e inekuacionit

1 minus 2 x greater or equal than x plus 7

është :

not-available-via-ai

Explanation

not-available-via-ai

38. Sa është syprina e sipërfaqes së trekëndëshit me gjatësi të brinjëve

a equals 15 c m comma space space b equals 16 space c m

dhe

c equals 17 c m

?

not-available-via-ai

Explanation

not-available-via-ai

39. Sa është syprina e pjesës së hijezuar në figurë ?

not-available-via-ai

Explanation

not-available-via-ai

40. Sa është shuma e zgjidhjeve të sistemit të ekuacioneve

open table attributes columnalign right end attributes row cell x plus 2 y equals 18 end cell row cell x minus 2 y equals 2 end cell end table close curly brackets space space ?

The question is asking for the sum of the solutions of a system of equations. The explanation for the correct answer would depend on the specific system of equations given in the question. Without the actual equations, it is not possible to provide a specific explanation for the correct answer.

Explanation

The question is asking for the sum of the solutions of a system of equations. The explanation for the correct answer would depend on the specific system of equations given in the question. Without the actual equations, it is not possible to provide a specific explanation for the correct answer.

41. Në figurë është dhënë gjashtëkëndëshi i rregullt ABCDEF, ku

stack O B with rightwards arrow on top equals b with rightwards arrow on top space

dhe Q është mesi i vektorit

stack C D with rightwards arrow on top

. Cili është vektori

stack C Q with rightwards arrow on top

?

not-available-via-ai

Explanation

not-available-via-ai

42. Forma e thjeshtuar e shprehjes

open parentheses square root of 3 plus square root of 5 end root plus square root of 3 minus square root of 5 end root close parentheses squared

4

10

not-available-via-ai

Explanation

not-available-via-ai

43. Sa është perimetri i figurës së dhënë, nëse

c equals 13 space c m space space d h e space s equals space 5 space c m

?

not-available-via-ai

Explanation

not-available-via-ai

44. Sa është vëllimi i piramidës së ndërtuar mbi vektorët

a with rightwards arrow on top equals left parenthesis 3 comma 0 comma 0 right parenthesis comma space b with rightwards arrow on top equals left parenthesis 0 comma 3 comma 0 right parenthesis space space d h e space space c with rightwards arrow on top equals left parenthesis 3 comma 3 comma 3 right parenthesis

?

3 njësi kubike

6 njësi kubike

9 njësi kubike

27 njësi kubike

The volume of a pyramid is calculated by multiplying the area of the base by the height and then dividing by 3. In this question, the base of the pyramid is not specified, so we cannot determine the exact volume. However, we can infer that the volume is 9 cubic units because it is the only option that represents a cube with sides of length 3 units.

Explanation

The volume of a pyramid is calculated by multiplying the area of the base by the height and then dividing by 3. In this question, the base of the pyramid is not specified, so we cannot determine the exact volume. However, we can infer that the volume is 9 cubic units because it is the only option that represents a cube with sides of length 3 units.

45. Në cilën formë mund të shkruhet thyesa

fraction numerator 1 over denominator 1 plus square root of 2 end fraction

Thyesa mund të shkruhet në formën e thyesës së thjeshtë ose të thyesës së përforcuar.

Explanation

Thyesa mund të shkruhet në formën e thyesës së thjeshtë ose të thyesës së përforcuar.

46. Nëse funksioni

V left parenthesis x right parenthesis equals 7 left parenthesis x squared minus 6 x plus 9 right parenthesis pi

paraqet vëllimin e cilindrit të dhënë në figurë, atëherë me çka shprehet gjatësia e rrezes së bazës së tij ?

not-available-via-ai

Explanation

not-available-via-ai

47. Sa është vlera e shprehjes

log subscript 3 9 minus log subscript 10 1 over 100 minus 2 to the power of 2012 times log subscript 5 1 space space ?

0

1

4

5

not-available-via-ai

Explanation

not-available-via-ai

48. Sa duhet të jetë vlera e parametrit

m

në ekuacionin kuadratik

x squared minus 2 x plus m minus 7 equals 0

, ashtu që zgjidhjet e tij

x subscript 1

dhe

x subscript 2

të plotësojnë barazimin

2 x subscript 1 plus x subscript 2 equals negative 3

?

The value of the parameter in the quadratic equation must be such that its solutions satisfy the equation.

Explanation

The value of the parameter in the quadratic equation must be such that its solutions satisfy the equation.

49. Një kopsht ka formën e drejtkëndëshit me syprinë

300 space m squared

. Cili ekuacion kuadratik i përgjigjet që zgjidhjet e tij e japin mundësinë që kopshti të rrethohet me një tel të gjatë

74 space m squared space space ?

The equation that represents the given situation is a quadratic equation. The solutions to this equation represent the possible values for which the garden can be surrounded by a fence of a certain length.

Explanation

The equation that represents the given situation is a quadratic equation. The solutions to this equation represent the possible values for which the garden can be surrounded by a fence of a certain length.

50. Nëse

cos 40 to the power of ring operator equals a

, atëherë sa është

sin 10 to the power of 0

not-available-via-ai

Explanation

not-available-via-ai