Yaadannoo boqonnaa fi gaaffii shaakalaa
Wanti fuula kana irra jiru hundi boqonnaa 1 kitaaba Herrega kutaa 10 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.
Kaardiiwwan fuula Herrega kutaa 10 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.
Yoom akka itti fayyadamtu
Yeroo function qooda ykn root quadratic qabu akka f(x)=4/(x-3) ykn g(x)=sqrt(x-2) domain barbaaddan kana fayyadami.
Of eeggadhu
Denominator zero godhu x hiiki, garuu root keessaa zero godhu x hin hiikin. f(x)=4/(x-3) irratti x 3 ta'uu hin qabu; g(x)=sqrt(x-2) irratti x 2 ol ta'uu qaba, x > 2 hin barreessin.
Grade 10 Mathematics, fuula 1-64 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Yeroo relation inequality akka y < x + 2 ykn y ≥ 3x - 4 ta'e grafii sakattaatan kana fayyadami.
Of eeggadhu
< ykn > irratti sararaa cabaa, ≤ ykn ≥ irratti sararaa cilee tarreessi. Gosa sararaa dogoggoruun marsariitii ni hir'isa, garuu gara shaakalamu sirrii ta'eyyuu.
Grade 10 Mathematics, fuula 1-64 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
| Kwaadraanti | Mallattoo x | Mallattoo y |
|---|---|---|
| I | + | + |
| II | - | + |
| III | - | - |
| IV | + | - |
Yoom akka itti fayyadamtu
Qabxii yeroo kaa'antu ykn kwaadraanti qabxiin koorronii isaatiin kennameen keessa jiru yeroo murtessitan kana fayyadami.
Of eeggadhu
Dursaa x ilaalaa booda y. Fakkeenyaaf (-2, 2) kwaadraanti II keessa jira, IV keessa miti.
Grade 10 Mathematics, fuula 1-64 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Yeroo ordered pairs ykn tarreen kenname y akka function of x ta'uu isaa murteessuuf barbaadamu kana fayyadami.
Of eeggadhu
(1, 5) lama barreessuun function sana hin balleessu. Yeroo elementiin jalqabaa tokko elementii lammaffaa adda addaa lamaa wajjin walitti hidhamu qofa function miti, akka (5, 3) fi (5, 8).
Grade 10 Mathematics, fuula 1-64 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Yoom akka itti fayyadamtu
Yeroo vertex fi axis of symmetry parabola argachuuf yookaan square guutanii booda ariitiin barreessuuf foormula kana fayyadami.
Of eeggadhu
Mallattoon keessa jiru bakka jijjiramti. (x+3)^2+2 keessatti vertex (-3, 2) dha, (3, 2) miti.
Grade 10 Mathematics, fuula 1-64 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e
Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.
Gaaffii 1
In which quadrant does the point T(-5, -3) lie?
Deebii: C Quadrant III
Sababa
In Quadrant III both coordinates are negative. The x-coordinate of T is -5 and the y-coordinate is -3, so T lies in Quadrant III.
Gaaffii 2
A function is a relation in which no two distinct ordered pairs have the same first element. Which of these sets is a function?
Deebii: B {(6, 7), (1, 9), (-1, 7), (0, 0), (4, -4)}
Sababa
In set B the first elements are 6, 1, -1, 0 and 4. None of them repeats, so no two pairs share the same first element. In sets A, C and D, some first element (2, 3, or 5) is paired with two different second elements, so they are not functions.
Gaaffii 3
Let the function be f(x) = 1 - 3x. What is the value of f(2)?
Deebii: A -5
Sababa
Replace x with 2: f(2) = 1 - 3(2) = 1 - 6 = -5.
Gaaffii 4
Find the range of the relation with ordered pairs (-2, 1), (-1, 0), (0, 0), (4, 2), (3, 5).
Deebii: B {1, 0, 2, 5}
Sababa
The range is the set of second components. These are 1, 0, 0, 2 and 5. Writing each value once gives {1, 0, 2, 5}. The set {-2, -1, 0, 3, 4} is the domain, not the range.
Gaaffii 5
Let f(x) = 2x + 4 and g(x) = 3x - 1. Find (f + g)(2).
Deebii: B 13
Sababa
First find (f + g)(x) = (2x + 4) + (3x - 1) = 5x + 3. Then (f + g)(2) = 5(2) + 3 = 10 + 3 = 13.
Gaaffii 6
Let f(x) = x2 - 1 and g(x) = x - 2. Find (f + g)(3).
Deebii: C 9
Sababa
Work out each function separately. f(3) = 32 - 1 = 8 and g(3) = 3 - 2 = 1. So (f + g)(3) = f(3) + g(3) = 8 + 1 = 9. Option A, 7, is what you get if you subtract instead of add.
Gaaffii 7
For the linear function f(x) = 3x - 6, which point is the x-intercept of the graph?
Deebii: A (2, 0)
Sababa
The x-intercept is where y = 0. Put 0 = 3x - 6, so 3x = 6 and x = 2. The x-intercept is (2, 0). The point (0, -6) is the y-intercept, not the x-intercept.
Gaaffii 8
Let R be the relation of all ordered pairs (x, y) of real numbers where y is greater than x. Which ordered pair belongs to R?
Deebii: B (1.1, 1.11)
Sababa
For a pair to belong to R, its second number must be greater than its first number. For (1.1, 1.11), 1.11 is greater than 1.1, so it belongs. In (4, 3) and (2, 1) the second number is smaller. In (7, 7) the two numbers are equal, so y is not greater than x.
Gaaffii 9
Let R be the relation of all ordered pairs (x, y) of real numbers with y2 = x. Which statement is correct?
Deebii: B R is not a function, because (4, 2) and (4, -2) both belong to R.
Sababa
Both (4, 2) and (4, -2) satisfy y2 = x, because 22 = 4 and (-2)2 = 4. A function cannot have two different ordered pairs with the same first element. So R is not a function. Being a curve does not make a relation a function, and the sign of x is not the reason.
Gaaffii 10
Find the domain of the function f(x) = √(x - 2).
Deebii: A x ≥ 2
Sababa
The expression under the square root must not be negative, so x - 2 ≥ 0. This gives x ≥ 2. The domain is the set of real numbers greater than or equal to 2.
Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.
Boqonnaan 1 Maxxansa Ministeera Barnootaa keessatti fuula 1 hanga fuula 64 ti.
Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 373
Temari boqonnaa kana gara shaakala yeroon daangeffametti jijjiira; utuu hojjettuu ni sirreessa; wanti si hin galinis barsiisaa AI tiin ni ibsama.
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