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Qormaata galuumsa kutaa 12ffaa Herregaa, bara 2017 A.L.I (2025), maxxansa 4

Gaaffilee dhugaa qormaata galuumsa yunivarsiitii kutaa 12 kan Herregaa, akkuma barattoonni bara 2017 A.L.I itti fudhatanitti. Tokkoon tokkoon gaaffii deebii sirrii fi ibsa qaba. Qormaanni bara 2017 A.L.I maxxansa adda addaatiin bahe. Fuulli kun maxxansa 4 qaba; kaan gadi aanee tarreeffamaniiru.

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Gaaffii 1

After rationalizing the denominator of 5/(3√3 - 2√2), the denominator is equal to ______.

  1. A.35
  2. B.5(3√3-2√2)/19
  3. C.19
  4. D.5(3√3+2√2)/19
Deebii fi ibsa ilaalaa

Deebii: C 19

Maaliif

Multiplying both the numerator and the denominator of the fraction by the conjugate of the denominator, 33+223\sqrt{3} + 2\sqrt{2}, yields (33)2−(22)2=27−8=19(3\sqrt{3})^2 - (2\sqrt{2})^2 = 27 - 8 = 19 in the denominator.

Gaaffii 2

The solution set of the equation 5|2x-1| - 3|4x+5| = 2 is equal to:

  1. A.{6/11}
  2. B.{-11, -9, -6/11}
  3. C.{}
  4. D.{-9, -6/11}
Deebii fi ibsa ilaalaa

Deebii: D {-9, -6/11}

Maaliif

By analyzing the critical points of the absolute values, x=1/2x = 1/2 and x=−5/4x = -5/4, we solve the equation in three intervals. Only x=−9x = -9 (for x<−5/4x < -5/4) and x=−6/11x = -6/11 (for −5/4≤x<1/2-5/4 \le x < 1/2) are valid solutions, giving the solution set {−9,−6/11}\{-9, -6/11\}.

Gaaffii 3

In a survey of 600 students, 250 drink tea, 225 drink coffee, 75 drink both. How many drink neither?

  1. A.400
  2. B.550
  3. C.200
  4. D.125
Deebii fi ibsa ilaalaa

Deebii: C 200

Maaliif

Using the principle of inclusion-exclusion, the number of students who drink tea or coffee is 250+225−75=400250 + 225 - 75 = 400. The number of students who drink neither is the total number of surveyed students minus this union, which is 600−400=200600 - 400 = 200.

Gaaffii 4

Given relation R = {(x,y): y > x-2, y > -x-2, y ≤ 4}. Which is the domain and range of R respectively?

  1. A.(-6,6) and (-2,4]
  2. B.(-2,4] and (-6,6)
  3. C.[-6,6] and (-2,4)
  4. D.(-2,4) and (-6,6)
Deebii fi ibsa ilaalaa

Deebii: A (-6,6) and (-2,4]

Maaliif

The region is bounded below by y=x−2y = x-2 and y=−x−2y = -x-2 (intersecting at (0,−2)(0,-2)), and above by y=4y = 4. Thus, the range of yy is (−2,4](-2, 4], and the maximum horizontal span (domain of xx) occurs at y=4y = 4, which gives −6<x<6-6 < x < 6.

Gaaffii 5

ΔABC and ΔDEF are similar. Area of ΔABC = 12 m². DE is twice AB. Area of ΔDEF?

  1. A.6 m²
  2. B.48 m²
  3. C.36 m²
  4. D.24 m²
Deebii fi ibsa ilaalaa

Deebii: B 48 m²

Maaliif

Since ΔABC\Delta ABC and ΔDEF\Delta DEF are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Since DE=2ABDE = 2AB, the area of ΔDEF\Delta DEF is 22×12 m2=48 m22^2 \times 12\text{ m}^2 = 48\text{ m}^2.

Gaaffii 6

Vector AB has initial A(2,-1) and terminal B(-4,7). Which is a unit vector in same direction?

  1. A.-(3/5)i + (4/5)j
  2. B.(3/5)i - (4/5)j
  3. C.-(3/50)i - (4/50)j
  4. D.(3/50)i + (4/50)j
Deebii fi ibsa ilaalaa

Deebii: A -(3/5)i + (4/5)j

Maaliif

The vector AB⃗\vec{AB} is given by B−A=(−4−2)i⃗+(7−(−1))j⃗=−6i⃗+8j⃗B - A = (-4-2)\vec{i} + (7-(-1))\vec{j} = -6\vec{i} + 8\vec{j}, which has magnitude (−6)2+82=10\sqrt{(-6)^2 + 8^2} = 10. The unit vector in the same direction is u⃗=−6i⃗+8j⃗10=−35i⃗+45j⃗\vec{u} = \frac{-6\vec{i} + 8\vec{j}}{10} = -\frac{3}{5}\vec{i} + \frac{4}{5}\vec{j}.

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Gaaffilee 59 kuusaa kana keessa jiran hunda akka waraqaa qormaataa maxxanfameetti, furtuu deebii ibsa 59 waliin immoo akka faayilii lammaffaatti. Maxxansaa yookiin daataa malee dubbisaa.

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