Stems are visible for study. Worked solutions stay inside each item and are unofficial.
Q1 · power functions
Which one of the following function is NOT a power function?
A. f ( x ) = x − 3 5 f(x) = x^{-\frac{3}{5}} f ( x ) = x − 5 3 B. f ( x ) = 2 x 3 2 f(x) = \sqrt{2} x^{\frac{3}{2}} f ( x ) = 2 x 2 3 C. f ( x ) = π x 5 f(x) = \pi x^5 f ( x ) = π x 5 D. f ( x ) = ( 3 ) x f(x) = (\sqrt{3})^x f ( x ) = ( 3 ) x Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q2 · derivatives
Let
f ( x ) = ( 1 − 2 x ) 1 2 f(x) = (1 - 2x)^\frac{1}{2} f ( x ) = ( 1 − 2 x ) 2 1 . Then what is the values of
f ′ ( x ) f'(x) f ′ ( x ) ?
A. 1 1 − 2 x \frac{1}{\sqrt{1 - 2x}} 1 − 2 x 1 B. − 1 2 1 − 2 x \frac{-1}{2} \sqrt{1 - 2x} 2 − 1 1 − 2 x C. 1 2 1 − 2 x \frac{1}{2} \sqrt{1 - 2x} 2 1 1 − 2 x D. − 1 1 − 2 x -\frac{1}{\sqrt{1 - 2x}} − 1 − 2 x 1 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q3 · vectors
Which of the following statement describes the difference between scalar and vector quantities?
A. Physical quantities that only have direction are scalars, while that have only magnitude are vectors.B. Physical quantities that only have magnitude are scalars, while that have both magnitude and direction are vectors.C. Physical quantities that only have magnitude are vectors, while that have both magnitude and direction are scalars.D. Physical quantities that only have direction are vectors, while that have both magnitude and direction are scalars.Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q4 · statistics (mean deviation)
Consider the following data: 1, 3, 7, 9, 11, 13, 18, 28. Then the coefficient of mean deviation about the median is equal to:
A. 1 4 \frac{1}{4} 4 1 B. 8 5 \frac{8}{5} 5 8 C. 5 8 \frac{5}{8} 8 5 D. 1 2 \frac{1}{2} 2 1 Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q5 · real numbers
Which one of the following is an irrational number?
A. 3.4000 3.4000 3.4000 B. 0.04 \sqrt{0.04} 0.04 C. 1.16222... 1.16222... 1.16222... D. 29 \sqrt{29} 29 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q7 · probability
Which one of the following statements defines favorable outcomes in a random experiment?
A. The outcomes that insure the occurrence of a particular result.B. The outcomes containing all sample elements.C. The outcomes containing only one sample element.D. The outcomes that have equal chance of being chosen.Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q8 · logarithms
Given that
log 4.8 = 0.6812 \log 4.8 = 0.6812 log 4.8 = 0.6812 ,
log 6.93 = 0.8406 \log 6.93 = 0.8406 log 6.93 = 0.8406 and
log 6.84 = 0.8351 \log 6.84 = 0.8351 log 6.84 = 0.8351 , then what is the value of
48 \sqrt{48} 48 ?
A. 6.83B. 6.71C. 6.93D. 6.84Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q9 · polynomial operations
Let
f ( x ) = x 3 + 2 x + 1 f(x) = x^3 + 2x + 1 f ( x ) = x 3 + 2 x + 1 and
g ( x ) = x 2 + 1 g(x) = x^2 + 1 g ( x ) = x 2 + 1 be given two polynomial functions. Then which of the following is true?
A. f ( x ) g ( x ) = x 2 + 1 x − 1 \frac{f(x)}{g(x)} = \frac{x^2 + 1}{x - 1} g ( x ) f ( x ) = x − 1 x 2 + 1 B. f ( x ) + g ( x ) = x 3 + x 2 f(x) + g(x) = x^3 + x^2 f ( x ) + g ( x ) = x 3 + x 2 C. f ( x ) − g ( x ) = x 3 − x 2 + 2 x f(x) - g(x) = x^3 - x^2 + 2x f ( x ) − g ( x ) = x 3 − x 2 + 2 x D. f ( x ) g ( x ) = x 5 + x 3 + x 2 − 2 x − 1 f(x) g(x) = x^5 + x^3 + x^2 - 2x - 1 f ( x ) g ( x ) = x 5 + x 3 + x 2 − 2 x − 1 Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q10 · sets (relative complement)
Let
A = { x ∣ 1 ≤ x ≤ 10 } A = \{x|1 \leq x \leq 10\} A = { x ∣1 ≤ x ≤ 10 } and
B = { x ∣ − 1 ≤ x ≤ 10 } B = \{x|-1 \leq x \leq 10\} B = { x ∣ − 1 ≤ x ≤ 10 } be two sets of real numbers. What is the relative complement of
A A A with respect to
B B B ?
A. { x ∣ − 1 ≤ x ≤ 0 } \{x|-1 \leq x \leq 0\} { x ∣ − 1 ≤ x ≤ 0 } B. ∅ \emptyset ∅ C. { x ∣ − 1 ≤ x ≤ 1 } \{x|-1 \leq x \leq 1\} { x ∣ − 1 ≤ x ≤ 1 } D. { x ∣ − 1 ≤ x < 1 } \{x|-1 \leq x < 1\} { x ∣ − 1 ≤ x < 1 } Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q11 · extrema of functions
Consider the function
f ( x ) = x 3 − 3 x 2 + 3 f(x) = x^3 - 3x^2 + 3 f ( x ) = x 3 − 3 x 2 + 3 on
( − 2 , 3 ) (-2, 3) ( − 2 , 3 ) . Then which of the following point is local minimum and local maximum of
f ( x ) f(x) f ( x ) respectively?
A. ( − 2 , − 27 ) (-2, -27) ( − 2 , − 27 ) ( 0 , 3 ) (0, 3) ( 0 , 3 ) B. ( 0 , 3 ) (0, 3) ( 0 , 3 ) ( 2 , − 1 ) (2, -1) ( 2 , − 1 ) C. ( 3 , 3 ) (3, 3) ( 3 , 3 ) ( − 2 , − 27 ) (-2, -27) ( − 2 , − 27 ) D. ( 2 , − 1 ) (2, -1) ( 2 , − 1 ) ( 0 , 3 ) (0, 3) ( 0 , 3 ) Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q12 · statistics (class midpoint)
The table below shows a grouped frequency distribution.
A. 34B. 34.5C. 35D. 39Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q13 · statistics (quartile deviation)
Given the data set: 29, 44, 46, 52, 35, 35, 25, 15, 10, 55, 56. What is the coefficient of quartile deviation?
A. 0.25B. 0.35C. 0.45D. 0.55Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q14 · exponents/radicals
Which of the following is the simplified form of the expression
81 1 / 5 27 3 / 5 \frac{81^{1/5}}{27^{3/5}} 2 7 3/5 8 1 1/5 ?
A. 3B. 9 5 \sqrt[5]{9} 5 9 C. 3 5 \sqrt[5]{3} 5 3 D. 1 3 \frac{1}{3} 3 1 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q15 · solid geometry (cylinder)
What is the total surface area (in cm²) of the cylinder whose radius is 2 cm and height is 7 cm?
A. 49 π 49\pi 49 π B. 28 π 28\pi 28 π C. 36 π 36\pi 36 π D. 98 π 98\pi 98 π Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q16 · permutations and combinations
Suppose that we have 4 objects chosen 3 at a time. Then which of the following statement is true?
A. The number of combinations is 6.B. The number of combinations is 24.C. The number of permutations is 24.D. The number of permutations is 6.Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q17 · logarithmic equations
Consider the equation
log x + log ( x − 3 ) = 1 \log x + \log (x-3) = 1 log x + log ( x − 3 ) = 1 . Then what is its solution set?
A. { 5 } \{5\} { 5 } B. { 2 , − 5 } \{2, -5\} { 2 , − 5 } C. { − 2 , 5 } \{-2, 5\} { − 2 , 5 } D. { 6 } \{6\} { 6 } Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q18 · probability
If a fair six-sided die is tossed once, then what is the probability of getting a factor of 4?
A. 1 2 \frac{1}{2} 2 1 B. 1 6 \frac{1}{6} 6 1 C. 5 6 \frac{5}{6} 6 5 D. 1 3 \frac{1}{3} 3 1 Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q19 · relations
Which of the following statement is true about a relation?
A. The domain and the range of a relation are equal sets.B. The range of a relation is the set of all its first coordinates.C. The domain of a relation is the set of all its second coordinates.D. A relation from A to B is any subset of A × B for non-empty sets A and B.Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q21 · average rate of change
What is the average rate of change of
g ( x ) = x 3 − 2 x g(x) = x^3 - 2x g ( x ) = x 3 − 2 x over the interval
1 ≤ x ≤ 6 1 \leq x \leq 6 1 ≤ x ≤ 6 ?
A. 203 5 \frac{203}{5} 5 203 B. 41C. 37 5 \frac{37}{5} 5 37 D. 46Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q22 · matrix inverse
Which of the following matrix is the inverse of the matrix
( 1 − 1 2 1 0 1 3 1 3 ) \begin{pmatrix} 1 & -1 & 2 \\ 1 & 0 & 1 \\ 3 & 1 & 3 \end{pmatrix} 1 1 3 − 1 0 1 2 1 3 ?
A. ( 1 5 − 1 − 3 0 1 − 4 − 1 1 ) \begin{pmatrix} 1 & 5 & -1 \\ -3 & 0 & 1 \\ -4 & -1 & 1 \end{pmatrix} 1 − 3 − 4 5 0 − 1 − 1 1 1 B. ( − 1 0 1 5 − 3 − 4 − 1 1 1 ) \begin{pmatrix} -1 & 0 & 1 \\ 5 & -3 & -4 \\ -1 & 1 & 1 \end{pmatrix} − 1 5 − 1 0 − 3 1 1 − 4 1 C. ( − 1 0 1 5 3 4 1 − 1 1 ) \begin{pmatrix} -1 & 0 & 1 \\ 5 & 3 & 4 \\ 1 & -1 & 1 \end{pmatrix} − 1 5 1 0 3 − 1 1 4 1 D. ( − 1 5 − 1 0 − 3 1 1 − 4 1 ) \begin{pmatrix} -1 & 5 & -1 \\ 0 & -3 & 1 \\ 1 & -4 & 1 \end{pmatrix} − 1 0 1 5 − 3 − 4 − 1 1 1 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q23 · standard form (scientific notation)
When the number
43 × 10 8 × 10 − 5 43 \times 10^8 \times 10^{-5} 43 × 1 0 8 × 1 0 − 5 is written in standard form, it equals
A. 4.3 × 10 4 4.3 \times 10^4 4.3 × 1 0 4 B. 43 × 10 3 43 \times 10^3 43 × 1 0 3 C. 4.3 × 10 3 4.3 \times 10^3 4.3 × 1 0 3 D. 0.43 × 10 5 0.43 \times 10^5 0.43 × 1 0 5 Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q24 · solid geometry (pyramid volume)
If a square pyramid has a base side of 6 cm long and its lateral faces are equilateral triangles, then what is its volume (in cm³)?
A. 72B. 3 2 3\sqrt{2} 3 2 C. 48D. 36 2 36\sqrt{2} 36 2 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q25 · linear programming (modeling)
A television company assembles flat screen and curved screen televisions. The company has to invest Birr 15,000 to assemble one flat screen and Birr 20,000 to assemble one curved screen television. The company allocates a maximum of Birr 900,000 in a week for assembling. The company gets Birr 1800 profit from a sale of one flat screen television and Birr 2000 profit from a sale of one curved screen television. Moreover, the company has a store of maximum capacity of storing 50 televisions. Let x be the number of flat screens and y be the number of curved screens. Then which one of the following inequalities should model the profit for the objective function Z=1800x+2000y?
A. { 20 , 000 x + 15 , 000 y ≤ 360 , 000 x + y ≤ 50 x , y ≥ 0 \begin{cases} 20,000x + 15,000y \leq 360,000 \\ x + y \leq 50 \\ x, y \geq 0 \end{cases} ⎩ ⎨ ⎧ 20 , 000 x + 15 , 000 y ≤ 360 , 000 x + y ≤ 50 x , y ≥ 0 B. { 15 , 000 x + 20 , 000 y ≤ 900 , 000 x + y ≤ 50 x , y ≥ 0 \begin{cases} 15,000x + 20,000y \leq 900,000 \\ x + y \leq 50 \\ x, y \geq 0 \end{cases} ⎩ ⎨ ⎧ 15 , 000 x + 20 , 000 y ≤ 900 , 000 x + y ≤ 50 x , y ≥ 0 C. { 15 , 000 x + 20 , 000 y ≤ 360 , 000 x + y ≤ 50 x , y ≥ 0 \begin{cases} 15,000x + 20,000y \leq 360,000 \\ x + y \leq 50 \\ x, y \geq 0 \end{cases} ⎩ ⎨ ⎧ 15 , 000 x + 20 , 000 y ≤ 360 , 000 x + y ≤ 50 x , y ≥ 0 D. { 20 , 000 x + 15 , 000 y ≤ 900 , 000 x + y ≤ 50 x , y ≥ 0 \begin{cases} 20,000x + 15,000y \leq 900,000 \\ x + y \leq 50 \\ x, y \geq 0 \end{cases} ⎩ ⎨ ⎧ 20 , 000 x + 15 , 000 y ≤ 900 , 000 x + y ≤ 50 x , y ≥ 0 Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q26 · statistics (mode)
Which one of the following distribution is multimodal?
A. 18, 14, 15, 10, 11, 3, 18, 12B. 6, 10, 9, 6, 10, 4C. 8, 7, 11, 13, 17, 9, 8, 7, 6, 11D. 12, 13, 26, 15, 25, 38, 28, 27, 32Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q27 · equation of a line
What is the equation of a line that passes through (-2,5) and has a slope
1 2 \frac{1}{2} 2 1 ?
A. 2 y − x − 12 = 0 2y - x - 12 = 0 2 y − x − 12 = 0 B. y = 2 x + 12 y = 2x + 12 y = 2 x + 12 C. 2 y + x = 5 2y + x = 5 2 y + x = 5 D. y = 1 2 x + 5 y = \frac{1}{2}x + 5 y = 2 1 x + 5 Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q28 · quadratic minimum
What is the minimum value of the function defined by
f ( x ) = − 3 + 4 x + x 2 f(x) = -3 + 4x + x^{2} f ( x ) = − 3 + 4 x + x 2 ?
A. − 7 -7 − 7 B. 1C. 0D. − 2 -2 − 2 Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q29 · systems of linear equations
Which of the following statement is true about the given system of linear equations?
A. { x + 3 y = 6 2 x − 5 y = 2 \begin{cases} x + 3y = 6 \\ 2x - 5y = 2 \end{cases} { x + 3 y = 6 2 x − 5 y = 2 B. { 2 x + y = 0 x − 4 y = 0 \begin{cases} 2x + y = 0 \\ x - 4y = 0 \end{cases} { 2 x + y = 0 x − 4 y = 0 C. { x + 3 y = 2 2 x − 5 y = 1 \begin{cases} x + 3y = 2 \\ 2x - 5y = 1 \end{cases} { x + 3 y = 2 2 x − 5 y = 1 D. { 3 x − y = 1 x + 3 y = 0 \begin{cases} 3x - y = 1 \\ x + 3y = 0 \end{cases} { 3 x − y = 1 x + 3 y = 0 Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q30 · derivatives
Suppose
f ( x ) = 3 x f(x) = 3\sqrt{x} f ( x ) = 3 x and
g ( x ) = 1 3 x 4 + 2 x g(x) = \frac{1}{3}x^4 + 2x g ( x ) = 3 1 x 4 + 2 x be given two functions. Then which of the following is equal to
( f + g ) ′ ( x ) (f + g)'(x) ( f + g ) ′ ( x ) ?
A. 3 x − 1 2 + 4 x 3 + 2 3x^{-\frac{1}{2}} + 4x^3 + 2 3 x − 2 1 + 4 x 3 + 2 B. 2 3 x − 1 3 + 4 x 3 + 2 x \frac{2}{3}x^{-\frac{1}{3}} + 4x^3 + 2x 3 2 x − 3 1 + 4 x 3 + 2 x C. 2 3 x − 1 3 + 4 x 3 + 2 \frac{2}{3}x^{-\frac{1}{3}} + 4x^3 + 2 3 2 x − 3 1 + 4 x 3 + 2 D. 3 2 x − 1 2 + 4 3 x 3 + 2 \frac{3}{2}x^{-\frac{1}{2}} + \frac{4}{3}x^3 + 2 2 3 x − 2 1 + 3 4 x 3 + 2 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q31 · statistics (grouped mean)
The table given below shows the ages distribution of children in a small village in years.
A. 6.9B. 6.6C. 7.5D. 7.2Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q32 · applications (loans/installments)
A worker of a company borrowed Birr 100,000 from the company's credit and saving association. She agreed to pay 10% of the loan during the agreement and on the remaining amount to pay Birr 3000 (monthly plus interest) in 36 monthly installments. What is the total amount of money she paid to the credit and saving association?
A. Birr 106,000B. Birr 118,000C. Birr 108,000D. Birr 116,000Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q33 · systems of linear equations
Given the system of linear equations
{ a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 \begin{cases} a_1 x + b_1 y = c_1 \\ a_2 x + b_2 y = c_2 \end{cases} { a 1 x + b 1 y = c 1 a 2 x + b 2 y = c 2 , where
a 1 , a 2 , b 1 , b 2 , c 1 , c 2 ∈ R a_1, a_2, b_1, b_2, c_1, c_2 \in \mathbb{R} a 1 , a 2 , b 1 , b 2 , c 1 , c 2 ∈ R and
a 2 , b 2 , c 2 ≠ 0 a_2, b_2, c_2 \neq 0 a 2 , b 2 , c 2 = 0 , then which of the following is true?
A. If a 1 a 2 ≠ b 1 b 2 \frac{a_1}{a_2} \neq \frac{b_1}{b_2} a 2 a 1 = b 2 b 1 B. If a 1 a 2 = c 1 c 2 \frac{a_1}{a_2} = \frac{c_1}{c_2} a 2 a 1 = c 2 c 1 C. If b 1 b 2 = c 1 c 2 \frac{b_1}{b_2} = \frac{c_1}{c_2} b 2 b 1 = c 2 c 1 D. If a 1 a 2 ≠ c 1 c 2 \frac{a_1}{a_2} \neq \frac{c_1}{c_2} a 2 a 1 = c 2 c 1 Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q34 · trigonometric values
Which of the following is true about the cosecant value of the given angles?
A. csc 135 ∘ = − 1 2 \csc 135^\circ = -\frac{1}{\sqrt{2}} csc 13 5 ∘ = − 2 1 B. csc 135 ∘ = − 2 \csc 135^\circ = -\sqrt{2} csc 13 5 ∘ = − 2 C. csc 45 ∘ = 1 2 \csc 45^\circ = \frac{1}{\sqrt{2}} csc 4 5 ∘ = 2 1 D. csc 45 ∘ = 2 \csc 45^\circ = \sqrt{2} csc 4 5 ∘ = 2 Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q35 · sequences (geometric progression)
Which of the following statement defines geometric progression?
A. It is a sequence in which the ratio between consecutive terms is a non-zero constant.B. It is a sequence in which the difference between consecutive terms is a positive constant.C. It is a sequence in which the difference between consecutive terms is a non-zero constant.D. It is a sequence in which the ratio between consecutive terms is a positive constant.Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q36 · coordinate geometry (section formula)
Consider the line segment
P Q PQ PQ with
P = ( 1 , − 1 ) P = (1, -1) P = ( 1 , − 1 ) and
Q = ( 4 , 2 ) Q = (4, 2) Q = ( 4 , 2 ) . Then which of the following point divides
P Q PQ PQ internally in the ratio of 2:1?
A. ( 3 , 1 ) (3, 1) ( 3 , 1 ) B. ( 2 , 0 ) (2, 0) ( 2 , 0 ) C. ( 2 , 1 ) (2, 1) ( 2 , 1 ) D. ( 3 , 0 ) (3, 0) ( 3 , 0 ) Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q37 · determinants
What is the determinant of the matrix
( 1 2 1 3 2 2 5 2 3 7 2 4 9 2 ) \begin{pmatrix} \frac{1}{2} & 1 & \frac{3}{2} \\ 2 & \frac{5}{2} & 3 \\ \frac{7}{2} & 4 & \frac{9}{2} \end{pmatrix} 2 1 2 2 7 1 2 5 4 2 3 3 2 9 ?
A. 0B. 1 2 \frac{1}{2} 2 1 C. 1 8 \frac{1}{8} 8 1 D. 1Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q38 · linear programming (optimization)
Given the objective function
Z = − x + 2 y Z = -x + 2y Z = − x + 2 y that is subjected to the constraints
{ x ≥ 3 x + y ≥ 5 x + 2 y ≤ 6 y ≥ 0 \begin{cases} x \geq 3 \\ x + y \geq 5 \\ x + 2y \leq 6 \\ y \geq 0 \end{cases} ⎩ ⎨ ⎧ x ≥ 3 x + y ≥ 5 x + 2 y ≤ 6 y ≥ 0 , what are the maximum and minimum values of Z respectively?
A. -2 and -6B. -2 and 1C. 1 and -2D. -6 and -2Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q39 · location theorem
Let
a , b ∈ R a, b \in \mathbb{R} a , b ∈ R such that
a < b a < b a < b and
f f f be a polynomial function. Then which one of the following statement states the location theorem?
A. If f ( a ) f(a) f ( a ) f ( b ) f(b) f ( b ) f f f a a a b b b B. If f ( a ) f(a) f ( a ) f ( b ) f(b) f ( b ) f f f a a a b b b C. If f ( a ) f(a) f ( a ) f ( b ) f(b) f ( b ) f f f a a a b b b D. If f ( a ) f(a) f ( a ) f ( b ) f(b) f ( b ) f f f a a a b b b Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q40 · similar triangles
Suppose two triangles are similar by SSS similarity theorem. If the side lengths of one triangle are 2 cm, 4 cm and 6 cm, and the shorter side of the other triangle is 9 cm long, then what are the lengths (in cm) of the other two sides of the triangle?
A. 9 and 21B. 18 and 27C. 9 and 27D. 18 and 21Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q43 · matrix equality
If
( x + y 2 5 3 ) = ( 7 2 5 x − y ) \begin{pmatrix} x + y & 2 \\ 5 & 3 \end{pmatrix} = \begin{pmatrix} 7 & 2 \\ 5 & x - y \end{pmatrix} ( x + y 5 2 3 ) = ( 7 5 2 x − y ) , then what is the value of
x x x ?
A. -2B. -5C. 5D. 2Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q44 · statistics (mean deviation about mode)
Consider the following data: 13, 16, 19, 19, 19, 19, 24, 27. What is the mean deviation about the mode?
A. 4B. 2.75C. 3.75D. 3Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q45 · types of data
Which of the following statement is true about types of data:
A. The age of students in a class is a quantitative data.B. The height of students in a class is a qualitative data.C. The weight of students in class is a qualitative data.D. The gender of students in a class is a quantitative data.Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q46 · percentage (discount)
A company offers a discount of 25% on one of its product for promotion. What is a regular price of the product if it is purchased for Birr 99?
A. 110B. 198C. 132D. 125Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q49 · infinite series (convergence)
Which of the following statement is true about the given infinite series?
A. ∑ n = 1 ∞ ( − 1 ) n 2 n \sum_{n=1}^{\infty} (-1)^n 2^n ∑ n = 1 ∞ ( − 1 ) n 2 n B. ∑ n = 1 ∞ ( 4 3 ) n \sum_{n=1}^{\infty} \left( \frac{4}{3} \right)^n ∑ n = 1 ∞ ( 3 4 ) n C. ∑ n = 1 ∞ 2 n \sum_{n=1}^{\infty} 2^n ∑ n = 1 ∞ 2 n D. ∑ n = 1 ∞ ( − 1 ) n ( 2 5 ) n \sum_{n=1}^{\infty} (-1)^n \left( \frac{2}{5} \right)^n ∑ n = 1 ∞ ( − 1 ) n ( 5 2 ) n Worked solutionUnofficial Unofficial keyed letter C. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q50 · trigonometry (definitions)
Let
θ \theta θ be an angle in standard position and
( x , y ) (x, y) ( x , y ) be a point on the terminal side of
θ \theta θ , which is different from the origin. Let
r r r be the distance from
( x , y ) (x, y) ( x , y ) to the origin. Then which of the following defines
cos θ \cos \theta cos θ ?
A. r y \frac{r}{y} y r B. y r \frac{y}{r} r y C. r x \frac{r}{x} x r D. x r \frac{x}{r} r x Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q51 · exponential equations (logs)
Which one of the following is the solution set of
5 x = 11.2 5^x = 11.2 5 x = 11.2 ? [Use
log 5 = 0.6990 \log 5 = 0.6990 log 5 = 0.6990 and
log 1.12 = 0.0485 \log 1.12 = 0.0485 log 1.12 = 0.0485 ]
A. 1.12B. 1.5C. 1.2D. 1.69Worked solutionUnofficial Unofficial keyed letter B. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q52 · similar triangles (shadows)
A boy and girl are both standing on a sun light. The boy’s height is 1.6m and casts a shadow of 2m. If the girl’s height casts a shadow of 1.8m, then what is the height (in meter) of the girl?
A. 1.5B. 1.54C. 1.68D. 1.44Worked solutionUnofficial Unofficial keyed letter D. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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Q53 · vectors (addition)
If two vectors
V ⃗ = A B ⃗ \vec{V} = \vec{AB} V = A B , and
U ⃗ = B C ⃗ \vec{U} = \vec{BC} U = BC are given as shown in the figure below. Then what is the vector
V ⃗ + U ⃗ \vec{V} + \vec{U} V + U ?
This item uses a figure in the original paper (not redrawn here).
A. A C ⃗ \vec{AC} A C B. B A ⃗ \vec{BA} B A C. C A ⃗ \vec{CA} C A D. C B ⃗ \vec{CB} CB Worked solutionUnofficial Unofficial keyed letter A. A full worked solution is not published for this item yet.
Unofficial — solved by Abrari, not an official EAES key.
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