Stems are visible for study. Worked solutions stay inside each item and are unofficial.
Q2 · Polynomials - Factor Theorem
Let
f ( x ) f(x) f ( x ) be a polynomial of degree at least 1,
g ( x ) g(x) g ( x ) be a non-zero polynomial and
c ∈ R c \in \mathbb{R} c ∈ R . Which of the following states the Factor Theorem?
A. f ( c ) = 0 f(c) = 0 f ( c ) = 0 x − c x - c x − c f ( x ) f(x) f ( x ) B. For distinct real numbers a a a b b b f ( a ) f ( b ) < 0 f(a)f(b) < 0 f ( a ) f ( b ) < 0 f ( x ) f(x) f ( x ) a a a b b b C. There exist polynomials q ( x ) q(x) q ( x ) r ( x ) r(x) r ( x ) f ( x ) = g ( x ) q ( x ) + r ( x ) f(x) = g(x)q(x) + r(x) f ( x ) = g ( x ) q ( x ) + r ( x ) D. If f ( x ) f(x) f ( x ) x − c x - c x − c f ( c ) f(c) f ( c ) 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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Q3 · Sets - Cartesian product
Let
A = { 1 , 2 } A = \{1,2\} A = { 1 , 2 } and
B = { 1 , 3 } B = \{1,3\} B = { 1 , 3 } be sets. Then which one of the following Cartesian products is correct?
A. B × A = { ( 1 , 1 ) , ( 3 , 1 ) , ( 1 , 2 ) , ( 3 , 2 ) , ( 2 , 3 ) } B\times A = \{(1,1),(3,1),(1,2),(3,2),(2,3)\} B × A = {( 1 , 1 ) , ( 3 , 1 ) , ( 1 , 2 ) , ( 3 , 2 ) , ( 2 , 3 )} B. B × B = { ( 1 , 1 ) , ( 1 , 3 ) , ( 3 , 3 ) , ( 2 , 3 ) } B\times B = \{(1,1),(1,3),(3,3),(2,3)\} B × B = {( 1 , 1 ) , ( 1 , 3 ) , ( 3 , 3 ) , ( 2 , 3 )} C. A × B = { ( 1 , 1 ) , ( 1 , 3 ) , ( 2 , 1 ) , ( 2 , 3 ) , ( 3 , 2 ) } A\times B = \{(1,1),(1,3),(2,1),(2,3),(3,2)\} A × B = {( 1 , 1 ) , ( 1 , 3 ) , ( 2 , 1 ) , ( 2 , 3 ) , ( 3 , 2 )} D. A × A = { ( 1 , 1 ) , ( 2 , 2 ) , ( 2 , 1 ) , ( 1 , 2 ) } A\times A = \{(1,1),(2,2),(2,1),(1,2)\} A × A = {( 1 , 1 ) , ( 2 , 2 ) , ( 2 , 1 ) , ( 1 , 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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Q4 · Matrices - cofactor
Consider the matrix
( 2 − 3 1 0 − 1 π 3 1 4 ) \begin{pmatrix} 2 & -3 & 1 \\ 0 & -1 & \pi \\ 3 & 1 & 4 \end{pmatrix} 2 0 3 − 3 − 1 1 1 π 4 . What is the cofactor of entry
π \pi π ?
A. 7 7 7 B. − 11 -11 − 11 C. − 11 π -11\pi − 11 π D. − 7 π -7\pi − 7 π 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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Q5 · Geometric series - recurring decimal
When converting the recurring decimal
0. 25 ‾ 0.\overline{25} 0. 25 into a fraction using convergent geometric series, then what are the first term and the common ratio respectively?
A. 0.25 0.25 0.25 0.01 0.01 0.01 B. 25 25 25 0.01 0.01 0.01 C. 0.25 0.25 0.25 0.1 0.1 0.1 D. 2.5 2.5 2.5 0.1 0.1 0.1 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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Q6 · Linear programming
What are the maximum and minimum values respectively of
z = 3 x + y z = 3x + y z = 3 x + y subject to constraints
{ 3 x + 2 y ≤ 20 2 x − y ≥ 4 x ≥ 0 , y ≥ 0 \begin{cases} 3x + 2y \leq 20 \\ 2x - y \geq 4 \\ x \geq 0, y \geq 0 \end{cases} ⎩ ⎨ ⎧ 3 x + 2 y ≤ 20 2 x − y ≥ 4 x ≥ 0 , y ≥ 0 ?
A. 20 20 20 6 6 6 B. 40 40 40 6 6 6 C. 16 16 16 6 6 6 D. 18 18 18 8 8 8 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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Q7 · Functions - domain
What is the domain of the function
f ( x ) = 3 − x 2 f(x) = \sqrt{3 - x^2} f ( x ) = 3 − x 2 ?
A. [ 3 , ∞ ) [\sqrt{3}, \infty) [ 3 , ∞ ) B. [ − 3 , 3 ] [-\sqrt{3}, \sqrt{3}] [ − 3 , 3 ] C. [ − 3 , 3 ] [-3, 3] [ − 3 , 3 ] D. ( − ∞ , 3 ] ∪ [ 3 , ∞ ) (-\infty, \sqrt{3}] \cup [\sqrt{3}, \infty) ( − ∞ , 3 ] ∪ [ 3 , ∞ ) 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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Q8 · Logarithms - mantissa
If
x = 0.00471 x = 0.00471 x = 0.00471 , then which of the following gives the mantissa of
log x \log x log x ?
A. − 3 -3 − 3 B. 3 3 3 C. log 4.71 \log 4.71 log 4.71 D. log 0.471 \log 0.471 log 0.471 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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Q9 · Arithmetic progression - application
Dibabe was hired in an elementary school with a monthly salary of Birr 30,000. The agreement was to raise her salary every year by Birr 3,000. What is the total amount of money that Dibabe will earn at the end of the 8th year in Birr?
A. 2,964,000B. 3,888,000C. 2,976,000D. 324,000Worked 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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Q10 · Matrices - invertibility
For what value of
x x x is the matrix
( 1 0 1 2 x + 1 3 0 1 − 1 x ) \begin{pmatrix} 1 & 0 & 1 \\ 2x+1 & 3 & 0 \\ 1 & -1 & x \end{pmatrix} 1 2 x + 1 1 0 3 − 1 1 0 x invertible?
A. { x ∈ R : x ≠ − 1 } \{x \in \mathbb{R}: x \neq -1\} { x ∈ R : x = − 1 } B. { x ∈ R : x ≠ 4 } \{x \in \mathbb{R}: x \neq 4\} { x ∈ R : x = 4 } C. { x ∈ R : x ≠ 0 } \{x \in \mathbb{R}: x \neq 0\} { x ∈ R : x = 0 } D. { x ∈ R : x ≠ 3 } \{x \in \mathbb{R}: x \neq 3\} { x ∈ R : x = 3 } 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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Q11 · Solid geometry - sphere surface area
What is the surface area (in cm
2 ^2 2 ) of leather material required to make a spherical shape ball of radius 25cm?
A. 625 π 625\pi 625 π B. 2500 π 2500\pi 2500 π C. 100 π 100\pi 100 π D. 1250 s p h e r e 1250\ sphere 1250 s p h ere 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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Q12 · Linear programming - formulation
Mr. Bekele finances two investments,
I 1 I_1 I 1 and
I 2 I_2 I 2 . The profits of
I 1 I_1 I 1 and
I 2 I_2 I 2 are 8% and 10%, respectively. The total investment is Birr one million with at least Birr 50,000 in
I 1 I_1 I 1 and at most Birr 300,000 in
I 2 I_2 I 2 . Which of the following is the Mathematical representation of the problem if Mr. Bekele wishes to maximize his profit? (Let
x x x and
y y y be the amount invested on
I 1 I_1 I 1 and
I 2 I_2 I 2 respectively)
A. Maximize z = 0.08 x + 0.1 y z=0.08x+0.1y z = 0.08 x + 0.1 y x + y ≥ 1,000,000 x+y\geq 1{,}000{,}000 x + y ≥ 1 , 000 , 000 x ≤ 50,000 x\leq 50{,}000 x ≤ 50 , 000 y ≥ 300,000 y\geq 300{,}000 y ≥ 300 , 000 x , y ≥ 0 x,y\geq 0 x , y ≥ 0 B. Maximize z = 0.08 x + 0.1 y z=0.08x+0.1y z = 0.08 x + 0.1 y x + y ≥ 1,000,000 x+y\geq 1{,}000{,}000 x + y ≥ 1 , 000 , 000 x ≥ 50,000 x\geq 50{,}000 x ≥ 50 , 000 y ≤ 300,000 y\leq 300{,}000 y ≤ 300 , 000 x , y ≥ 0 x,y\geq 0 x , y ≥ 0 C. Maximize z = 0.08 x + 0.1 y z=0.08x+0.1y z = 0.08 x + 0.1 y x + y ≤ 1,000,000 x+y\leq 1{,}000{,}000 x + y ≤ 1 , 000 , 000 x ≤ 50,000 x\leq 50{,}000 x ≤ 50 , 000 y ≥ 300,000 y\geq 300{,}000 y ≥ 300 , 000 x , y ≥ 0 x,y\geq 0 x , y ≥ 0 D. Maximize z = 0.08 x + 0.1 y z=0.08x+0.1y z = 0.08 x + 0.1 y x + y ≤ 1,000,000 x+y\leq 1{,}000{,}000 x + y ≤ 1 , 000 , 000 x ≥ 50,000 x\geq 50{,}000 x ≥ 50 , 000 y ≤ 300,000 y\leq 300{,}000 y ≤ 300 , 000 x , y ≥ 0 x,y\geq 0 x , y ≥ 0 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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Q13 · Radicals - subtraction
What is the result when
3 2 − 7 6 3\sqrt{2} - 7\sqrt{6} 3 2 − 7 6 is subtracted from
2 2 + 4 3 2\sqrt{2} + 4\sqrt{3} 2 2 + 4 3 ?
A. 2 + ( 4 − 7 2 ) 3 \sqrt{2} + (4 - 7\sqrt{2})\sqrt{3} 2 + ( 4 − 7 2 ) 3 B. − 2 + 11 2 3 -\sqrt{2} + 11\sqrt{2}\sqrt{3} − 2 + 11 2 3 C. − 2 + ( 4 + 7 2 ) 3 -\sqrt{2} + (4 + 7\sqrt{2})\sqrt{3} − 2 + ( 4 + 7 2 ) 3 D. 2 − 3 ( 7 2 + 4 ) \sqrt{2} - \sqrt{3}(7\sqrt{2} + 4) 2 − 3 ( 7 2 + 4 ) 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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Q14 · Statistics - data types
Which one of the following is qualitative data?
A. The time Derartu took to win Atlanta Olympic.B. Age of President Trump.C. The volume of oil in a container.D. The type of Coffee produced in Keffa.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 · Functions - domain and range
Consider the functions
f ( x ) = 5 x f(x)=5^x f ( x ) = 5 x and
g ( x ) = log 5 x g(x)=\log_5 x g ( x ) = log 5 x . Which of the following is correct about the relations of domains and ranges of
f f f and
g g g ?
A. Domain ( f ) = Range ( g ) \text{Domain}(f) = \text{Range}(g) Domain ( f ) = Range ( g ) B. Domain ( f ) ⊆ Domain ( g ) \text{Domain}(f) \subseteq \text{Domain}(g) Domain ( f ) ⊆ Domain ( g ) C. Domain ( f ) = Domain ( g ) \text{Domain}(f) = \text{Domain}(g) Domain ( f ) = Domain ( g ) D. Range ( f ) = Range ( g ) \text{Range}(f) = \text{Range}(g) Range ( f ) = Range ( g ) 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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Q17 · Calculus - derivative at stationary point
Let
f f f be a function and let
c c c be an element of domain of
f f f at which the gradient of
f f f is zero. Which one of the following statements is true about
f ′ ( c ) f'(c) f ′ ( c ) ?
A. f ′ ( c ) = 0 f'(c)=0 f ′ ( c ) = 0 B. f ′ ( c ) ≠ 0 f'(c)\neq 0 f ′ ( c ) = 0 C. f ′ ( c ) > 0 f'(c)>0 f ′ ( c ) > 0 D. f ′ ( c ) < 0 f'(c)<0 f ′ ( c ) < 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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Q18 · Absolute value equations
What is the solution set of the equation
∣ 2 x − 3 ∣ − 1 = 0 |2x - 3| - 1 = 0 ∣2 x − 3∣ − 1 = 0 ?
A. [ 3 2 , ∞ ) \left[\frac{3}{2}, \infty\right) [ 2 3 , ∞ ) B. { 2 } \{2\} { 2 } C. { 1 , 2 } \{1, 2\} { 1 , 2 } D. { } \{\} { } 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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Q19 · Circle geometry - inscribed triangle
An equilateral triangle is inscribed in a circle with radius
3 \sqrt{3} 3 cm. Then what is the perimeter (in cm) of the triangle?
A. 9 2 \frac{9}{2} 2 9 B. 9 3 8 \frac{9\sqrt{3}}{8} 8 9 3 C. 9 9 9 D. 3 3 3\sqrt{3} 3 3 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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Q20 · Solid geometry - frustum
Which of the following statements defines frustum of a pyramid?
A. It is part of a pyramid excluded the base of the pyramid and horizontal cross-section made by the plane slant to the base.B. It is part of a pyramid included between the base of the pyramid and a horizontal cross-section made by the plane parallel to the base.C. It is part of a cone included between the base of the cone and a plane parallel to the base.D. It is a surface in space all points of which are equidistant from a point.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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Q21 · Vectors - subtraction
If
u = ( 1 , − 1 ) \mathbf{u} = (1, -1) u = ( 1 , − 1 ) and
v = ( 2 , − 4 ) \mathbf{v} = (2, -4) v = ( 2 , − 4 ) are vectors, then
u − v \mathbf{u} - \mathbf{v} u − v is equal to:
A. ( − 1 , 3 ) (-1,3) ( − 1 , 3 ) B. ( − 3 , 5 ) (-3,5) ( − 3 , 5 ) C. ( 3 , − 5 ) (3,-5) ( 3 , − 5 ) D. ( 1 , − 3 ) (1,-3) ( 1 , − 3 ) 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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Q22 · Calculus - gradient
The gradient of a function
f ( x ) = 1 x 2 f(x) = \frac{1}{x^2} f ( x ) = x 2 1 at
x = a x = a x = a ,
a ≠ 0 a \neq 0 a = 0 is equal to:
A. − 2 a 4 -\frac{2}{a^4} − a 4 2 B. − 2 a 3 -\frac{2}{a^3} − a 3 2 C. 2 a 2 \frac{2}{a^2} a 2 2 D. 2 a 3 \frac{2}{a^3} a 3 2 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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Q23 · Financial literacy
Which of the following is NOT a valid reason for a person to save money?
A. To buy shares from private banksB. To give loan to other people and collect profitC. For down payment of a houseD. To support life after retirementWorked 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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Q24 · Statistics - quartiles
Consider the following data. 12, 21, 16, 15, 10, 11, 12, 18, 9, 10, 13, 14, 15, 13, 19. Which one of the following is true?
A. Q 3 = 16 Q_3 = 16 Q 3 = 16 B. Q 2 = 13.5 Q_2 = 13.5 Q 2 = 13.5 C. Q 1 = 4 Q_1 = 4 Q 1 = 4 D. Q 1 = 12 Q_1 = 12 Q 1 = 12 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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Q25 · Coordinate geometry - perpendicular lines
A line
ℓ 1 \ell_1 ℓ 1 in the
x , y x, y x , y -plane has equation
x − y + 3 = 0 x - y + 3 = 0 x − y + 3 = 0 . A second line
ℓ 2 \ell_2 ℓ 2 which is perpendicular to
ℓ 1 \ell_1 ℓ 1 contains the point
( 2 , 3 ) (2, 3) ( 2 , 3 ) . Which one of the following gives equation of
ℓ 2 \ell_2 ℓ 2 ?
A. 3 y + 2 x + 3 = 0 3y + 2x + 3 = 0 3 y + 2 x + 3 = 0 B. y − x + 5 = 0 y - x + 5 = 0 y − x + 5 = 0 C. y + x − 5 = 0 y + x - 5 = 0 y + x − 5 = 0 D. y − x − 3 = 0 y - x - 3 = 0 y − x − 3 = 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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Q26 · Number theory - Division Algorithm
When the Division Algorithm is applied to the fraction
283 20 \frac{283}{20} 20 283 , then which one of the following is the corresponding representation?
A. 283 = 10 × 20 + 83 283 = 10 \times 20 + 83 283 = 10 × 20 + 83 B. 283 = 1 × 283 + 0 283 = 1 \times 283 + 0 283 = 1 × 283 + 0 C. 283 = 7 × 20 + 143 283 = 7 \times 20 + 143 283 = 7 × 20 + 143 D. 283 = 14 × 20 + 3 283 = 14 \times 20 + 3 283 = 14 × 20 + 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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Q27 · Statistics - range
Consider the data 7, 12, 21, x, 14. What is the value of
x x x if its range is 23?
A. 30B. 33.5C. 2D. 23Worked 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 · Rational functions
Let
R 1 ( x ) = x 3 − 9 x x 2 − 2 , x ≠ ± 2 R_1(x) = \frac{x^3 - 9x}{x^2 - 2}, x \neq \pm \sqrt{2} R 1 ( x ) = x 2 − 2 x 3 − 9 x , x = ± 2 , and
R 2 ( x ) = x 2 + 3 x x − 2 , x ≠ 2 R_2(x) = \frac{x^2 + 3x}{x - \sqrt{2}}, x \neq \sqrt{2} R 2 ( x ) = x − 2 x 2 + 3 x , x = 2 be rational functions. Then what is the simplified form of
R 1 ( x ) R 2 ( x ) \frac{R_1(x)}{R_2(x)} R 2 ( x ) R 1 ( x ) ?
A. 1 1 1 B. x − 3 x - 3 x − 3 C. x − 2 x + 3 , x ≠ − 3 , 0 \frac{x - \sqrt{2}}{x + 3}, x \neq -3, 0 x + 3 x − 2 , x = − 3 , 0 D. x − 3 x + 2 , x ≠ ± 2 , 0 \frac{x - 3}{x + \sqrt{2}}, x \neq \pm \sqrt{2}, 0 x + 2 x − 3 , x = ± 2 , 0 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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Q30 · Vectors - scalar quantities
Which one of the following is a scalar quantity?
A. Displacement of an object to change its position.B. The average velocity of airplane to travel.C. Force applied on an object to change its place.D. The total time taken to complete surgery.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 · Exponential functions - graphs
Let
a > 0 a > 0 a > 0 and
a ≠ 1 a \neq 1 a = 1 . Then which one of the following is NOT true about the graphs of exponential functions
f ( x ) = a x f(x) = a^x f ( x ) = a x and
g ( x ) = ( 1 a ) x g(x) = \left(\frac{1}{a}\right)^x g ( x ) = ( a 1 ) x ?
A. They intersect each other at ( 0 , 1 ) (0, 1) ( 0 , 1 ) B. They are increasing function.C. They have the same domain.D. They have the same range.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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Q32 · Solid geometry - sphere volume
A spherical fuel container with radius 3m is filled with fuel. What is the amount (in m
3 ^3 3 ) of fuel in the container?
A. 12 3 π \frac{12}{3}\pi 3 12 π B. 9 π 9\pi 9 π C. 36 π 36\pi 36 π D. 18 π 18\pi 18 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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Q33 · Related rates - circle area
A circle with radius 3 cm increases its radius at a rate of 0.2 cm/sec. What is the area of the circle at the 5
th ^{\text{th}} th second?
A. 9.64 π 9.64\pi 9.64 π 2 ^2 2 B. 4 π 4\pi 4 π 2 ^2 2 C. 16 π 16\pi 16 π 2 ^2 2 D. 9 π 9\pi 9 π 2 ^2 2 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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Q34 · Ratio and proportion
A school has 6,000 students. The ratio of female students to the total number of students is 2:3. Which one of the following is true about the students in the school?
A. The number of female students is twice the number of male students.B. The ratio of male students to female students is 1:3.C. The number of male students is greater than that of female students.D. About 33% of the students in the school are female.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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Q35 · Sets - equality and equivalence
Let
S S S be a set given by
{ x ∈ N : 1 < x ≤ 100 } \{x \in \mathbb{N}: 1 < x \leq 100\} { x ∈ N : 1 < x ≤ 100 } . Then which one of the following statement is true?
A. S S S { 2 , 3 , 4 , … , 99 , 100 } \{2,3,4, \dots, 99,100\} { 2 , 3 , 4 , … , 99 , 100 } B. S S S { 1 , 2 , 3 , … , 100 } \{1,2,3, \dots, 100\} { 1 , 2 , 3 , … , 100 } C. S S S { 2 , 3 , 4 , … , 99 } \{2,3,4,\dots,99\} { 2 , 3 , 4 , … , 99 } D. S S S { 101 , 102 , … , 198 } \{101,102, \dots, 198\} { 101 , 102 , … , 198 } 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 · Matrices - inverse
What is the inverse of the matrix
( − 2 1 0 3 ) \begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix} ( − 2 0 1 3 ) ?
A. ( 2 − 1 0 3 ) \begin{pmatrix} 2 & -1 \\ 0 & 3 \end{pmatrix} ( 2 0 − 1 3 ) B. − 1 6 ( − 2 1 0 3 ) \frac{-1}{6} \begin{pmatrix} -2 & 1 \\ 0 & 3 \end{pmatrix} 6 − 1 ( − 2 0 1 3 ) C. ( − 1 2 1 6 0 1 3 ) \begin{pmatrix} -\frac{1}{2} & \frac{1}{6} \\ 0 & \frac{1}{3} \end{pmatrix} ( − 2 1 0 6 1 3 1 ) D. ( − 2 0 1 3 ) \begin{pmatrix} -2 & 0 \\ 1 & 3 \end{pmatrix} ( − 2 1 0 3 ) 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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Q37 · Sequences and series - summation
Which one of the following is equal to
∑ k = 1 4 ( 2 k − 1 ) \sum_{k=1}^{4} (2k - 1) ∑ k = 1 4 ( 2 k − 1 ) ?
A. 20B. 30C. 16D. 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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Q38 · Polynomials - degree, leading coefficient, constant
Given the polynomial function
p ( x ) = 5 x 2 − x 3 − 2 p(x) = 5x^2 - x^3 - \sqrt{2} p ( x ) = 5 x 2 − x 3 − 2 . Then what are the degree, leading coefficient and constant term of the polynomial function
p ( x ) p(x) p ( x ) respectively?
A. 3 , 5 , − 2 3, 5, -\sqrt{2} 3 , 5 , − 2 B. 3 , − 1 , − 2 3, -1, -\sqrt{2} 3 , − 1 , − 2 C. 2 , 5 , − 2 2, 5, -\sqrt{2} 2 , 5 , − 2 D. 3 , 1 , 2 3, 1, \sqrt{2} 3 , 1 , 2 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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Q39 · Trigonometry - right triangle application
A person, whose height is 2 m, is standing away from a 16 m tall building. The angle of depression from the top of the building to the head of the person is
30 ∘ 30^\circ 3 0 ∘ . How far is the person from the building in meters?
A. 14 3 14\sqrt{3} 14 3 B. 16 3 \frac{16}{\sqrt{3}} 3 16 C. 16 3 16\sqrt{3} 16 3 D. 14 3 \frac{14}{\sqrt{3}} 3 14 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 · Sampling techniques
If a sampling interval is calculated by dividing the size of the population by the size of the sample, then which probability sampling technique is used?
A. Stratified SamplingB. Systematic SamplingC. Simple Random SamplingD. Cluster SamplingWorked 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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Q41 · Systems of equations - no solution
Which one of the following systems of equations possesses no solution?
A. − x + 3 y = − 2 -x + 3y = -2 − x + 3 y = − 2 − 2 x + 6 y = − 4 -2x + 6y = -4 − 2 x + 6 y = − 4 B. − 2 x + y = 2 -2x + y = 2 − 2 x + y = 2 4 x − 2 y = 4 4x - 2y = 4 4 x − 2 y = 4 C. x − 3 y = 0 x - 3y = 0 x − 3 y = 0 2 x + y = − 7 2x + y = -7 2 x + y = − 7 D. x + y = 2 x + y = \sqrt{2} x + y = 2 − x + y = π -x + y = \pi − x + y = π 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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Q42 · Vectors - position vector
Let
A ( − 1 , 2 ) A(-1, 2) A ( − 1 , 2 ) and
B ( 0 , 5 ) B(0, 5) B ( 0 , 5 ) be initial and terminal points of vector
A B → \overrightarrow{AB} A B . What is the position vector of
A B → \overrightarrow{AB} A B ?
A. − i + 7 j -i + 7j − i + 7 j B. 5 j 5j 5 j C. − i − 3 j -i - 3j − i − 3 j D. i + 3 j i + 3j i + 3 j 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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Q43 · Matrices - system in matrix form
The system of linear equations
{ x + z = 0 2 x + y = 1 x + 2 y + z = 0 \begin{cases} x + z = 0 \\ 2x + y = 1 \\ x + 2y + z = 0 \end{cases} ⎩ ⎨ ⎧ x + z = 0 2 x + y = 1 x + 2 y + z = 0 in matrix form is equal to:
A. coeff ( 1 1 0 2 1 0 1 2 1 ) \begin{pmatrix} 1 & 1 & 0 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} 1 2 1 1 1 2 0 0 1 B. coeff ( 1 0 1 2 1 1 1 0 1 ) \begin{pmatrix} 1 & 0 & 1 \\ 2 & 1 & 1 \\ 1 & 0 & 1 \end{pmatrix} 1 2 1 0 1 0 1 1 1 C. coeff ( 1 0 1 2 1 0 1 2 1 ) \begin{pmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} 1 2 1 0 1 2 1 0 1 D. coeff ( 1 1 1 2 1 0 1 2 1 ) \begin{pmatrix} 1 & 1 & 1 \\ 2 & 1 & 0 \\ 1 & 2 & 1 \end{pmatrix} 1 2 1 1 1 2 1 0 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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Q45 · Combinatorics - combinations
Which of the following describe combination of objects?
A. The number of ways of arrangement of n objects in a specific order using r objects at a time.B. The number of ways of arranging the seat of n people in a circle.C. The number of ways of choosing r objects from n objects disregarding the order of selection.D. The number of ways of arranging n objects taking n at a time considering the order of the objects.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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Q46 · Statistics - measures of dispersion
Which one of the following is true about measures of dispersion?
A. It gives representative of the whole data.B. It locates the central value of the data.C. It measures the scatter of the data.D. It gives the middle value of the data.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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Q47 · Exponential equations
The solution set of
64 x − 1 3 = ( 1 16 ) 2 x + 3 \sqrt[3]{64^{x-1}} = \left(\frac{1}{16}\right)^{2x+3} 3 6 4 x − 1 = ( 16 1 ) 2 x + 3 is equal to:
A. { − 1 2 } \left\{-\frac{1}{2}\right\} { − 2 1 } B. { 1 3 } \left\{\frac{1}{3}\right\} { 3 1 } C. { − 1 } \{-1\} { − 1 } D. { 1 } \{1\} { 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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Q48 · Permutations
In how many ways can the name for vertices of a triangle be given in different order by using letters A, B, C, D, E?
A. 20B. 120C. 10D. 60Worked 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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Q49 · Trigonometry - identities
If
sin ( − 53 ∘ ) = β \sin(-53^\circ) = \beta sin ( − 5 3 ∘ ) = β , then which one of the following is correct?
A. sin ( 37 ∘ ) = β \sin(37^\circ) = \beta sin ( 3 7 ∘ ) = β B. sin ( 127 ∘ ) = β \sin(127^\circ) = \beta sin ( 12 7 ∘ ) = β C. sin ( − 37 ∘ ) = β \sin(-37^\circ) = \beta sin ( − 3 7 ∘ ) = β D. sin ( 307 ∘ ) = β \sin(307^\circ) = \beta sin ( 30 7 ∘ ) = β 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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Q50 · Rational inequalities
What is the solution set of the inequality
1 − 3 x ≤ 4 x 2 1 - \frac{3}{x} \le \frac{4}{x^2} 1 − x 3 ≤ x 2 4 ?
A. [ − 1 , 0 ) ∪ ( 0 , 4 ] [-1, 0) \cup (0, 4] [ − 1 , 0 ) ∪ ( 0 , 4 ] B. [ − 1 , 4 ] [-1, 4] [ − 1 , 4 ] C. ( − ∞ , − 1 ) ∪ ( 4 , ∞ ) (-\infty, -1) \cup (4, \infty) ( − ∞ , − 1 ) ∪ ( 4 , ∞ ) D. ( − ∞ , − 1 ] ∪ [ 4 , ∞ ) (-\infty, -1] \cup [4, \infty) ( − ∞ , − 1 ] ∪ [ 4 , ∞ ) 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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Q51 · Coordinate geometry - slope
The slope of a line passing through
P ( 1 , − 1 ) P(1, -1) P ( 1 , − 1 ) and
Q ( 0 , 1 ) Q(0, 1) Q ( 0 , 1 ) is equal to:
A. 2B. -1C. 3D. -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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Q52 · Functions - signum function
Given the function
f ( x ) = 2 sgn x + 1 f(x) = 2\operatorname{sgn} x + 1 f ( x ) = 2 sgn x + 1 . Then what are the domain and the range of
f ( x ) f(x) f ( x ) respectively?
A. R \mathbb{R} R { − 3 , 1 , 3 } \{-3, 1, 3\} { − 3 , 1 , 3 } B. R \mathbb{R} R { − 3 , − 1 , 3 } \{-3, -1, 3\} { − 3 , − 1 , 3 } C. R \mathbb{R} R { − 2 , 0 , 2 } \{-2, 0, 2\} { − 2 , 0 , 2 } D. R \mathbb{R} R { − 1 , 1 , 3 } \{-1, 1, 3\} { − 1 , 1 , 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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Q53 · Radicals - rationalizing factor
What is the rationalizing factor of the number
5 3 3 − 2 \frac{5\sqrt{3}}{\sqrt{3} - \sqrt{2}} 3 − 2 5 3 ?
A. 1 3 + 2 \frac{1}{\sqrt{3} + \sqrt{2}} 3 + 2 1 B. 3 3 + 2 \frac{\sqrt{3}}{\sqrt{3} + \sqrt{2}} 3 + 2 3 C. 3 − 2 3 − 2 \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} 3 − 2 3 − 2 D. 3 + 2 3 + 2 \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}} 3 + 2 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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Q54 · Statistics - grouped data (frequency table)
An entrance examination for a certain job was given to 35 applicants with results grouped: 41-50 (3), 51-60 (14), 61-70 (10), 71-80 (5), 81-90 (2), 91-100 (1). Then which one of the following is NOT true?
A. The upper class limit of the second class is 60.B. The class midpoint of the second class is 55.C. 61-70 is the class interval of the third class.D. The lower class limit of the fifth class is 81.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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Q55 · Calculus - tangent line
What is the equation of the tangent line to the graph of
f ( x ) = 2 x 3 − 3 x 2 + 1 f(x) = 2x^3 - 3x^2 + 1 f ( x ) = 2 x 3 − 3 x 2 + 1 at
x = 2 x = 2 x = 2 ?
A. y = 120 x − 235 y = 120x - 235 y = 120 x − 235 B. y = 6 x − 7 y = 6x - 7 y = 6 x − 7 C. y = 2 x + 5 y = 2x + 5 y = 2 x + 5 D. y = 12 x − 19 y = 12x - 19 y = 12 x − 19 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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Q60 · Number systems - natural numbers set (variant)
Let
S = { x ∈ N : 1 < x ≤ 100 } S = \{x \in \mathbb{N}: 1 < x \leq 100\} S = { x ∈ N : 1 < x ≤ 100 } (duplicate variant appearing on the site). Which statement is true about
S S S ?
A. S S S { 2 , 3 , 4 , … , 99 , 100 } \{2,3,4, \dots, 99,100\} { 2 , 3 , 4 , … , 99 , 100 } B. S S S { 1 , 2 , 3 , … , 100 } \{1,2,3, \dots, 100\} { 1 , 2 , 3 , … , 100 } C. S S S { 2 , 3 , 4 , … , 99 } \{2,3,4,\dots,99\} { 2 , 3 , 4 , … , 99 } D. S S S { 101 , 102 , … , 198 } \{101,102, \dots, 198\} { 101 , 102 , … , 198 } 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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