Stems are visible for study. Worked solutions stay inside each item and are unofficial.
Q1 · statistics (mean deviation)
Consider the data: 11, 13, 15, 17, 19, 21. Which one of the following is the mean deviation from the mean?
A. 4B. 3.5C. 4.5D. 3Worked 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 · coordinate geometry (parallel/perpendicular lines)
Consider the quadrilateral ABCD where
A = ( 0 , 0 ) A=(0,0) A = ( 0 , 0 ) ,
B = ( − 1 , 1 ) B=(-1,1) B = ( − 1 , 1 ) ,
C = ( 0 , 2 ) C=(0,2) C = ( 0 , 2 ) and
D = ( 2 , 2 ) D=(2,2) D = ( 2 , 2 ) . Which one of the following is true?
A. CD is perpendicular to AB.B. BC is parallel to AD.C. CD is perpendicular to BE.D. AB is parallel to CD.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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Q3 · functions (greatest integer function)
Consider the greatest integer function defined by
f ( x ) = [ x − 1 ] f(x) = [x - 1] f ( x ) = [ x − 1 ] . Which of the following sets is the domain of
f f f ?
A. The set of rational numbers.B. The set of integers.C. The set of real numbers.D. The set of natural numbers.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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Q4 · relations and functions
Which one of the following relations is a function?
A. R = { ( x , y ) : x , y ∈ R and y 2 = x } R=\{(x,y): x,y \in \mathbb{R} \text{ and } y^2 = x\} R = {( x , y ) : x , y ∈ R and y 2 = x } B. R = { ( x , y ) : x , y ∈ R and ∣ y ∣ = x } R=\{(x,y): x,y \in \mathbb{R} \text{ and } |y| = x\} R = {( x , y ) : x , y ∈ R and ∣ y ∣ = x } C. R = { ( x , y ) : x , y ∈ R and y = x 2 } R=\{(x,y): x,y \in \mathbb{R} \text{ and } y = x^2\} R = {( x , y ) : x , y ∈ R and y = x 2 } D. R = { ( x , y ) : x , y ∈ R and y 4 = x } R=\{(x,y): x,y \in \mathbb{R} \text{ and } y^4 = x\} R = {( x , y ) : x , y ∈ R and y 4 = x } 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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Q6 · average rate of change
What is the average rate of change of
y = f ( x ) y = f(x) y = f ( x ) with respect to
x x x on the interval
[ a , b ] [a, b] [ a , b ] ?
A. f ( b ) + f ( a ) 2 \frac{f(b)+f(a)}{2} 2 f ( b ) + f ( a ) B. b − a f ( b ) − f ( a ) \frac{b-a}{f(b)-f(a)} f ( b ) − f ( a ) b − a C. f ( b ) − f ( a ) 2 \frac{f(b)-f(a)}{2} 2 f ( b ) − f ( a ) D. f ( b ) − f ( a ) b − a \frac{f(b)-f(a)}{b-a} b − a f ( b ) − f ( a ) 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 · logarithmic equations
Which one of the following sets is the solution of
log 3 x + log 3 ( x − 2 ) = 1 \log_3 x + \log_3 (x - 2) = 1 log 3 x + log 3 ( x − 2 ) = 1 ?
A. { − 1 , 3 } \{-1, 3\} { − 1 , 3 } B. { 3 } \{3\} { 3 } C. { 2 } \{2\} { 2 } D. { 0 , 2 } \{0, 2\} { 0 , 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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Q9 · statistics (mode)
Consider the test results of 20 students in a given class.
A. 16B. 15C. 14D. 18Worked 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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Q10 · vectors (addition)
Consider the figure given below.
[Figure: points A, B, C and D; arrow from A to B (vector AB), arrow from C to D (vector CD), and a segment joining C and A.]
Which one of the following vectors is equal to
A B ⃗ + C D ⃗ + B C ⃗ \vec{AB} + \vec{CD} + \vec{BC} A B + C D + BC ?
A. C D ⃗ \vec{CD} C D B. A C ⃗ \vec{AC} A C C. A D ⃗ \vec{AD} A D D. B D ⃗ \vec{BD} B 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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Q11 · equation of a line
Which one of the following equations represents a line that passes through the points
( 2 , − 1 ) (2, -1) ( 2 , − 1 ) and
( − 3 , 4 ) (-3, 4) ( − 3 , 4 ) ?
A. x + y − 1 = 0 x + y - 1 = 0 x + y − 1 = 0 B. x + y + 1 = 0 x + y + 1 = 0 x + y + 1 = 0 C. x − y − 1 = 0 x - y - 1 = 0 x − y − 1 = 0 D. x − y + 1 = 0 x - y + 1 = 0 x − y + 1 = 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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Q12 · binomial theorem
What is the coefficient of
x 3 y 4 x^3 y^4 x 3 y 4 in the expansion of
( x − 2 y ) 7 (x - 2y)^7 ( x − 2 y ) 7 ?
A. 35B. 70C. 560D. -280Worked 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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Q13 · power functions
Which one of the following is NOT a power function?
A. f ( x ) = x 3 f(x) = x^3 f ( x ) = x 3 B. f ( x ) = 3 x f(x) = 3^x f ( x ) = 3 x C. f ( x ) = 4 x − 6 f(x) = 4x^{-6} f ( x ) = 4 x − 6 D. f ( x ) = 7 x − 1 / 3 f(x) = 7x^{-1/3} f ( x ) = 7 x − 1/3 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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Q14 · linear programming
Given the problem: Maximize
Z = 3 x + y Z = 3x + y Z = 3 x + y subject to:
{ x + y ≥ 2 y + 2 x ≤ 4 y ≥ 1 , x ≥ 0 \begin{cases} x + y \geq 2 \\ y + 2x \leq 4 \\ y \geq 1, x \geq 0 \end{cases} ⎩ ⎨ ⎧ x + y ≥ 2 y + 2 x ≤ 4 y ≥ 1 , x ≥ 0 Which one of the following is the maximum value of
Z Z Z ?
A. 2B. 5.5C. 4D. 5.8Worked 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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Q15 · quadratic equations (roots)
Let
r 1 r_1 r 1 and
r 2 r_2 r 2 be the roots of the quadratic equation
2 x 2 + 3 x − 4 = 0 2x^2 + 3x - 4 = 0 2 x 2 + 3 x − 4 = 0 . Which one of the following is equal to
1 r 1 2 + 1 r 2 2 \frac{1}{r_1^2} + \frac{1}{r_2^2} r 1 2 1 + r 2 2 1 ?
A. 3 4 \frac{3}{4} 4 3 B. 25 16 \frac{25}{16} 16 25 C. 3 16 \frac{3}{16} 16 3 D. 1 4 \frac{1}{4} 4 1 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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Q16 · matrices (minors and cofactors)
Consider the matrix
A = ( − 1 2 1 3 4 2 1 1 5 ) A = \begin{pmatrix} -1 & 2 & 1 \\ 3 & 4 & 2 \\ 1 & 1 & 5 \end{pmatrix} A = − 1 3 1 2 4 1 1 2 5 . Which of the following statements is true about the minor of the entries of
A A A ?
A. The cofactor of 3 is 9.B. The cofactor of 4 is -6.C. The minor of 4 is 6.D. The minor of 3 is -9.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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Q17 · circles (tangent-secant angle)
In the figure below, let
m ( ∠ D A C ) = 15 ∘ m(\angle DAC) = 15^\circ m ( ∠ D A C ) = 1 5 ∘ and
m ( arc B C ) = 70 ∘ m(\text{arc } BC) = 70^\circ m ( arc BC ) = 7 0 ∘ . What is the measure of arc CD?
[Figure: circle with center O; point A outside the circle on the right; a secant from A meets the circle at D and then at B (upper left); a tangent from A touches the circle at C (bottom); angle DAC = 15°.]
A. 42.5 ∘ 42.5^\circ 42. 5 ∘ B. 55 ∘ 55^\circ 5 5 ∘ C. 30 ∘ 30^\circ 3 0 ∘ D. 40 ∘ 40^\circ 4 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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Q18 · right triangles (altitude to hypotenuse)
Consider the right-angled triangle
△ A B C \triangle ABC △ A BC below, where
A C = 5 cm AC = 5\text{ cm} A C = 5 cm and
B C = 4 cm BC = 4\text{ cm} BC = 4 cm . Which one of the following is the length of
B D BD B D ?
[Figure: right triangle ABC with the right angle at B; BD is drawn from B perpendicular to the hypotenuse AC, meeting it at D.]
A. 5.76 cmB. 2.4 cmC. 5 cmD. 7 cmWorked 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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Q19 · definite integrals (properties)
Which one of the following is true about definite integrals?
A. ∫ a b f ( x ) d x = 0 , a ≠ 0 \int_a^b f(x)\,dx = 0, a \neq 0 ∫ a b f ( x ) d x = 0 , a = 0 B. ∫ a b ( f ( x ) + g ( x ) ) d x = ∫ a b f ( x ) d x + ∫ a b g ( x ) d x \int_a^b (f(x) + g(x))\,dx = \int_a^b f(x)\,dx + \int_a^b g(x)\,dx ∫ a b ( f ( x ) + g ( x )) d x = ∫ a b f ( x ) d x + ∫ a b g ( x ) d x C. ∫ a b f ( x ) d x = ∫ a b g ( x ) d x \int_a^b f(x)\,dx = \int_a^b g(x)\,dx ∫ a b f ( x ) d x = ∫ a b g ( x ) d x D. ∫ a b ( f ( x ) − g ( x ) ) d x = ∫ a b ( g ( x ) − f ( x ) ) d x \int_a^b (f(x) - g(x))\,dx = \int_a^b (g(x) - f(x))\,dx ∫ a b ( f ( x ) − g ( x )) d x = ∫ a b ( g ( x ) − f ( x )) d x 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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Q20 · circles (definition)
Which of the following statements defines a circle?
A. It is the set of points in a plane formed by the intersection of two secants in the plane.B. It is the set of points in a space formed by the intersection of two secants in the space.C. It is the set of points in a space each of which is equidistant from a fixed point in the space.D. It is the set of points in a plane each of which is equidistant from a fixed point in the plane.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 · matrices (transpose)
What is the transpose of the matrix
M = ( 1 2 1 0 − 1 3 2 1 5 ) M = \begin{pmatrix} 1 & 2 & 1 \\ 0 & -1 & 3 \\ 2 & 1 & 5 \end{pmatrix} M = 1 0 2 2 − 1 1 1 3 5 ?
A. ( 1 0 2 2 − 1 1 1 3 5 ) \begin{pmatrix} 1 & 0 & 2 \\ 2 & -1 & 1 \\ 1 & 3 & 5 \end{pmatrix} 1 2 1 0 − 1 3 2 1 5 B. ( 1 2 1 2 − 1 3 0 1 5 ) \begin{pmatrix} 1 & 2 & 1 \\ 2 & -1 & 3 \\ 0 & 1 & 5 \end{pmatrix} 1 2 0 2 − 1 1 1 3 5 C. ( 2 1 5 0 − 1 3 1 2 1 ) \begin{pmatrix} 2 & 1 & 5 \\ 0 & -1 & 3 \\ 1 & 2 & 1 \end{pmatrix} 2 0 1 1 − 1 2 5 3 1 D. ( 1 2 2 0 − 1 1 1 3 5 ) \begin{pmatrix} 1 & 2 & 2 \\ 0 & -1 & 1 \\ 1 & 3 & 5 \end{pmatrix} 1 0 1 2 − 1 3 2 1 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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Q22 · rational functions (domain)
Which one of the following sets is the domain of the rational function
f ( x ) = x 3 + x 2 x 4 + 2 x 2 − 3 f(x) = \frac{x^3 + x^2}{x^4 + 2x^2 - 3} f ( x ) = x 4 + 2 x 2 − 3 x 3 + x 2 ?
A. R ∖ { 1 } \mathbb{R} \setminus \{1\} R ∖ { 1 } B. R ∖ { − 1 , 1 } \mathbb{R} \setminus \{-1, 1\} R ∖ { − 1 , 1 } C. R ∖ { − 3 , 1 } \mathbb{R} \setminus \{-3, 1\} R ∖ { − 3 , 1 } D. R ∖ { − 1 , 1 , − 3 } \mathbb{R} \setminus \{-1, 1, -3\} R ∖ { − 1 , 1 , − 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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Q23 · business mathematics (borrowing)
Which of the following statements is true in borrowing money?
A. The borrower only pays back the principal amount.B. The lender assumes no risk when giving out a loan.C. Borrowing money involves an agreement to repay the principal amount along with accrued interest.D. Collateral is always required for any type of financial borrowing.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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Q24 · derivatives (tangent line)
Let
f ( x ) = 2 x + 1 x − 1 f(x) = \frac{2x+1}{x-1} f ( x ) = x − 1 2 x + 1 . Which of the following equations is the equation of the tangent line to the graph of
f f f at
( 2 , f ( 2 ) ) (2, f(2)) ( 2 , f ( 2 )) ?
A. 3 x + y = 11 3x + y = 11 3 x + y = 11 B. y − 3 x = − 1 y - 3x = -1 y − 3 x = − 1 C. x + 3 y = 17 x + 3y = 17 x + 3 y = 17 D. 3 x − y = 13 3x - y = 13 3 x − y = 13 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 · regular polygons (interior angle)
What is the measure of each interior angle of a regular polygon with 15 sides?
A. 144 ∘ 144^\circ 14 4 ∘ B. 150 ∘ 150^\circ 15 0 ∘ C. 156 ∘ 156^\circ 15 6 ∘ D. 162 ∘ 162^\circ 16 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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Q26 · derivatives
Let
f ( x ) = x 3 + 4 x f(x) = x^3 + 4x f ( x ) = x 3 + 4 x and
g ( x ) = 3 x 3 − x 2 g(x) = 3x^3 - x^2 g ( x ) = 3 x 3 − x 2 . What is the derivative of
( f + g ) ( x ) (f+g)(x) ( f + g ) ( x ) ?
A. 12 x 2 − 2 x + 4 12x^2 - 2x + 4 12 x 2 − 2 x + 4 B. 4 x 3 − x 2 + 4 x 4x^3 - x^2 + 4x 4 x 3 − x 2 + 4 x C. 12 x 2 − x + 4 12x^2 - x + 4 12 x 2 − x + 4 D. 9 x 2 − 2 x + 4 9x^2 - 2x + 4 9 x 2 − 2 x + 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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Q27 · sets (relative complement)
Let
A = { x ∈ R : x 3 − x = 0 } A = \{x \in \mathbb{R} : x^3 - x = 0\} A = { x ∈ R : x 3 − x = 0 } and
B = { x ∈ Z : − 1 ≤ x } B = \{x \in \mathbb{Z} : -1 \leq x\} B = { x ∈ Z : − 1 ≤ x } . What is the relative complement of
B B B with respect to
A A A (i.e.,
A ∖ B A \setminus B A ∖ B )?
A. { 2 } \{2\} { 2 } B. { 0 , 1 } \{0, 1\} { 0 , 1 } C. ∅ \emptyset ∅ D. { − 1 , 0 , 1 } \{-1, 0, 1\} { − 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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Q28 · sets (power set)
Given the set
B = { ∅ , { − 2 , 0 } } B = \{\emptyset, \{-2, 0\}\} B = { ∅ , { − 2 , 0 }} , what is the power set of
B B B ?
A. { ∅ , { − 2 , 0 } } \{\emptyset, \{-2, 0\}\} { ∅ , { − 2 , 0 }} B. { ∅ , { ∅ } , { { − 2 , 0 } } , { ∅ , { − 2 , 0 } } } \{\emptyset, \{\emptyset\}, \{\{-2, 0\}\}, \{\emptyset, \{-2, 0\}\}\} { ∅ , { ∅ } , {{ − 2 , 0 }} , { ∅ , { − 2 , 0 }}} C. { { ∅ } , { { − 2 , 0 } } } \{\{\emptyset\}, \{\{-2, 0\}\}\} {{ ∅ } , {{ − 2 , 0 }}} D. { ∅ , { − 2 } , { 0 } , { − 2 , 0 } } \{\emptyset, \{-2\}, \{0\}, \{-2, 0\}\} { ∅ , { − 2 } , { 0 } , { − 2 , 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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Q29 · logarithms
What is the simplified form of
log 16 ( 4 ) − log 2 ( 12.5 ) + log 0.5 ( 2 ) \log_{16}(4) - \log_2(\sqrt{12.5}) + \log_{0.5}(2) log 16 ( 4 ) − log 2 ( 12.5 ) + log 0.5 ( 2 ) ?
A. log 2 ( 5 ) \log_2(5) log 2 ( 5 ) B. 1 − log 2 ( 5 ) 1 - \log_2(5) 1 − log 2 ( 5 ) C. − log 2 ( 5 ) -\log_2(5) − log 2 ( 5 ) D. 0Worked 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 · exponential functions (graphs)
Which statement is true about the graphs of the 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 where
a > 1 a > 1 a > 1 ?
A. They are reflections of each other across the x-axis.B. They are reflections of each other across the y-axis.C. They never intersect each other.D. Both functions are monotonically increasing.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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Q31 · statistics (mean properties)
Which of the following statements is NOT true about the mean of a given data set?
A. It is highly affected by extreme values (outliers).B. The sum of the deviations of the items from the mean is always zero.C. It must always be one of the actual data values present in the set.D. It uses every value in the data set for its calculation.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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Q32 · real numbers (irrational numbers)
Which one of the following numbers is an irrational number?
A. 3.14159 (terminating)B. 16 \sqrt{16} 16 C. 22 7 \frac{22}{7} 7 22 D. π \pi π 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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Q33 · vectors in space (cross product)
What is the area of the parallelogram spanned by the vectors
u ⃗ = i − 2 j + k \vec{u} = i - 2j + k u = i − 2 j + k and
v ⃗ = 2 i + 2 j − k \vec{v} = 2i + 2j - k v = 2 i + 2 j − k ?
A. 14 \sqrt{14} 14 B. 3 5 3\sqrt{5} 3 5 C. 9D. 35 \sqrt{35} 35 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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Q34 · trigonometric functions (period)
What is the fundamental period of the function
f ( x ) = sin ( x ) f(x) = \sin(x) f ( x ) = sin ( x ) ?
A. π 2 \frac{\pi}{2} 2 π B. π \pi π C. 2 π 2\pi 2 π D. 4 π 4\pi 4 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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Q35 · radicals
What is the simplified form of the expression
( 45 + 1 5 ) ( 5 − 20 ) \left(\sqrt{45} + \frac{1}{\sqrt{5}}\right)\left(\sqrt{5} - \sqrt{20}\right) ( 45 + 5 1 ) ( 5 − 20 ) ?
A. 16B. -16C. 8D. -8Worked 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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Q36 · statistics (sampling methods)
In statistical sampling, if a population is divided into homogeneous groups and a random sample is drawn from each group, this method is known as:
A. Simple random samplingB. Cluster samplingC. Stratified samplingD. Systematic samplingWorked 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 · counting (multiplication principle)
A mathematics exam contains 10 multiple-choice questions and 3 short-answer questions. According to the multiplication principle, how many ways can a student select exactly one multiple-choice question and exactly one short-answer question to solve first?
A. 13B. 30C. 10 3 10^3 1 0 3 D. ( 13 2 ) \binom{13}{2} ( 2 13 ) 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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Q38 · transformations (translation)
A translation vector maps the origin
( 0 , 0 ) (0,0) ( 0 , 0 ) to the point
( − 2 , 4 ) (-2,4) ( − 2 , 4 ) . Under this same translation, what is the image of the point
( 3 , 1 ) (3,1) ( 3 , 1 ) ?
A. ( 5 , − 3 ) (5,-3) ( 5 , − 3 ) B. ( 1 , 5 ) (1,5) ( 1 , 5 ) C. ( − 6 , 4 ) (-6,4) ( − 6 , 4 ) D. ( − 5 , 3 ) (-5,3) ( − 5 , 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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Q39 · vectors in space
If the initial point of a vector is
A ( 2 , − 1 , 4 ) A(2,-1,4) A ( 2 , − 1 , 4 ) and the terminal point is
B ( 4 , 3 , 2 ) B(4,3,2) B ( 4 , 3 , 2 ) , what is the position vector
A B ⃗ \vec{AB} A B ?
A. ⟨ − 2 , − 4 , 2 ⟩ \langle -2, -4, 2 \rangle ⟨ − 2 , − 4 , 2 ⟩ B. ⟨ 6 , 2 , 6 ⟩ \langle 6, 2, 6 \rangle ⟨ 6 , 2 , 6 ⟩ C. ⟨ 2 , 4 , − 2 ⟩ \langle 2, 4, -2 \rangle ⟨ 2 , 4 , − 2 ⟩ D. ⟨ 8 , − 3 , 8 ⟩ \langle 8, -3, 8 \rangle ⟨ 8 , − 3 , 8 ⟩ 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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Q40 · vectors (scalar multiplication)
Let vector
u ⃗ \vec{u} u have an initial point at
( 1 , 2 ) (1,2) ( 1 , 2 ) and a terminal point at
( − 3 , 6 ) (-3,6) ( − 3 , 6 ) . What are the components of the vector
− 1 2 u ⃗ -\frac{1}{2}\vec{u} − 2 1 u ?
A. ⟨ 2 , − 2 ⟩ \langle 2, -2 \rangle ⟨ 2 , − 2 ⟩ B. ⟨ − 2 , 2 ⟩ \langle -2, 2 \rangle ⟨ − 2 , 2 ⟩ C. ⟨ 4 , − 4 ⟩ \langle 4, -4 \rangle ⟨ 4 , − 4 ⟩ D. ⟨ 1 , − 1 ⟩ \langle 1, -1 \rangle ⟨ 1 , − 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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Q41 · rational functions (domain)
Consider the rational function
f ( x ) = x 2 − 4 x − 2 f(x) = \frac{x^2 - 4}{x - 2} f ( x ) = x − 2 x 2 − 4 . The domain of
f f f is the set of all real numbers EXCEPT:
A. -2B. 2C. 0D. The domain is all real numbers.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 · matrices (properties)
Which of the following properties of matrices and scalar multiplication
r r r is TRUE for any two matrices
A A A and
B B B of the same dimension?
A. r ( A B ) = ( r A ) ( r B ) r(AB) = (rA)(rB) r ( A B ) = ( r A ) ( r B ) B. r ( A + B ) = r A + r B r(A+B) = rA + rB r ( A + B ) = r A + r B C. ( A + B ) T = A T − B T (A + B)^T = A^T - B^T ( A + B ) T = A T − B T D. det ( A + B ) = det ( A ) + det ( B ) \det(A+B) = \det(A) + \det(B) det ( A + B ) = det ( A ) + det ( B ) 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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Q43 · determinants (transpose)
If
A A A is a
3 × 3 3 \times 3 3 × 3 square matrix, which of the following is always true about its transpose
A T A^T A T ?
A. det ( A T ) = − det ( A ) \det(A^T) = -\det(A) det ( A T ) = − det ( A ) B. det ( A T ) = 1 det ( A ) \det(A^T) = \frac{1}{\det(A)} det ( A T ) = d e t ( A ) 1 C. det ( A T ) = det ( A ) \det(A^T) = \det(A) det ( A T ) = det ( A ) D. A T = A − 1 A^T = A^{-1} A T = A − 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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Q44 · determinants (inverse and scalar multiple)
Let
A A A be a
3 × 3 3 \times 3 3 × 3 invertible matrix with determinant
∣ A ∣ = 4 |A| = 4 ∣ A ∣ = 4 . What is the determinant of
2 ( A − 1 ) 2(A^{-1}) 2 ( A − 1 ) ?
A. 1 2 \frac{1}{2} 2 1 B. 2C. 8D. 1 4 \frac{1}{4} 4 1 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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Q45 · radical equations
What is the solution set for the radical equation
x 2 + 3 x = 2 \sqrt{x^2 + 3x} = 2 x 2 + 3 x = 2 ?
A. { 1 , − 4 } \{1, -4\} { 1 , − 4 } B. { 1 , 4 } \{1, 4\} { 1 , 4 } C. { − 1 , 4 } \{-1, 4\} { − 1 , 4 } D. { − 1 , − 4 } \{-1, -4\} { − 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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Q46 · exponential functions (monotonicity)
Given the exponential functions
f ( x ) = 2 x f(x) = 2^x f ( x ) = 2 x and
g ( x ) = 0.5 x g(x) = 0.5^x g ( x ) = 0. 5 x , which statement describes their monotonicity?
A. Both functions are increasing.B. Both functions are decreasing.C. f ( x ) f(x) f ( x ) g ( x ) g(x) g ( x ) D. f ( x ) f(x) f ( x ) g ( x ) g(x) g ( 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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Q47 · arithmetic sequences (sum)
In an arithmetic progression, the first term is 11 and the common difference is
− 13 -13 − 13 . What is the sum of the first 7 terms?
A. -28B. -196C. -67D. 196Worked 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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Q48 · geometric sequences
In a geometric sequence, the first term is
g 1 = 2 g_1 = 2 g 1 = 2 and the fifth term is
g 5 = 8 g_5 = 8 g 5 = 8 (assume the common ratio is positive). What is the value of the 13th term (
g 13 g_{13} g 13 )?
A. 32B. 64C. 128D. 256Worked 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 · repeating decimals
The infinite repeating decimal
0.373737 … 0.373737\ldots 0.373737 … can be expressed as which rational fraction in lowest terms?
A. 37 100 \frac{37}{100} 100 37 B. 37 99 \frac{37}{99} 99 37 C. 37 90 \frac{37}{90} 90 37 D. 1 3 \frac{1}{3} 3 1 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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Q50 · integration (properties)
According to the properties of integration, which of the following is equivalent to
∫ ( 3 f ( x ) − g ( x ) ) d x \int (3f(x) - g(x))\,dx ∫ ( 3 f ( x ) − g ( x )) d x ?
A. 3 ∫ f ( x ) d x ⋅ ∫ g ( x ) d x 3\int f(x)\,dx \cdot \int g(x)\,dx 3 ∫ f ( x ) d x ⋅ ∫ g ( x ) d x B. ∫ 3 f ( x ) d x − ∫ g ( x ) d x \int 3f(x)\,dx - \int g(x)\,dx ∫ 3 f ( x ) d x − ∫ g ( x ) d x C. 3 ( ∫ f ( x ) d x − ∫ g ( x ) d x ) 3\left(\int f(x)\,dx - \int g(x)\,dx\right) 3 ( ∫ f ( x ) d x − ∫ g ( x ) d x ) D. ∫ f ( x ) d x − 3 ∫ g ( x ) d x \int f(x)\,dx - 3\int g(x)\,dx ∫ f ( x ) d x − 3 ∫ g ( x ) d x 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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Q51 · coordinate geometry (parallelogram)
Three vertices of a parallelogram ABCD are
A ( 0 , 0 ) A(0,0) A ( 0 , 0 ) ,
B ( 5 , 0 ) B(5,0) B ( 5 , 0 ) , and
C ( 7 , 4 ) C(7,4) C ( 7 , 4 ) . If AD is parallel to BC, what are the coordinates of vertex D?
A. ( 2 , 4 ) (2,4) ( 2 , 4 ) B. ( − 2 , 4 ) (-2,4) ( − 2 , 4 ) C. ( 12 , 4 ) (12,4) ( 12 , 4 ) D. ( 2 , − 4 ) (2,-4) ( 2 , − 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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Q52 · trigonometry (complementary angles)
If
α \alpha α and
β \beta β are complementary angles (
α + β = 90 ∘ \alpha + \beta = 90^\circ α + β = 9 0 ∘ ), which of the following trigonometric relations is always true?
A. sin ( α ) = sin ( β ) \sin(\alpha) = \sin(\beta) sin ( α ) = sin ( β ) B. tan ( α ) = tan ( β ) \tan(\alpha) = \tan(\beta) tan ( α ) = tan ( β ) C. sin ( α ) = cos ( β ) \sin(\alpha) = \cos(\beta) sin ( α ) = cos ( β ) D. sec ( α ) = cos ( β ) \sec(\alpha) = \cos(\beta) sec ( α ) = cos ( β ) 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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Q53 · statistics (deciles and percentiles)
In descriptive statistics, the third decile (
D 3 D_3 D 3 ) corresponds to which percentile?
A. 3rd percentileB. 30th percentileC. 33rd percentileD. 70th percentileWorked 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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Q54 · matrices (definition)
Which one of the following statements defines a matrix?
A. A matrix is a rectangular array of numbers.B. A matrix is a vertical array of letters.C. A matrix is a horizontal array of letters.D. A matrix is a circular array of numbers.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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Q55 · partial fractions
Which one of the following is the decomposition of the rational expression
3 x 2 + 5 x − 1 ( x + 2 ) ( x + 1 ) 2 \frac{3x^2 + 5x - 1}{(x + 2)(x + 1)^2} ( x + 2 ) ( x + 1 ) 2 3 x 2 + 5 x − 1 as a sum of partial fractions?
A. 2 x + 2 + 3 x + 1 + 1 ( x + 1 ) 2 \frac{2}{x+2} + \frac{3}{x+1} + \frac{1}{(x+1)^2} x + 2 2 + x + 1 3 + ( x + 1 ) 2 1 B. 3 x + 2 − 3 ( x + 1 ) 2 \frac{3}{x+2} - \frac{3}{(x+1)^2} x + 2 3 − ( x + 1 ) 2 3 C. 1 x + 2 + 2 x + 1 − 3 ( x + 1 ) 2 \frac{1}{x+2} + \frac{2}{x+1} - \frac{3}{(x+1)^2} x + 2 1 + x + 1 2 − ( x + 1 ) 2 3 D. 5 x + 2 + 4 ( x + 1 ) 2 \frac{5}{x+2} + \frac{4}{(x+1)^2} x + 2 5 + ( x + 1 ) 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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Q56 · linear programming (modeling)
A farmer having a total capital of Birr 400,000 bought oxen and sheep. An ox costs Birr 60,000 and a sheep Birr 5,000. He sold each ox at Birr 65,000 and each sheep at Birr 6,000. Which one of the following is a representation of the problem in order to maximize his profit, assuming uniform prices where
x x x is the number of oxen and
y y y is the number of sheep?
A. Z ( x , y ) = 6000 x + 5000 y Z(x,y) = 6000x + 5000y Z ( x , y ) = 6000 x + 5000 y x + y ≤ 35 x + y \leq 35 x + y ≤ 35 12 x + y ≤ 80 12x + y \leq 80 12 x + y ≤ 80 x ≥ 0 x \geq 0 x ≥ 0 y ≥ 0 y \geq 0 y ≥ 0 B. Z ( x , y ) = 60000 x + 5000 y Z(x,y) = 60000x + 5000y Z ( x , y ) = 60000 x + 5000 y x + y ≤ 35 x + y \leq 35 x + y ≤ 35 12 x + y ≤ 80 12x + y \leq 80 12 x + y ≤ 80 x ≥ 0 x \geq 0 x ≥ 0 y ≥ 0 y \geq 0 y ≥ 0 C. Z ( x , y ) = 5000 x + 1000 y Z(x,y) = 5000x + 1000y Z ( x , y ) = 5000 x + 1000 y x + y ≤ 35 x + y \leq 35 x + y ≤ 35 12 x + y ≤ 800 12x + y \leq 800 12 x + y ≤ 800 x ≥ 0 x \geq 0 x ≥ 0 y ≥ 0 y \geq 0 y ≥ 0 D. Z ( x , y ) = 5000 x + 1000 y Z(x,y) = 5000x + 1000y Z ( x , y ) = 5000 x + 1000 y x + y ≤ 35 x + y \leq 35 x + y ≤ 35 12 x + y ≤ 80 12x + y \leq 80 12 x + y ≤ 80 x ≥ 0 x \geq 0 x ≥ 0 y ≥ 0 y \geq 0 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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Q57 · real numbers (number line)
Which one of the following statements is true about the given numbers and points on the number line?
A. There is a one-to-one correspondence between the set of natural numbers and points on the number line.B. There is a one-to-one correspondence between the set of rational numbers and points on the number line.C. There is a one-to-one correspondence between the set of irrational numbers and points on the number line.D. There is a one-to-one correspondence between the set of real numbers and points on the number line.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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Q58 · solid geometry (sphere surface area)
A spherical ball has diameter 30 cm. What is its surface area (in
cm 2 \text{cm}^2 cm 2 )?
A. 3600 π 3600\pi 3600 π B. 1000 π 1000\pi 1000 π C. 900 π 900\pi 900 π D. 600 π 600\pi 600 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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