Stems are visible for study. Worked solutions stay inside each item and are unofficial.
Q1 · Number theory
In the set of natural numbers, which one of the following defines a composite number?
A. A number that has only two distinct factors.B. A number that is divisible by numbers from 2 to 9.C. A number that has two or more different factors.D. A number that has three or more different divisors.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 · Radicals
Which of the following is true about rationalizing the denominator?
A. Only denominators can be multiplied by an irrational number.B. Only numerators can be rationalized when there is a radical.C. It is a method of changing the denominator into a rational number.D. It is a technique of multiplying a given number by an irrational expression.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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Q3 · Division algorithm
When dividing 142 by 13 and expressed the result by applying the division algorithm, we get?
A. 142 = 10 ( 13 ) + 2 142 = 10(13) + 2 142 = 10 ( 13 ) + 2 B. 142 = 11 ( 13 ) − 1 142 = 11(13) - 1 142 = 11 ( 13 ) − 1 C. 142 = 11 ( 13 ) + 1 142 = 11(13) + 1 142 = 11 ( 13 ) + 1 D. 142 = 10 ( 14 ) + 2 142 = 10(14) + 2 142 = 10 ( 14 ) + 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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Q6 · Similar figures
Which one of the following refers to the definition of similar plane figures?
A. Figures whose corresponding angles have the same ratio.B. Figures where one is an enlargement of the other.C. Figures whose ratios of length of corresponding sides are different.D. Figures that have different shapes but might have same size.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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Q7 · Right triangle trig
In
△ A B C \triangle ABC △ A BC , m(<B) = 90°, m(<A) = 30° and BC = 11cm, then what is the length of
A C ‾ \overline{AC} A C ?
A. 22 cmB. 22 3 3 \frac{22\sqrt{3}}{3} 3 22 3 C. 11 3 11\sqrt{3} 11 3 D. 11 3 3 \frac{11\sqrt{3}}{3} 3 11 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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Q8 · Circle chord
Given a circle of diameter 16 cm, a chord of the circle is 6 cm far from the center. Which of the following is the length of the chord?
A. 2 7 2\sqrt{7} 2 7 B. 8 cmC. 4 7 4\sqrt{7} 4 7 D. 16 cmWorked 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 · Statistics - mean
Let
x ‾ \overline{x} x denote the arithmetic mean. If each observation is multiplied by 0.5, which is the new mean?
A. x ‾ \overline{x} x B. 1 2 x ‾ \frac{1}{2}\overline{x} 2 1 x C. 2 x ‾ 2\overline{x} 2 x D. x ‾ − 0.5 \overline{x}- 0.5 x − 0.5 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 · Probability
A regular triangular pyramid labeled 1, 2 and 3 is thrown twice. What is the probability that the sum of the numbers faced down is less than 5?
A. 1 3 \frac{1}{3} 3 1 B. 2 3 \frac{2}{3} 3 2 C. 4 9 \frac{4}{9} 9 4 D. 5 9 \frac{5}{9} 9 5 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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Q13 · Polynomial function
Which one of the following is the definition of a polynomial function?
A. f ( x ) = a n x n + a n − 1 x n − 1 + . . . + a 1 x + a 0 f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 f ( x ) = a n x n + a n − 1 x n − 1 + ... + a 1 x + a 0 a n ≠ 0 a_n \ne 0 a n = 0 R \mathbb{R} R B. f ( x ) = a n x n + . . . + a 1 x n + 1 + a 0 f(x) = a_n x^n + ... + a_1 x^{n+1} + a_0 f ( x ) = a n x n + ... + a 1 x n + 1 + a 0 C. f ( x ) = a n x n + . . . + a 1 x n − 1 + a 0 f(x) = a_n x^n + ... + a_1 x^{n-1} + a_0 f ( x ) = a n x n + ... + a 1 x n − 1 + a 0 D. f ( x ) = a n x n − a n − 1 x n − 1 + . . . + a 1 x + a 0 f(x) = a_n x^n - a_{n-1} x^{n-1} + ... + a_1 x + a_0 f ( x ) = a n x n − a n − 1 x n − 1 + ... + a 1 x + a 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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Q14 · Remainder theorem
When
f ( x ) = 4 x 3 + k x − 1 f(x) = 4x^3 + kx - 1 f ( x ) = 4 x 3 + k x − 1 is divided by
x − 1 2 x - \frac{1}{2} x − 2 1 , the remainder is 3, what is the value of k?
A. 14B. 7C. 7 2 \frac{7}{2} 2 7 D. 9Worked 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 · Logarithms
What is the solution set of the equation
log 4 ( x + 1 ) − 2 log 4 x = 0.5 \log_4(x + 1) - 2\log_4 x = 0.5 log 4 ( x + 1 ) − 2 log 4 x = 0.5 ?
A. { 1 , − 1 2 } \{1, -\frac{1}{2}\} { 1 , − 2 1 } B. { 1 2 , − 1 } \{\frac{1}{2}, -1\} { 2 1 , − 1 } C. { 1 } \{1\} { 1 } 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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Q16 · Logarithms - characteristic
Which of the following is the characteristic of
log ( 20 + 1 5 ) \log(20 + \frac{1}{5}) log ( 20 + 5 1 ) ?
A. -1B. 1C. 2.02D. 0.2Worked 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 · Trigonometric values
Which of the following is true about a trigonometric value of angles?
A. sin ( 270 ∘ ) = 0 \sin(270^\circ) = 0 sin ( 27 0 ∘ ) = 0 B. cos ( − 180 ∘ ) = − 1 \cos(-180^\circ) = -1 cos ( − 18 0 ∘ ) = − 1 C. tan ( − 90 ∘ ) = 0 \tan(-90^\circ) = 0 tan ( − 9 0 ∘ ) = 0 D. cot ( 540 ∘ ) = − 1 \cot(540^\circ) = -1 cot ( 54 0 ∘ ) = − 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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Q23 · Co-function identities
For
0 ∘ ≤ θ ≤ 90 ∘ 0^\circ \le \theta \le 90^\circ 0 ∘ ≤ θ ≤ 9 0 ∘ , which of the following relationships describes the co-relationship of angle
θ \theta θ ?
A. cos θ \cos \theta cos θ B. csc θ \csc \theta csc θ C. cot θ \cot \theta cot θ D. sec θ \sec \theta sec θ 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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Q25 · Rhombus
Let ABCD be a Rhombus and E be the mid-point of the shortest diagonal AC. Then which of the following is NOT true?
A. Δ A B C \Delta ABC Δ A BC B. A C ‾ \overline{AC} A C C. Δ B E C \Delta BEC Δ BEC D. Δ D A B \Delta DAB Δ D A 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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Q26 · Regular hexagon
A person would like to fence all sides of a regular hexagonal polygonal park of radius 12 meter. What is the length of a fencing material needed in meter?
A. 72 3 72\sqrt{3} 72 3 B. 72C. 36 3 36\sqrt{3} 36 3 D. 36Worked 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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Q27 · Cylinder volume
Given a right circular cylinder of base radius 5 cm and lateral surface area
150 π 150\pi 150 π sq. cm, which is the volume in cubic centimeters?
A. 375 π 375\pi 375 π B. 350 π 350\pi 350 π C. 315.5 π 315.5\pi 315.5 π D. 200 π 200\pi 200 π 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 · Sphere volume
A spherical container of diameter 3 meters is filled with water. What is the amount of water in cubic meters?
A. 27 4 π \frac{27}{4}\pi 4 27 π B. 27 2 π \frac{27}{2}\pi 2 27 π C. 9 2 π \frac{9}{2}\pi 2 9 π D. 9 4 π \frac{9}{4}\pi 4 9 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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Q30 · Inverse functions
Which of the following is the inverse of
f ( x ) = x − 3 f(x) = \sqrt{x - 3} f ( x ) = x − 3 ?
A. f − 1 ( x ) = x 2 + 3 , x ≥ 0 f^{-1}(x) = x^2 + 3, x \ge 0 f − 1 ( x ) = x 2 + 3 , x ≥ 0 B. f − 1 ( x ) = x 2 + 3 , x ≥ 3 f^{-1}(x) = x^2 + 3, x \ge 3 f − 1 ( x ) = x 2 + 3 , x ≥ 3 C. f − 1 ( x ) = x + 3 , − ∞ < x < ∞ f^{-1}(x) = \sqrt{x + 3}, -\infty < x < \infty f − 1 ( x ) = x + 3 , − ∞ < x < ∞ D. f − 1 ( x ) = 1 x − 3 , x ≥ 3 f^{-1}(x) = \frac{1}{\sqrt{x - 3}}, x \ge 3 f − 1 ( x ) = x − 3 1 , x ≥ 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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Q31 · Rational expressions
Which of the following is the simplified form of
[ x − x + 3 x − 1 ] ÷ x − 3 x 2 − 2 x + 1 [x-\frac{x + 3}{x - 1}] \div \frac{x - 3}{x^2 - 2x + 1} [ x − x − 1 x + 3 ] ÷ x 2 − 2 x + 1 x − 3 ?
A. x 2 − 2 x + 3 x − 1 , x ≠ 3 \frac{x^2 - 2x + 3}{x - 1}, x \ne 3 x − 1 x 2 − 2 x + 3 , x = 3 B. − 1 + x x − 3 , x ≠ 1 \frac{-1 + x}{x-3}, x \ne 1 x − 3 − 1 + x , x = 1 C. x 2 − 1 , x ≠ 1 , 3 x^2 - 1, x \ne 1, 3 x 2 − 1 , x = 1 , 3 D. x 2 − 2 x + 1 , x ≠ 1 , 3 x^2 - 2x + 1, x \ne 1,3 x 2 − 2 x + 1 , x = 1 , 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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Q32 · Class interval
A data on scores of 32 students (min 32, max 78). If the data is to be grouped in 6 classes, what has to be the class interval (w)?
A. 6B. 7C. 8D. 9Worked 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 · Permutations
Five English books, 3 of which identical, and 3 different Mathematics books are to be arranged in a row. If one particular Mathematics book is placed first, in how many ways can this be done?
A. 240B. 840C. 5040D. 6720Worked 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 · Probability
Identical balls labeled 1 to 10 are placed in a box. If a ball is drawn at random, what is the probability that the ball is labeled neither odd nor a multiple of 3?
A. 3 10 \frac{3}{10} 10 3 B. 1 2 \frac{1}{2} 2 1 C. 3 5 \frac{3}{5} 5 3 D. 2 5 \frac{2}{5} 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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Q37 · Complex numbers
If
w = i − 3 + i 5 w = i - \frac{3+i}{5} w = i − 5 3 + i , then which of the following is equal to the modulus of w?
A. 3 5 5 \frac{3}{5}\sqrt{5} 5 3 5 B. 1 1 1 C. 1 − 1 5 10 1 - \frac{1}{5}\sqrt{10} 1 − 5 1 10 D. 1 + 1 5 10 1 + \frac{1}{5}\sqrt{10} 1 + 5 1 10 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 · Sequences
Few terms of a sequence are given: -2, 0, 4, 10, ... Which of the following can be a fifth term?
A. 14B. 16C. 18D. 20Worked 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 · Infinite series
Suppose a and b are real numbers with a ≠ 0 and b > 0. If
∑ n = 1 ∞ b ( a b ) n \sum_{n=1}^{\infty} b(\frac{a}{b})^n ∑ n = 1 ∞ b ( b a ) n converges, which of the following is true?
A. ∣ a ∣ = b |a| = b ∣ a ∣ = b B. ∣ a ∣ > b |a| > b ∣ a ∣ > b C. a < b a < b a < b D. ∣ a ∣ < b |a| < b ∣ a ∣ < 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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Q41 · Average rate of change
An enterprise found its profit by
f ( t ) = t 2 − t + 100 f(t) = t^2 - t + 100 f ( t ) = t 2 − t + 100 , t in days. Which of the following is the average rate of change of its profit on
0 ≤ t ≤ 2 0 \leq t \leq 2 0 ≤ t ≤ 2 ?
A. f ( 0 ) − f ( 2 ) 2 \frac{f(0) - f(2)}{2} 2 f ( 0 ) − f ( 2 ) B. f ( 2 ) − f ( 1 ) 2 \frac{f(2) - f(1)}{2} 2 f ( 2 ) − f ( 1 ) C. f ( 2 ) − f ( t ) t − 2 \frac{f(2) - f(t)}{t-2} t − 2 f ( 2 ) − f ( t ) D. 1 2 ( f ( 2 ) − f ( 0 ) ) \frac{1}{2}(f(2) - f(0)) 2 1 ( f ( 2 ) − f ( 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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Q43 · Integration
Which of the following gives the definition of integration for a function?
A. It is a process of reversing the derivative of the function.B. It is the derivative of a function at a point.C. It is the rate of change of a function.D. It is the derivative of a function on the given intervalWorked 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 · Coefficient of range
Given two sets of data A and B with ranges 15 and 15 respectively, coefficient of range (CR) of A is 0.2 and CR of B is 0.21. Then which of the following is true?
A. The dispersion of A is slightly greater than that of B.B. The dispersion of B is slightly greater than that of A.C. Data A has the same dispersion as B even if CR varies.D. No enough information to compare dispersion roughly.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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Q47 · Sampling
In a homogeneous population where there is a categorical difference, items are selected randomly in each category. Which of the following describes the sampling method?
A. Simple random samplingB. Systematic samplingC. Stratified samplingD. Cluster 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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