Stems are visible for study. Worked solutions stay inside each item and are unofficial.
Q4 · Similar triangles
A 20m high building casts a shadow of 4m, at the same time a 35m tree casts a shadow of x m. What is the value of x?
A. 8mB. 11mC. 7mD. 15mWorked 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 · Pythagorean / displacement
A car started moving 9km to the East then moved 4 km to the North and then 12km towards West to reach its destination. How far the car it travelled from its starting point?
A. 25kmB. 12kmC. 4kmD. 5kmWorked 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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Q6 · Remainder theorem
When the polynomial
P ( x ) = 3 x 6 + 5 x 4 − 7 x 3 + 2 k x 2 + 3 P(x) = 3x^{6} + 5x^{4} - 7x^{3} + 2kx^{2} + 3 P ( x ) = 3 x 6 + 5 x 4 − 7 x 3 + 2 k x 2 + 3 is divided by (x + 1), the remainder is 4. What is the value of k?
A. -5B. -7C. 3D. 6Worked 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 · Quadratic functions
Which of the following statement is true about
f ( x ) = x 2 − 6 x + 10 f(x) = x^{2} - 6x + 10 f ( x ) = x 2 − 6 x + 10 ?
A. f ( x ) ≥ 2 f(x) \geq 2 f ( x ) ≥ 2 B. The line x = 1 x = 1 x = 1 C. The graph of f opens downward.D. The vertex of the graph of f is (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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Q9 · Area of regular polygon
What is the area of a regular hexagon inscribed in a circle of radius 6cm?
A. 48 3 cm 2 48\sqrt{3} \,\text{cm}^{2} 48 3 cm 2 B. 54 3 cm 2 54\sqrt{3} \,\text{cm}^{2} 54 3 cm 2 C. 48 cm2D. 36 3 cm 2 36\sqrt{3} \,\text{cm}^{2} 36 3 cm 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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Q10 · Number theory
Which of the following defines a prime number?
A. It is a number that has more than two positive factors.B. It is a number whose only factor is 1.C. It is a number that has only two positive factors.D. It is a number whose only factor is itself.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 · Domain of functions
The domain of the function
f ( x ) = 2 x 2 3 f(x) = 2x^{\frac{2}{3}} f ( x ) = 2 x 3 2 is
A. R ∖ { 0 } \mathbb{R}\setminus\{0\} R ∖ { 0 } B. [0,∞)C. R \mathbb{R} R D. (0, 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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Q17 · Slope of a line
The slope of the line that makes an angle of 135° with the positive x-axis is equal to
A. 2B. -1C. 1D. 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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Q18 · Trigonometry (coterminal angles)
If tan31° = 0.81 then what is the value of tan509°
A. 0.19B. -0.81C. 0.81D. -0.91Worked 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 · Trigonometric ratios
If
sin θ = − 3 5 \sin\theta = -\frac{3}{5} sin θ = − 5 3 and
θ \theta θ is a 4th quadrant angle, then what is the value of
sec θ \sec\theta sec θ ?
A. -5/3B. 5/4C. 5/3D. -5/4Worked 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 · Parallelogram properties
If ABCD is a parallelogram with P a mid-point of
A B ‾ \overline{AB} A B and Q a mid-point of
C D ‾ \overline{CD} C D , then which of the following is NOT necessarily true?
A. Δ ADQ ≡ Δ CBP \Delta\text{ADQ} \equiv \Delta\text{CBP} Δ ADQ ≡ Δ CBP B. A Q ‾ ≡ P C ‾ \overline{AQ} \equiv \overline{PC} A Q ≡ PC C. APCD is a trapeziumD. APCQ is a rhombusWorked 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 · Surface area of pyramid
A regular pyramid has a hexagonal base whose side length is 12cm. What is the lateral surface area of the pyramid in square centimeters if the length of each lateral edge is 10cm?
A. 360B. 72C. 288D. 720Worked 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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Q22 · Matrix multiplication
If
( 2 − 1 a 4 ) ( 1 b − 1 3 ) = ( 3 1 − 1 18 ) \begin{pmatrix} 2 & -1 \\ a & 4 \end{pmatrix} \begin{pmatrix} 1 & b \\ -1 & 3 \end{pmatrix} = \begin{pmatrix} 3 & 1 \\ -1 & 18 \end{pmatrix} ( 2 a − 1 4 ) ( 1 − 1 b 3 ) = ( 3 − 1 1 18 ) Then what are the values of a and b respectively?
A. 3, 2B. 2, -2C. -1, 2D. 0, -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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Q23 · Matrix transpose
Let
A = ( 1 − 1 0 2 − 3 6 ) A = \begin{pmatrix}1 & -1 \\0 & 2 \\-3 & 6 \end{pmatrix} A = 1 0 − 3 − 1 2 6 Then A^T is
A. ( 1 0 − 3 − 1 2 6 ) \begin{pmatrix} 1 & 0 & -3 \\ -1 & 2 & 6 \end{pmatrix} ( 1 − 1 0 2 − 3 6 ) B. ( 1 0 − 1 2 − 3 6 ) \begin{pmatrix} 1 & 0 \\ -1 & 2 \\ -3 & 6 \end{pmatrix} 1 − 1 − 3 0 2 6 C. ( − 1 2 6 1 0 6 ) \begin{pmatrix} -1 & 2 & 6 \\ 1 & 0 & 6 \end{pmatrix} ( − 1 1 2 0 6 6 ) D. ( − 1 1 2 0 6 − 3 ) \begin{pmatrix} -1 & 1 \\ 2 & 0 \\ 6 & -3 \end{pmatrix} − 1 2 6 1 0 − 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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Q24 · Logic / quantifiers
On the set of Natural numbers
N \mathbb{N} N , which one of the following propositions has a truth value True?
A. ( ∃ x ) ( ∃ y ) ( x − y = y − x ) (\exists x)(\exists y)(x-y=y-x) ( ∃ x ) ( ∃ y ) ( x − y = y − x ) B. ( ∀ x ) ( ∀ y ) (\forall x)(\forall y) ( ∀ x ) ( ∀ y ) ⟹ x > y ) \implies x > y) ⟹ x > y ) C. ( ∀ x ) ( ∃ y ) ( x − y = 5 ) (\forall x)(\exists y)(x - y = 5) ( ∀ x ) ( ∃ y ) ( x − y = 5 ) D. ( ∀ x ) ( ∃ y ) ( x y < x ) (\forall x)(\exists y)(xy < x) ( ∀ x ) ( ∃ y ) ( x y < x ) 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 · Cumulative frequency
In a certain month of the year, the temperature of a city was recorded with classes 10-14, 15-19, 20-24, 25-29, 30-34 having frequencies 2, 9, 11, 5, 3. Which one of the following is the cumulative frequency of the fourth class?
A. 22B. 27C. 18D. 20Worked 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 · Probability (mutually exclusive)
A fair die is going to be rolled once. E1 = even number, E2 = prime number, E3 = multiple of 3, E4 = multiple of 5. Then which of the following pairs of events are mutually exclusive?
A. E1 and E3B. E3 and E4C. E1 and E2D. E2 and E4Worked 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 · Median (grouped data)
The distribution of the weight of 40 students has classes 40-48, 49-57, 58-66, 67-75, 76-84 with frequencies 8, 18, 7, 5, 2. What is the median weight in kg?
A. 54.5B. 55C. 53D. 53.8Worked 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 · Probability
A group of students, 5 from grade 10, 8 from grade 11 and 2 from grade 12. If a student is chosen randomly, what is the probability that the chosen student is either from grade 10 or grade 12?
A. 7/15B. 5/15C. 12/15D. 1/7Worked 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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Q30 · Logic (compound propositions)
If the truth value of p is T, then which of the following compound propositions has a truth value T for any proposition q?
A. ¬ p ⇔ ( p ∨ ¬ q ) \neg p \Leftrightarrow (p \vee \neg q) ¬ p ⇔ ( p ∨ ¬ q ) B. ( ¬ p ∧ q ) ⇒ q (\neg p \wedge q) \Rightarrow q ( ¬ p ∧ q ) ⇒ q C. ( p ⇒ ¬ p ) ∧ q (p \Rightarrow \neg p) \wedge q ( p ⇒ ¬ p ) ∧ q D. ( p ⇒ q ) ∧ ¬ p (p \Rightarrow q) \wedge \neg p ( p ⇒ q ) ∧ ¬ p 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 · One-to-one functions
Which of the following functions is one to one?
A. f = { ( 1 , 5 ) , ( 2 , 3 ) , ( 5 , 4 ) , ( 6 , 5 ) } f = \{ (1,5), (2,3), (5,4), (6,5) \} f = {( 1 , 5 ) , ( 2 , 3 ) , ( 5 , 4 ) , ( 6 , 5 )} B. f : ( 0 , ∞ ) → R , f ( x ) = ∣ x ∣ − 1 f : (0, \infty) \to \mathbb{R}, \, f(x) = |x| - 1 f : ( 0 , ∞ ) → R , f ( x ) = ∣ x ∣ − 1 C. f : R → R , f ( x ) = x 2 − 1 f: \mathbb{R} \to \mathbb{R}, \, f(x) = x^{2} - 1 f : R → R , f ( x ) = x 2 − 1 D. f = { ( x , y ) ∣ y is the mother of x } f = \{ (x,y) \mid y \text{ is the mother of } x \} f = {( x , y ) ∣ y is the mother of 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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Q32 · Partial fractions
If
x 2 + 14 ( x + 2 ) ( x − 1 ) 2 = A x + 2 + B x − 1 + C ( x − 1 ) 2 \frac{x^{2} + 14}{(x+2)(x-1)^{2}} = \frac{A}{x+2} + \frac{B}{x-1} + \frac{C}{(x-1)^{2}} ( x + 2 ) ( x − 1 ) 2 x 2 + 14 = x + 2 A + x − 1 B + ( x − 1 ) 2 C then what are the values of A, B and C respectively?
A. 1, -1, 3B. 3, -2, 6C. 2, -2, -5D. 2, -1, 5Worked 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 · Symmetry of graphs
Which of the following line is true about the intercept and symmetry of the graph of
f ( x ) = x 3 − 3 x x 2 − 6 f(x) = \frac{x^3 - 3x}{x^2 - 6} f ( x ) = x 2 − 6 x 3 − 3 x ?
A. The graph is symmetrical with respect to the y-axis.B. Its y-intercept is 3.C. Its x-intercepts are ±√6.D. The graph is symmetrical with respect to the origin.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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Q34 · Angle between lines
Consider the lines
l 1 : y = 2 x + 3 l1: y = 2x + 3 l 1 : y = 2 x + 3 and
l 2 : y = 1 − 3 x l2: y = 1-3x l 2 : y = 1 − 3 x . Then the angle between
l 1 l1 l 1 and
l 2 l2 l 2 is
A. π/4B. 3π/2C. π/2D. π/6Worked 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 · Parabola
The equation of the parabola with vertex V(2, -1) and focus F(-1, -1) is
A. ( x + 1 ) 2 = − 12 ( y + 1 ) (x+1)^{2} = -12(y+1) ( x + 1 ) 2 = − 12 ( y + 1 ) B. ( y + 1 ) 2 = − 12 ( x − 2 ) (y+1)^{2} = -12(x-2) ( y + 1 ) 2 = − 12 ( x − 2 ) C. ( y + 1 ) 2 = 12 ( x − 2 ) (y+1)^{2} = 12(x-2) ( y + 1 ) 2 = 12 ( x − 2 ) D. ( x − 2 ) 2 = − 12 ( y + 1 ) (x-2)^{2} = -12(y+1) ( x − 2 ) 2 = − 12 ( y + 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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Q36 · Limits
What is the value of
lim x → 1 x 2 − 1 x 2 + 1 \lim_{x \to 1} \frac{x^{2} - 1}{x^{2} + 1} lim x → 1 x 2 + 1 x 2 − 1 ?
A. 3B. 1C. 2D. 0Worked solutionUnofficial Answer: D
The rational function
x 2 − 1 x 2 + 1 \frac{x^{2}-1}{x^{2}+1} x 2 + 1 x 2 − 1 is defined at
x = 1 x=1 x = 1 because the denominator is
1 2 + 1 = 2 ≠ 0 1^{2}+1=2\neq 0 1 2 + 1 = 2 = 0 . The limit is ordinary substitution.
lim x → 1 x 2 − 1 x 2 + 1 = 1 2 − 1 1 2 + 1 = 0 2 = 0. \lim_{x\to 1}\frac{x^{2}-1}{x^{2}+1}=\frac{1^{2}-1}{1^{2}+1}=\frac{0}{2}=0. x → 1 lim x 2 + 1 x 2 − 1 = 1 2 + 1 1 2 − 1 = 2 0 = 0. Why not A/B/C?
A. 3 3 3 x = 1 x=1 x = 1 1 + 2 1+2 1 + 2 0 0 0 2 2 2 B. 1 1 1 x 2 − 1 x 2 − 1 \frac{x^{2}-1}{x^{2}-1} x 2 − 1 x 2 − 1 2 / 2 2/2 2/2 x 2 + 1 x^{2}+1 x 2 + 1 0 / 2 = 0 0/2=0 0/2 = 0 C. 2 2 2 x = 1 x=1 x = 1 Unofficial — solved by Abrari, not an official EAES key.
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Q37 · Continuity
Which one of the following is the value of a so that the function given by
f ( x ) = { a x + 1 for x ≥ 1 x 2 − 4 for x < 1 f(x) = \begin{cases} ax + 1 & \text{for } x \geq 1\\ x^2 - 4 & \text{for } x < 1\end{cases} f ( x ) = { a x + 1 x 2 − 4 for x ≥ 1 for x < 1 is continuous at 1?
A. 4B. -4C. -1D. 1Worked 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 · Sequences
What is the fifth term of the sequence
{ 2 n + 4 n − 5 } n = 0 ∞ \{ 2^n + 4n - 5 \}_{n=0}^{\infty} { 2 n + 4 n − 5 } n = 0 ∞ ?
A. 27B. 17C. 47D. 15Worked 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 · Bounded sequences
Which one of the following numbers is the upper bounds of the sequence
{ 2 n + 1 n + 1 } n = 1 ∞ \{ \frac{2n + 1}{n + 1} \}_{n=1}^{\infty} { n + 1 2 n + 1 } n = 1 ∞ ?
A. 3/2B. 0C. 1D. 4Worked 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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Q42 · Limits of sequences
Let the sequence {an} converges to 3 while {bn} converges to -1. Then the sequence {an-bn} converges to
A. 1B. 4C. 3D. 1/3Worked 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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Q43 · Logic (validity)
Which of the following argument is valid?
A. p ∨ q , p ⇒ q ⊢ ¬ q p \lor q, \, p \Rightarrow q \vdash \neg q p ∨ q , p ⇒ q ⊢ ¬ q B. p ⇒ q , q , r ⇒ p ⊢ r p \Rightarrow q, \, q, \, r \Rightarrow p \vdash r p ⇒ q , q , r ⇒ p ⊢ r C. p , p ⇒ q , r ∨ ¬ q ⊢ p ∧ r p, \, p \Rightarrow q, \, r \lor \neg q \vdash p \land r p , p ⇒ q , r ∨ ¬ q ⊢ p ∧ r D. p ⇒ q , ¬ r ∧ q ⊢ p ∨ r p \Rightarrow q, \, \neg r \land q \vdash p \lor r p ⇒ q , ¬ r ∧ q ⊢ p ∨ r 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 · Mathematical induction
Which of the following assertions is true applying the Principle of Mathematical Induction?
A. 1 + 2 + 2 2 + … + 2 n = 2 n + 1 − 1 for n ≥ 0 1 + 2 + 2^2 + \ldots + 2^n = 2^{n+1} - 1 \quad \text{for } n \geq 0 1 + 2 + 2 2 + … + 2 n = 2 n + 1 − 1 for n ≥ 0 B. n ! ≥ 2 n for n ≥ 0 n! \geq 2^n \quad \text{for } n \geq 0 n ! ≥ 2 n for n ≥ 0 C. 2 + 3 + 4 + … + n = n ( n + 1 ) 2 + 1 for n ≥ 2 2 + 3 + 4 + \ldots + n = \frac{n(n + 1)}{2} + 1 \quad \text{for } n \geq 2 2 + 3 + 4 + … + n = 2 n ( n + 1 ) + 1 for n ≥ 2 D. 3 + 5 + 7 + … + ( 2 n + 1 ) = n 2 for n ≥ 1 3 + 5 + 7 + \ldots + (2n + 1) = n^2 \quad \text{for } n \geq 1 3 + 5 + 7 + … + ( 2 n + 1 ) = n 2 for n ≥ 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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Q45 · Integration
Which of the following is equal to
∫ 3 cos 3 x d x ∫3\cos 3x\,dx ∫ 3 cos 3 x d x ?
A. 1 3 sin 3 x + c \frac{1}{3}\sin 3x + c 3 1 sin 3 x + c B. sin 3 x + c \sin 3x+c sin 3 x + c C. sin x + c \sin x+c sin x + c D. − sin x + c -\sin x+c − sin x + c 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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Q46 · Area under curve
What is the area of the region bounded by the graph of
f ( x ) = x 2 − 4 f(x) = x^{2} - 4 f ( x ) = x 2 − 4 and the x-axis in square units?
A. 16B. 32C. 16/3D. 32/3Worked 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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Q48 · Coordinate geometry (planes)
Which of the following set of equations define the xz-plane?
A. {(x,y,z)|x,y,z ∈ ℝ and x=9}B. {(x,y,z)|x,y,z ∈ ℝ and y=0}C. {(x,y,z)|x,y,z ∈ ℝ and x=0}D. {(x,y,z)|x,y,z ∈ ℝ and z=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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Q50 · Trigonometric graphs
Which of the following is true about the graph of
y = 3 sin ( 4 x ) y = 3\sin(4x) y = 3 sin ( 4 x ) ?
A. The graph completes one cycle on the interval [0, π].B. The graph lies below the x-axis on ( π/4, π/2 ).C. The graph completes one cycle on the interval [0, π/4].D. The graph rises up on (0, π/4).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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Q52 · Determinants
Let A be a square matrix of order n and let B be a matrix obtained by multiplying one row of A by 2 and C be a matrix found by adding one row of A to another row of A. If det(A) = 10, what are det(B) and det(C)?
A. 20 and 10B. 20 and 0C. 10 and 20D. 10 and 10Worked 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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Q53 · Systems of equations
The solution set of the system
{ 2 x − y + 3 z = 1 x + y + 3 z = 5 x − y + z = − 1 \left\{\begin{aligned}2x - y + 3z &= 1\\x + y + 3z &= 5 \\x - y + z &= -1\end{aligned} \right. ⎩ ⎨ ⎧ 2 x − y + 3 z x + y + 3 z x − y + z = 1 = 5 = − 1 is
A. { ( − 4 − 2 k , k , 2 − k ) : k ∈ R } \left\{ (-4 - 2k, k, 2 - k): k \in \mathbb{R} \right\} { ( − 4 − 2 k , k , 2 − k ) : k ∈ R } B. { ( k + 1 , 2 k , k − 1 ) : k ∈ R } \left\{ (k + 1, 2k, k - 1): k \in \mathbb{R} \right\} { ( k + 1 , 2 k , k − 1 ) : k ∈ R } C. { ( 2 − 2 k , 3 − k , k ) : k ∈ R } \left\{ (2 - 2k, 3 - k, k): k \in \mathbb{R} \right\} { ( 2 − 2 k , 3 − k , k ) : k ∈ R } D. { ( k , k + 1 , k − 1 ) : k ∈ R } \left\{ (k, k + 1, k - 1): k \in \mathbb{R} \right\} { ( k , k + 1 , k − 1 ) : k ∈ R } 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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Q54 · Complex numbers (properties)
Let
z 1 , z 2 , a n d z 3 z1, z2, and z3 z 1 , z 2 , an d z 3 be complex numbers. Then which of the following is NOT necessarily true?
A. z 1 − ( z 2 + z 3 ) = ( z 1 − z 2 ) − z 3 z1 - (z2 + z3) = (z1 - z2) - z3 z 1 − ( z 2 + z 3 ) = ( z 1 − z 2 ) − z 3 B. z 1 − ( z 2 − z 3 ) = ( z 1 − z 2 ) − z 3 z1 - (z2 - z3) = (z1 - z2) - z3 z 1 − ( z 2 − z 3 ) = ( z 1 − z 2 ) − z 3 C. ( z 1 z 2 ) z 3 = ( z 2 z 1 ) z 3 (z1 z2)z3 = (z2 z1) z3 ( z 1 z 2 ) z 3 = ( z 2 z 1 ) z 3 D. ( z 1 z 2 ) z 3 = z 1 ( z 2 z 3 ) (z1 z2)z3 = z1(z2 z3) ( z 1 z 2 ) z 3 = z 1 ( z 2 z 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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Q55 · Complex numbers (Argand plane)
Which of the following complex numbers corresponds to the point (-3, -1) in the Argand plane?
A. -3 + iB. 3 + iC. -1 - 3iD. -3 - iWorked 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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Q56 · Transformations (translation)
If a translation T takes a point (-1, 1) to a point (3, 2), then the image of the circle
x 2 + y 2 − 2 x + 4 y + 1 = 0 x^2 + y^2 - 2x + 4y + 1 = 0 x 2 + y 2 − 2 x + 4 y + 1 = 0 under T is
A. ( x − 3 ) 2 + ( y − 3 ) 2 = 4 (x - 3)^2 + (y - 3)^2 = 4 ( x − 3 ) 2 + ( y − 3 ) 2 = 4 B. ( x − 2 ) 2 + ( y + 3 ) 2 = 4 (x - 2)^2 + (y + 3)^2 = 4 ( x − 2 ) 2 + ( y + 3 ) 2 = 4 C. ( x − 5 ) 2 + ( y + 1 ) 2 = 4 (x - 5)^2 + (y + 1)^2 = 4 ( x − 5 ) 2 + ( y + 1 ) 2 = 4 D. ( x + 3 ) 2 + ( y + 3 ) 2 = 4 (x + 3)^2 + (y + 3)^2 = 4 ( x + 3 ) 2 + ( y + 3 ) 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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Q57 · Vectors
Let u = (-1,6) and v = (2, 4) be position vectors. Then the vector 4u - 3v is
A. (-10,12)B. (-10,11)C. (-4,24)D. (-15,18)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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Q58 · Related rates
Water is running into a conical tank, which is pointed down at a constant rate of 6π cm³/sec. The cone has a height of 10 cm and a base radius of 5 cm, then how fast is the water level rising when the water reaches 2 cm deep?
A. 4 π \frac{4}{\pi} π 4 B. 6 cm/secC. 4 cm/secD. 6 π \frac{6}{\pi} π 6 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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Q59 · Antiderivatives
Let F be the anti-derivative of f. Then which of the following is NOT true about F and f?
A. d d x ∫ F ( x ) d x = f ( x ) \frac{d}{dx} \int F(x) \, dx = f(x) d x d ∫ F ( x ) d x = f ( x ) B. F ′ ( x ) = f ( x ) F^{'}(x) = f(x) F ′ ( x ) = f ( x ) C. ∫ F ( x ) d x = f ( x ) + c \int F(x) \, dx = f(x) + c ∫ F ( x ) d x = f ( x ) + c D. ∫ d d x f ( x ) d x = f ( x ) + c \int \frac{d}{dx} f(x) \, dx = f(x) + c ∫ d x d f ( x ) d x = f ( x ) + c 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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Q60 · Derivatives (tangent slopes)
Let
f ( x ) = 1 x f(x) = \frac{1}{\sqrt{x}} f ( x ) = x 1 and
g ( x ) = 2 − 1 6 x 3 g(x) = 2 - \frac{1}{6}x^{3} g ( x ) = 2 − 6 1 x 3 be two functions. For what values of x do the graphs of f and g have tangent lines of the same slope?
A. 3 2 \frac{\sqrt{3}}{2} 2 3 B. 1C. 4D. 1/4Worked 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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Q61 · Mean Value Theorem
What is the value of a number in the interval (0, 1) that satisfies the Mean Value Theorem for the function
f ( x ) = 3 x 2 − 5 x + 1 f(x) = 3x^2 - 5x + 1 f ( x ) = 3 x 2 − 5 x + 1 ?
A. 1/2B. 3/5C. 5/6D. 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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Q63 · Chain rule
Let f and g be differentiable functions, and
h ( x ) = g ( f ( 3 x + 1 ) ) h(x) = g(f(3x+1)) h ( x ) = g ( f ( 3 x + 1 )) . If
f ′ ( 1 ) = f ( 1 ) = 2 f^{'}(1) = f(1) = 2 f ′ ( 1 ) = f ( 1 ) = 2 and
g ′ ( 2 ) = 1 g^{'}(2) = 1 g ′ ( 2 ) = 1 , then what is the value of
h ′ ( 0 ) h^{'}(0) h ′ ( 0 ) ?
A. 2B. 1C. 6D. 4Worked 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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Q64 · Concept of derivative
Which of the following describes the mechanical meaning of derivative?
A. Gradient of graphs of functionsB. Area under the curveC. Instantaneous rate of changeD. Slope of tangent lineWorked 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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Q65 · Zeros of functions
Which of the following is true about the zero(s) of a function f(x)?
A. If f(a)=0, then x-a is a factor for f(x).B. If f(a)=0, then (x-a)² is a factor of f(x).C. If f(a)=0, then a is not necessarily in the domain.D. If f(a)=0, then y=a is the y-intercept.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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