AbrariAbrari
Practice
Menu
PapersTopicsTextbooksCOC / TVET

Unofficial practice · EUEE

2016 E.C. Mathematics Natural stream EUEE past paper

49 questions · 2016 E.C. / 2024 G.C. · Natural stream · unofficial

Unofficial practice for the 2016 E.C. / 2024 G.C. Natural stream Mathematics Ethiopian University Entrance Exam (EUEE / matric). 49 question stems from the Abrari bank are listed below. Not an official Ministry, EAES, MoLS, or OCACC paper.

ይሞክሩ · Try 5

Try 5 Mathematics questions

5 የሒሳብ ጥያቄዎች

መግቢያ አያስፈልግም · No sign-in needed

Unofficial EUEE past-paper items. Not an official key.

1 / 5mathstatistics

Which one of the following is true about the Range and Interquartile Range of a given data?

Unofficial practice. Abrari is an independent study aid and is not affiliated with, endorsed by, or an official product of the Ethiopian Ministry of Education (MoE), EAES, MoLS, or OCACC. Answers are Abrari keys, not an official marking scheme.

Related study

Grade 12 Mathematics textbookMathematics exam topicsFull Mathematics practice

Other Mathematics papers

Questions on this paper

Stems are visible for study. Worked solutions stay inside each item and are unofficial.

Q1 · statistics

Which one of the following is true about the Range and Interquartile Range of a given data?
  1. A. Both are measures of the variability of each item in the data.
  2. B. Both are measures of variation of the data.
  3. C. Both are affected by extreme values in the data.
  4. D. Both are considering only the middle 50% of the data.
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.

Practice this subject

Q2 · binomial-theorem

Which one of the following numbers is the coefficient of x6y4x^{6}y^{4} in the expansion of (x+y)10(x + y)^{10}?
  1. A. 240
  2. B. 1260
  3. C. 210
  4. D. 4860
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.

Practice this subject

Q3 · solid-geometry

The altitude of a frustum of a regular square pyramid is 9 cm. What is the volume of the frustum if the side length of the upper base is 6 cm and the side length of the lower base is 10 cm?
  1. A. 196 cm3^3
  2. B. 324 cm3^3
  3. C. 588 cm3^3
  4. D. 108 cm3^3
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.

Practice this subject

Q5 · circles

A sector of a circle of diameter 8 cm is formed by a central angle of 45°. What is the area of the sector?
  1. A. (2π+8)(2\pi+8) cm²
  2. B. 2π2\pi cm²
  3. C. π\pi cm²
  4. D. 8π8\pi cm²
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.

Practice this subject

Q8 · polynomials

Which one of the following statements is the polynomial division theorem?
  1. A. If ff is a non-constant polynomial and cc is a real number, then x−cx - c is a factor of f(x)f(x) if and only if f(c)=0f(c) = 0.
  2. B. If f(x)f(x) and d(x)d(x) are polynomials such that d(x)≠0d(x) \neq 0 and deg⁡(d(x))≤deg⁡(f(x))\deg(d(x)) \leq \deg(f(x)), then there exist unique polynomials q(x)q(x) and r(x)r(x) such that f(x)=d(x)q(x)+r(x)f(x) = d(x)q(x)+r(x), where r(x)=0r(x) = 0 or deg⁡(r(x))<deg⁡(d(x))\deg(r(x)) < \deg(d(x)).
  3. C. If ff is a non-constant polynomial and cc is a real number, then the remainder when f(x)f(x) divided by x−cx - c is f(c)f(c).
  4. D. Rational root theorem statement.
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.

Practice this subject

Q10 · logic

Let pp and qq be propositions with truth values true and false respectively. Which one of the following statements is NOT correct?
  1. A. p∨qp \vee q is true.
  2. B. p⇔qp \Leftrightarrow q is true.
  3. C. p∧qp \land q is false.
  4. D. p⇒qp \Rightarrow q is false.
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.

Practice this subject

Q11 · sequences-series

Which one of the following is equal to the sum ∑n=152n2\sum_{n=1}^{5} 2n^2?
  1. A. 2+8+18+32+50
  2. B. 2+4+8+16+32
  3. C. 2+4+6+8+10
  4. D. 2+8+16+32+64
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.

Practice this subject

Q12 · linear-programming

A company produces shirts of black and white colors from polyester and cotton. The company has 6000 units of polyester and 3000 units of cotton. A black shirt requires 5 units of polyester and 3 units of cotton, whereas a white shirt requires 3 units of polyester and 3 units of cotton. If the factory gets a profit of Birr 120 from each black shirt and Birr 100 from each white shirt, what is the maximum profit of the company?
  1. A. Birr 200,000
  2. B. Birr 120,000
  3. C. Birr 144,000
  4. D. Birr 164,000
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.

Practice this subject

Q14 · sequences-series

If the fifth and the tenth terms of a geometric sequence are 640 and 20 respectively, then which of the following numbers are the first term and the common ratio of the given geometric sequence respectively?
  1. A. 10240 and 12\frac{1}{2}
  2. B. 1024 and 12\frac{1}{2}
  3. C. 10240 and 2
  4. D. 1024 and 2
Worked solutionUnofficial

Unofficial keyed letter A. A full worked solution is not published for this item yet.

Unofficial — solved by Abrari, not an official EAES key.

Practice this subject

Q15 · conic-sections

Which one of the following conic sections is defined by "the set of points in a plane such that the sum of the distances from two given points is constant"?
  1. A. Circle
  2. B. Hyperbola
  3. C. Parabola
  4. D. Ellipse
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.

Practice this subject

Q16 · trigonometry

Let θ\theta be an angle in standard position and P(−3,4)P(-3, 4) be a point on the terminal side of θ\theta. Which one of the following is true about the corresponding trigonometric functions?
  1. A. cos⁡θ=45\cos\theta = \frac{4}{5}
  2. B. sin⁡θ=−45\sin\theta = -\frac{4}{5}
  3. C. sin⁡θ=35\sin\theta = \frac{3}{5}
  4. D. cos⁡θ=−35\cos\theta = -\frac{3}{5}
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.

Practice this subject

Q17 · vectors

Which one of the following is the position vector of the vector with initial point A(1, -1) and terminal point B(2, -3)?
  1. A. i−2ji-2j
  2. B. i−4ji-4j
  3. C. 3i−4j3i-4j
  4. D. 3i+4j3i+4j
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.

Practice this subject

Q18 · sets

Let A and B be two sets that contain 15 and 17 elements respectively. If A ∩ B contains 10 elements, what is the number of elements in A ∪ B?
  1. A. 32
  2. B. 12
  3. C. 42
  4. D. 22
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.

Practice this subject

Q19 · statistics

Which one of the following is a simple random sampling?
  1. A. Selecting a population into groups formed by dividing the population into groups.
  2. B. First divide a city into ten groups and choose the secondary school principals from the randomly selected 3 groups.
  3. C. Selecting five students from grade 12 students of the same school randomly.
  4. D. First the population is divided into homogenous groups and a sample is selected from each homogenous group.
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.

Practice this subject

Q20 · matrices

Which one of the following numbers is the determinant of the matrix M=(1234567810)M = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10 \end{pmatrix}?
  1. A. 3
  2. B. 6
  3. C. -6
  4. D. -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.

Practice this subject

Q21 · functions

Which one of the following pairs of functions is an inverse of each other in their respective domains?
  1. A. f(x)=x+1x−1f(x) = \frac{x+1}{x-1} and g(x)=x−1x+1g(x) = \frac{x-1}{x+1}
  2. B. f(x)=x5f(x) = x^5 and g(x)=1x5g(x) = \frac{1}{x^5}
  3. C. f(x)=x3−1f(x) = x^3-1 and g(x)=x+13g(x) = \sqrt[3]{x+1}
  4. D. f(x)=x+3f(x) = \sqrt{x+3} and g(x)=x2−9g(x) = x^2-9
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.

Practice this subject

Q22 · coordinate-geometry

Which one of the following ordered pairs of numbers gives the coordinates of the point that divides a line segment with end points A(1, 1) and B(-6, 8) in the ratio of 3:4?
  1. A. (-2, 4)
  2. B. (-2, -4)
  3. C. (2, 4)
  4. D. (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.

Practice this subject

Q23 · statistics

Which one of the following is a primary data?
  1. A. The data obtained from a document prepared by the MOE regarding the achievements of students in a National Examination.
  2. B. The data obtained by reading a journal regarding the opinion of the society about holidays.
  3. C. The data obtained by measuring the heights of students in a certain school.
  4. D. The data obtained from a chart prepared by Ministry of Health regarding the spread of HIV/AIDS.
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.

Practice this subject

Q24 · exponents

Which one of the following is the solution set of the equation (16)2x−1=(40963)3x−5(\sqrt{16})^{2x-1} = (\sqrt[3]{4096})^{3x-5}?
  1. A. {114}\{\frac{11}{4}\}
  2. B. {92}\{\frac{9}{2}\}
  3. C. {112}\{\frac{11}{2}\}
  4. D. {94}\{\frac{9}{4}\}
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.

Practice this subject

Q25 · plane-geometry

If the measure of each interior angle of a regular polygon is 135°, then which one of the following is the number of lines of symmetry of the polygon?
  1. A. 8
  2. B. 6
  3. C. 9
  4. D. 7
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.

Practice this subject

Q27 · plane-geometry

What is the perimeter of a regular hexagon of radius 6 cm?
  1. A. 36.3 cm
  2. B. 18 cm
  3. C. 36 cm
  4. D. 18.3 cm
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.

Practice this subject

Q28 · statistics

Which one of the following is a quantitative data?
  1. A. Checking the quality of a new product.
  2. B. Determining the tastes of foods in a restaurant.
  3. C. Identifying the social status of individuals.
  4. D. Measuring the heights of each students in the given class.
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.

Practice this subject

Q29 · calculus

Which one of the following is true about the integral of a function f(x) with respect to a variable x?
  1. A. ∫f(x) dx\int f(x)\,dx is the set of all derivatives of f.
  2. B. ∫f′(x) dx\int f'(x)\,dx is the set of all derivatives of f.
  3. C. ∫f(x) dx\int f(x)\,dx is the set of all anti-derivatives of f.
  4. D. ∫f′(x) dx\int f'(x)\,dx is the set of all anti-derivatives of f.
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.

Practice this subject

Q30 · financial-math

Which one of the following is NOT a valid reason for saving?
  1. A. For the time of retirement
  2. B. For vacation
  3. C. To maximize interest
  4. D. For betting in football
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.

Practice this subject

Q31 · linear-programming

What is the maximum value of z=2x+3yz = 2x + 3y subject to the constraints x+y≤6x + y \leq 6, 2x−y≤62x - y \leq 6, x≥0x \geq 0, y≥0y \geq 0?
  1. A. 14
  2. B. 22
  3. C. 12
  4. D. 18
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.

Practice this subject

Q32 · sequences-series

Which one of the following is equal to the sum ∑k=17729(31−k)\sum_{k=1}^{7} 729(3^{1-k})?
  1. A. 1092
  2. B. 1079
  3. C. 1093
  4. D. 1088
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.

Practice this subject

Q33 · conic-sections

Which one of the following is an equation of the parabola with vertex V(0, 0) and focus F(2, 0)?
  1. A. y2=18xy^2 = \frac{1}{8}x
  2. B. x2=18yx^2 = \frac{1}{8}y
  3. C. y2=8xy^2 = 8x
  4. D. x2=8yx^2 = 8y
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.

Practice this subject

Q34 · trigonometry

Which one of the following is true about the function f(x) = tan x?
  1. A. The range of f is the set of real numbers, R.
  2. B. The graph of f intersects y-axis at (π2,0)(\frac{\pi}{2}, 0).
  3. C. The domain of f is R∖(−π2,π2)\mathbb{R} \setminus (-\frac{\pi}{2},\frac{\pi}{2}).
  4. D. f is a periodic function with period π2\frac{\pi}{2}.
Worked solutionUnofficial

Unofficial keyed letter A. A full worked solution is not published for this item yet.

Unofficial — solved by Abrari, not an official EAES key.

Practice this subject

Q35 · polynomials

Which one of the following is equal to the polynomial function f(x)=x2+4x+4f(x) = x^2 + 4x + 4?
  1. A. h(x)=(x2+6x+8)−(2x−4)h(x) = (x^2 + 6x + 8) - (2x - 4)
  2. B. l(x)=(x2+10x+3)+(−6x+1)l(x) = (x^2 + 10x + 3) + (-6x + 1)
  3. C. g(x)=x4+4x2+4x2+2g(x) = \frac{x^4 + 4x^2 + 4}{x^2 + 2}
  4. D. k(x)=(x−2)(x+2)k(x) = (x - 2)(x + 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.

Practice this subject

Q36 · sets

Let S, R and T be any three sets. Which one of the following is NOT true about the union of the sets?
  1. A. S∪T=TS\cup T = T
  2. B. S∪S=SS\cup S = S
  3. C. S∪R=R∪SS\cup R = R\cup S
  4. D. (S∪R)∪T=T∪(R∪S)(S\cup R)\cup T = T\cup (R\cup S)
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.

Practice this subject

Q37 · quadratics

Let r1r_1 and r2r_2 be the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0, such that r1+r2=−2.5r_1 + r_2 = -2.5 and r1r2=1.5r_1 r_2 = 1.5. Which one of the following can be the values of a,ba, b and cc respectively?
  1. A. 2, 5, and 3
  2. B. 2, 3, and 5
  3. C. 1, 5, and 6
  4. D. 1, 6, and 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.

Practice this subject

Q38 · statistics

The following data gives the scores of 10 students in a Mathematics examination: 6, 10, 8, 5, 9, 8, 5, 10, 10, 9. Which one of the following is the standard deviation of the given data?
  1. A. 5.8\sqrt{5.8}
  2. B. 3.6\sqrt{3.6}
  3. C. 5.8
  4. D. 3.6
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.

Practice this subject

Q39 · coordinate-geometry

Which of the following pairs of lines with the given equations are parallel?
  1. A. ℓ1:x−2y+1=0\ell_1: x - 2y + 1 = 0 and ℓ2:x+2y−1=0\ell_2: x + 2y - 1 = 0
  2. B. ℓ1:4x−y=2\ell_1: 4x - y = 2 and ℓ2:−x+4y−3=0\ell_2: -x + 4y - 3 = 0
  3. C. ℓ1:2x+3y=5\ell_1: 2x + 3y = 5 and ℓ2:3x+2y=4\ell_2: 3x + 2y = 4
  4. D. ℓ1:x−y+3=0\ell_1: x - y + 3 = 0 and ℓ2:−x+y−9=0\ell_2: -x + y - 9 = 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.

Practice this subject

Q41 · complex-numbers

Let z=−a+2iz = -a + 2i and w=5−biw = 5 - bi be two complex numbers, where aa and bb are real numbers. If z=wz = w, then which one of the following pairs of numbers are equal to aa and bb respectively?
  1. A. −5-5 and 22
  2. B. −5-5 and −2-2
  3. C. 55 and 22
  4. D. 55 and −2-2
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.

Practice this subject

Q42 · statistics

The following table presents the number of traffic accidents in a certain city per year for five consecutive years: 2019: 3500, 2020: 2750, 2021: 2850, 2022: 3500, 2023: 3750. What is the average number of accidents per year for the given five years?
  1. A. 3210
  2. B. 3270
  3. C. 3200
  4. D. 3250
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.

Practice this subject

Q43 · statistics

Consider the data set: 10, 8, 10, 2, 12, 6, 12, 18, 3, 7, 10, 8, 8. Which one of the following is the coefficient of range of the data?
  1. A. 4/5
  2. B. 20
  3. C. 16
  4. D. 5/4
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.

Practice this subject

Q44 · matrices

Let M=(9246−1218150273)M = \begin{pmatrix} 9 & 24 & 6 \\ -12 & 18 & 15 \\ 0 & 27 & 3 \end{pmatrix}. Which one of the following matrices is equal to 23M\frac{2}{3}M?
  1. A. (684−8610092)\begin{pmatrix} 6 & 8 & 4 \\ -8 & 6 & 10 \\ 0 & 9 & 2 \end{pmatrix}
  2. B. (6164−812100182)\begin{pmatrix} 6 & 16 & 4 \\ -8 & 12 & 10 \\ 0 & 18 & 2 \end{pmatrix}
  3. C. (382−465091)\begin{pmatrix} 3 & 8 & 2 \\ -4 & 6 & 5 \\ 0 & 9 & 1 \end{pmatrix}
  4. D. (6162−812100182)\begin{pmatrix} 6 & 16 & 2 \\ -8 & 12 & 10 \\ 0 & 18 & 2 \end{pmatrix}
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.

Practice this subject

Q45 · functions

Which one of the following is an onto function from R\mathbb{R} onto R\mathbb{R}?
  1. A. f(x)=x2+1f(x) = \sqrt{x^2 + 1}
  2. B. f(x)=5x3+1f(x) = 5x^3 + 1
  3. C. f(x)=∣x−1∣f(x) = |x - 1|
  4. D. f(x)=2x−3x2f(x) = 2x - 3x^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.

Practice this subject

Q47 · plane-geometry

If the lengths of the sides of a triangle are 8 cm, 6 cm and 4 cm, then which one of the following is the area of the triangle?
  1. A. 12 cm²
  2. B. 1.5151.5\sqrt{15} cm²
  3. C. 24 cm²
  4. D. 3153\sqrt{15} cm²
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.

Practice this subject

Q48 · exponents

Which one of the following is equal to the expression (125)2/3(81)−3/4(27)−2/3(625)3/4\frac{(125)^{2/3}(81)^{-3/4}}{(27)^{-2/3}(625)^{3/4}}?
  1. A. 53\frac{5}{3}
  2. B. 15
  3. C. 35\frac{3}{5}
  4. D. 115\frac{1}{15}
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.

Practice this subject

Q49 · number-theory

Which one of the following numbers is a common multiple of 324 and 1152?
  1. A. 7776
  2. B. 20736
  3. C. 5184
  4. D. 13824
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.

Practice this subject

Q51 · exponents

Which one of the following is the solution of the equation (243)2x−3=(81)−3x+23(243)^{2x-3} = \frac{(81)^{-3x+2}}{3} in the set of real numbers?
  1. A. 1
  2. B. -2
  3. C. -1
  4. D. 2
Worked solutionUnofficial

Unofficial keyed letter A. A full worked solution is not published for this item yet.

Unofficial — solved by Abrari, not an official EAES key.

Practice this subject

Q52 · solid-geometry

What is the total surface area of a regular square pyramid with slant height 8 cm and base area 25 cm²?
  1. A. 90 cm²
  2. B. 65 cm²
  3. C. 105 cm²
  4. D. 80 cm²
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.

Practice this subject

Q53 · statistics

Grouped scores of Grade 11 students: 31-40: 10, 41-50: 9, 51-60: 15, 61-70: 12, 71-80: 10, 81-90: 4, 91-100: 2. What is the median of the data?
  1. A. 55.5
  2. B. 60.5
  3. C. 50.5
  4. D. 58.5
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.

Practice this subject

Q54 · calculus

What is the area of the region bounded by the graph of f(x)=x3f(x) = x^3 and the x-axis on the interval [−4,2][-4, 2]?
  1. A. 68 square units
  2. B. 136 square units
  3. C. 60 square units
  4. D. 120 square units
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.

Practice this subject

Q55 · functions

Let f(x)=x+1x−1f(x) = \frac{x+1}{x-1} and g(x)=x+2g(x) = \sqrt{x+2}. Which one of the following is true about the combination values of ff and gg at x=2x = 2?
  1. A. (f−g)(2)=−1(f-g)(2) = -1
  2. B. (fg)(2)=23(\frac{f}{g})(2) = \frac{2}{3}
  3. C. (f+g)(2)=3(f+g)(2) = 3
  4. D. (f⋅g)(2)=6(f \cdot g)(2) = 6
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.

Practice this subject

Q56 · exponential-functions

Which one of the following defines an exponential function?
  1. A. f:(0,∞)→Rf:(0,\infty) \to \mathbb{R} defined by f(x)=xbf(x) = x^b, where b>0b > 0 and b≠1b \neq 1.
  2. B. f:R→(0,∞)f:\mathbb{R} \to (0,\infty) defined by f(x)=xbf(x) = x^b, where b>0b > 0 and b≠1b \neq 1.
  3. C. f:(0,∞)→Rf:(0,\infty) \to \mathbb{R} defined by f(x)=bxf(x) = b^x, where b>0b > 0 and b≠1b \neq 1.
  4. D. f:R→(0,∞)f:\mathbb{R} \to (0,\infty) defined by f(x)=bxf(x) = b^x, where b>0b > 0 and b≠1b \neq 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.

Practice this subject

Q59 · calculus

Let ff be differentiable at aa. In the expression f(a+h)−f(a)h\frac{f(a+h) - f(a)}{h} for h≠0h \neq 0, as hh gets closer to zero from both directions, the expression approaches f′(a)f'(a), which is equal to:
  1. A. The gradient of the tangent line to the graph of ff at (a,f(a))(a, f(a)).
  2. B. The gradient of the vertical line to the graph of ff at (a,f(a))(a, f(a)).
  3. C. The gradient of the secant line to the graph of ff at (a,f(a))(a, f(a)).
  4. D. The gradient of the normal line to the graph of ff at (a,f(a))(a, f(a)).
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.

Practice this subject

Q60 · proportion

If 180 individuals can complete a job in 15 days by working 10 hours a day, how many individuals are needed to complete the job in 10 days if they work 12 hours a day?
  1. A. 220
  2. B. 144
  3. C. 225
  4. D. 200
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.

Practice this subject

Frequently asked questions

Are these official EUEE past papers?
No. Abrari publishes unofficial practice reconstructed from the study bank for this 2016 E.C. Mathematics paper. It is not an official EAES or Ministry paper and does not use government logos.
Are the answers official?
No. Letters and worked solutions are unofficial Abrari keys. Verified write-ups are labelled Unofficial. Do not treat them as an official marking scheme.
Is Abrari part of MoE, EAES, MoLS, or OCACC?
No. Abrari is an independent study aid. It is not affiliated with, endorsed by, or an official product of those agencies.
Do I need to pay to practice?
No. The questions on this page are free to read and try. There is no payment step.

Try 5 from this paper