Welcome to your MATHEMATICS ENTRANCE 2016
1.
Let f(x) = (x + 1)/(x - 1) and g(x) = √(x + 2) be two functions. Which one of the following is true about the combination values of f and g at x = 2?
2.
Which one of the following defines an exponential function?
3.
Let f be a differentiable function at a number 'a' for a ∈ Domain f. In the expression (f(a+h) - f(a))/h for h≠0, as h gets closer and closer to zero from both directions, the expression becomes closer to f'(a) which is equal to
4.
In the following figure, O is the center of the circle and the line segments AB and AC are intersecting the circle at D and E respectively. If m(∠ACD)=30° and m(∠BEC)=50°, then which one of the following is equal to m(∠BAC)?
5.
Let P and q be propositions. Which one of the following propositions is a tautology?
6.
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?
7.
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?
8.
Consider the following graph of a given exponential function f (x)
Which one of the following functions represents the graph shown above?
9.
What is the perimeter of a regular hexagon of side 3 cm?
10.
Which one of the following is a quantitative data?
11.
Which one of the following is true about the integral of a function f(x) with respect to a variable x ?
12.
Which one of the following is NOT a valid reason for saving?
13.
The shaded region in the following figure is the graph of a relation R.
Which one of the following is the domain and range of R respectively?
14.
Which one of the following statements is the polynomial division theorem?
15.
Which one of the following is equal to cot (1755°)?
16.
Let p and q be propositions with truth values true and false respectively. Which one of the following statements is NOT correct?
17.
Which one of the following is equal to the sum Σ (2n²) ?
18.
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 in its store. A black shirt requires 5 units of polyester and 4 units of cotton where as 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 200 from each white shirt, what is the maximum profit of the company?
19.
Let S, R, and T be any three sets. Which one of the following is NOT true about the union of the sets?
20.
Which one of the following is equal to the polynomial function
21.
Which one of the following is true about the function f(x) = tan x ?
22.
Which one of the following is an equation of the parabola with vertex V(0,0) and focus F(2,0) ?
23.
Which one of the following is equal to the sum
24.
hat is the maximum value of z = 2x + 3y subject to the constraints:
25.
which one of the following numbers is common multiple of 324 and 1152?
28.
What is the total surface area of a regular square pyramid with slant height 8 cm and base area 25 cm²?
29.
The following table presents the scores of Grade 11 students of a certain school in a Mathematics Examination.
What is the median of the data given in the above table?
30.
What is the area of the region bounded by the graph of f(x) = x³ and the x-axis on the interval [-4, 2]?
31.
If a = 2 - 3√5 and b = 3 + 2√5, then which one of the following is true?
32.
A sector of a circle diameter 8 cm is formed by a central angle of 45°. What is the area of the sector?
33.
Which one of the following intervals is the solution set of the inequality |3 - (1/2)x| < 5?
34.
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?
35.
Which one of the following numbers is the coefficient of x⁶y⁴ in the expansion of (x + y)¹⁰?
36.
Which one of the following is true about the Range and Interquartile Range of a given data?
37.
Which one of the following is equal to the expression (125)^(2/3) * (81)^(-3/4) / (27)^(-2/3) * (625)^(3/4)?
38.
If the length 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?
39.
The following figure is the graph of a quadratic function f(x) = ax² + bx + c in the set of real numbers.
Which one of the following is the solution set of the inequality f(x) ≤ 0?
40.
Which one of the following is an onto function from R onto R?
42.
Consider that a data set is given below:
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?
43.
Let r₁ and r₂ be the roots of a quadratic equation ax² + bx + c = 0, such that r₁ + r₂ = -2.5 and r₁r₂ = 1.5, for a, b, and c are real numbers and a ≠ 0. Which one of the following can be the values of a, b, and c respectively?
