Welcome to your 2016 E.C GRADE 12 MATHEMATICS social science MODEL EXAMINATION
GRADE 12 MATHEMATICS (FOR NATURAL SCIENCE) MODEL EXAMINATIONS
2016E.C/ 2024G.C
1.
For what values of B the function f: R → B such that f(x) = x^2 + 6x + 3 is an onto function?
2.
What is the inverse of the function f(x) = (x+1)/(2x-1)?
3.
If f(x) = π² + 1, then f'(x) =
4.
Let f(x) = 6x/(x + a). For what value of a is f'(a) = 1?
5.
If f(x) = x²√(2x + 12), what is the slope of the tangent line to the graph of f at x = 2?
6.
What is the equation of the normal line to the graph of f(x) = 3x² + 4x - 5 at (1,2)?
7.
For what value(s) of x does the graph of f(x) = √(x² - x) have a vertical tangent line?
8.
Which one of the following is not a rational expression?
9.
Which one of the following is the partial fraction of 2x/(x² - 4)?
10.
What is the center and radius of the circle with equation x² + y² - 4x + 6y + 8 = 0?
11.
What is the distance between the point P(-2, -3) and the line L: 12x - 5y - 30 = 0?
12.
If A = [1 2; -2 0], B = [-1 -2; 3 1] and C = [1 0; 0 -1], then 3A - 2B + 2C is:
13.
For a square matrix A and a non-singular matrix B of the same order, the value of the determinant of A⁻¹BA is equal to:
14.
If A = [5 2y-3x 2; -2 3 6; 3 0 4] and B = [5 -2 2; -2 3 4x-y; 3 0 4], where A = B. What is the value of the variables x and y respectively?
15.
What is the determinant of matrix A = [2 0 -2; 1 0 3; 7 0 5]?
16.
If A is a 3×3 matrix with det(A) = 6, then what is det(2Aᵀ)?
17.
Which of the following is neither an arithmetic nor a geometric progression?
18.
In an A.P., if a₅ = 10 and a₁₀ = 45, what is the common difference and the first term?
19.
If x + 3, 2x + 3 and 4x - 1 are consecutive terms of a Geometric progression, then what is the possible value of x?
20.
In an arithmetic progression, if A₁ = 1, Aₙ = 20 and Sₙ = 399, then what is the value of n?
21.
What is the sum of ∑_{n=2}^{20} (1/(n-1) - 1/n)?
22.
If A₁ = 4 and d = 5 of an arithmetic progression, then what is the value of S₁₂?
23.
What is the nth term of an arithmetic progression whose nth partial sum is 5n² - 1?
24.
It is given that a, b, c, d, e are an arithmetic sequence. If a + b + c = 9 and d + e = 26, what is the first term and common difference respectively?
25.
If {aₙ} is a sequence such that a₁ = 2 and aₙ₊₁ = aₙ + 4 for all n ≥ 1, then ∑_{n=1}^{35} aₙ is equal to:
26.
The sum of the series ∑_{n=0}^∞ 5(2/3)ⁿ is equal to:
27.
The sum of the first 12 terms of a geometric sequence with first term 0.3 and common ratio 0.1 is equal to:
28.
A certain item gains one-tenth of its value each year. If the item is worth Birr 30,000 today, how much will it be worth 3 years from now?
29.
The equation of an ellipse with center at (1,4) and vertices at (10,4) and (1,2) is:
30.
If the equation (x - 2)² - (y + 2)² = 1 represents a hyperbola, which one of the following represents the equation of an asymptote of the hyperbola?
31.
If A(5, -5), B(4, 4) and C(0, 2) are the vertices of △ABC and AD ⊥ BC as shown figure 1.1 below. Find the equation of altitude AD.
32.
Which one of the following is not true about the equation of the parabola y = -½x²?
33.
If f is integrable on a closed interval [a,b] and c ∈ [a,b], then which one of the following properties is not true about f?
34.
What is the area of the region bounded by f(x) = x² + 3 and x-axis on the closed interval [-1, 3]?
35.
If f(x) = 2x³ - 5x, then what is the value of (f(1 + h) - f(1))/h as h → 0?
36.
Let f(x) = x³ - 3x, what is the possible values of x at which the slope of the line tangent to f(x) is 9?
37.
Which one of the following is the average rate of change the function f(x) = x³ + 9x + 6, on the interval 0 ≤ x ≤ 3.
38.
Which one of the following is the instantaneous rate of change of the function f(x) = 12x² + 8x at x = -3?
39.
For what values of B the function f: R → B such that f(x) = x² + 6x + 3 is an onto function?
40.
what is the inverse of the function f(x) = (x + 1)/(2x - 1)
41.
Which of the following is true about the function f(x) = 2x³?
42.
which of the following is a valid logical argument?
43.
If the truth value of p is T, then which of the following compound propositions has a truth value T for any proposition q?
44.
Which of the following sentences is a statement?
45.
Consider the following frequency distribution table
What is the sixth decile?
46.
The following is the frequency of a grouped data. The mean of the following frequency table is 50. Then what is the value of f₁ and f₂ respectively.
47.
How many three-digit numbers can be formed from 3, 4, 5, 6 and 7 if each digit is used at most once?
48.
A fair die is tossed once. the probability that either an even number or 3 will be appear is
49.
A committee of 3 members is to be selected from 4 men and 5 women. what is the probability of selecting exactly two women in the committee?
50.
A group of 8 students mean average score is 67 in a test, a second group of 17 student has a mean average score of 81 in the same test. What is the mean average score of all 25 students?
51.
Let Z be complex number. Then the solution set of z² - z + 1 = 0
52.
If z = 4 + 4√3 then what is principal argument of z¹⁰?
53.
what is the modulus of z = 1 - i√3?
54.
What is the sum of all multiples of 4 that are between 30 and 301?
55.
If y = 3/x³, then what is value of dy/dx |_{x=1}
56.
On which of the following interval f(x) = 2x⁵ + 3 increase?
57.
If the Volume of sphere is increasing at rate of 0.4π cm³/s, then what is the rate of increase of the radius at r = 10 cm?
58.
The maximum value of the objective function Z = 8x + 10y subject to 2x + 5y ≤ 10, x ≥ 0, y ≥ 0 is:
59.
.
The possible values of x and y which minimizes the value of the Objective function Z = -4x + y Subject to x + y ≤ 7
x - y ≤ 3,
y ≤ 4
x ≥ 0, y ≥ 0 are
60.
A profit of Birr 19000 is to be divided between three friends in the ratio of 6:1:3. Then how much will the third person receive?
61.
In an examination 25% of the candidates were absent. 65% of those who appeared were passed and if 525 candidates were failed. Then how many of those were enrolled in the examination?
62.
Which is the best deal?
63.
A pair of shoes has a markup of Birr 75, which is 15% of the selling price. Then the value of the selling price is?
64.
One of the following is indirect tax
65.
A carpenter’s daily production of chairs increased from 30 to 45 units. At the same time his income increased from 2400 Birr to 3000 Birr. Then what is the rate of change of income in Birr
66.
A farmer has Birr 17000 to buy sheep and goats. Suppose the unit price of sheep is Birr 3000 and the unit price of goats is Birr 2000. Then which of the following is not a possible purchase?
