Welcome to your 2016 E.C GRADE 12 MATHEMATICS N.SC 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.
Which of the following is TRUE about the function f(x) = 2x^(2/3)?
32.
Which of the following is a valid logical argument?
33.
If the truth value of p is T, then which of the following compound propositions has a truth value T for any proposition q?
34.
Which of the following sentences is a statement?
35.
Consider the following frequency distribution table:
What is the sixth decile?
36.
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?
37.
How many three-digit numbers can be formed from 3,4,5,6 and 7 if each digit is used at most once?
38.
A fair die is tossed once. The probability that either an even number or 3 will appear is:
39.
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?
40.
A group of 8 students mean average score is 67 in a test, a second group of 17 students has a mean average score of 81 in the same test. What is the mean average score of all 25 students?
41.
Let Z be a complex number. Then the solution set of z² - z + 1 = 0 is:
42.
If z = 4 + 4√3i, then what is the principal argument of z¹⁰?
43.
What is the modulus of 1 - i√3?
44.
A translation takes x² + (y + 1)² = 5 to (x - 2)² + y² = 5. Then what is the image of (1,3) under this transformation?
45.
What is the cosine of the angle between u = (1,-1) and v = (1,1)?
46.
What is the image of (-1,5) when reflected about the line l: y = x - 2?
47.
What is the image of the circle x² + y² - 4x - 6y + 12 = 0 when it is reflected with respect to the line y = -x?
48.
Which of the following is true?
49.
If cot(θ) = 2, then which of the following is equal to csc(θ)?
50.
What is the period (P) and the range (R) of f(x) = 5 sin((1/3)x + 2) + 3?
51.
What is the value of cot270° + 2cos90° + 4sec²180°?
52.
What is the sum of all multiples of 4 that are between 30 and 301?
53.
If y = 3/x³, then what is the value of dy/dx at x = 1?
54.
On which of the following intervals does f(x) = 2x⁵ + 3 increase?
55.
If the volume of a sphere is increasing at a rate of 0.4π cm³/s, then what is the rate of increase of the radius at r = 10 cm?
56.
If g(x) = x f(x) - √f(x), f(2) = f'(2) = 4, then which of the following is equal to g'(2)?
57.
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?
58.
What is the area of the region bounded by f(x) = x² + 3 and the x-axis on the closed interval [-1, 3]?
59.
If f(x) = x⁵ + 2x, then what is the value of (f(1+h) - f(1))/h as h → 0?
60.
Let f(x) = x³ - 3x. What are the possible values of x at which the slope of the line tangent to f(x) is 0?
61.
Which one of the following is the average rate of change of the function f(x) = x³ - 9x on the interval 1 ≤ x ≤ 6?
62.
Which one of the following is the instantaneous rate of change of the function f(x) = 2x² + 9 at x = 3?
63.
If A(5, -5), B(4, 4) and C(0, 2) are the vertices of △ABC and AD ⊥ BC as shown in figure 1.1 below. Find the equation of altitude AD.
64.
The sum of the series ∑_{n=0}^∞ 5(2/3)ⁿ is equal to:
