Welcome to your GRADE 12 MATHEMATICS N.Sc MODEL EXAMINATIONS 2017
MATHEMATICS MODEL
EXAMINATION FOR GRADE 12 NATURAL SCIENCES 2017
1.
Which one of the following defines prime number?
2.
he GCF of two numbers is 9 and their LCM is 54. If one of the number is 18. What is the other number?
3.
If x = 0.424424442... and y = 0.242242224... then the fraction form of x + y is equal to:
4.
For any real numbers a, b and c. Which one of the following is true?
5.
The simplified form of (6√20 - 3√45) / (3√75) is equal to:
6.
Let a and b be positive integers and p and q are real numbers. Which of the following is true?
7.
Which one of the following is the rationalizing factor to rationalize the denominator of 7 / (3 + √5)?
8.
According to division algorithm what should be the value of q and r respectively so that 290 = 11q + r?
9.
If 8^(3x - 1) = (1/2)^(4x) * 128^(-x - 1). What is the value of x?
10.
Kidest bought 2 kilogram of sugar and a can of tomato and paid 100 birr. Her sister Tigist paid 150 birr for a kilogram of sugar and 3 cans of tomato. What was the price of a can of tomato?
11.
Let {4x - 8y = -3, 2x + ky = 16} be a system of linear equations in two variables. What is the value of k so that the system of equation has no solution?
12.
Which of the following is the solution set of the equation |3 - 2x| = |x - 6|?
13.
The solution set of the quadratic equation 2x(x + 3) - 4x = 4 - 6x² + 6x is:
14.
If one root of the quadratic equation x² - x + m = 0 exceeds the other by 5. What is the value of m?
15.
Let A = {1, 2, {3, 4}, 5} be a set. Which of the following is not true?
16.
Let A = {x: x² - 4 = 0} and B = {x: x is a positive factor of 4}. Which one of the following is B \ A?
17.
For any two non-empty sets A and B if A ⊂ B, then which one of the following is always true?
18.
In a class of 52 students, 34 students passed in Mathematics and 28 passed in English. If the number of students who failed in both subjects is 9, what is the number of students who passed in both subjects?
19.
What is the domain of the relation R given by R = {(x, y): y ≥ x² - 1 and y < 3}?
20.
Let R = {(x, y): y < x - 1 and y ≤ -x} be a relation. What is the inverse of the relation R?
21.
Which one of the following relations is a function?
22.
Which one of the following is the range of the function f(x) = (2x + 3) / (x - 1)?
23.
What is the value of (2x - |x|) / |x|, if x < 0?
24.
Which one of the following is true about the function f(x) = 4 / (3x⁵)?
25.
What is the solution set of the equation sgn(x² - 1) = -1?
26.
Let f(x) = [2x - 3] be the greatest integer function. For what value of x, f(x) = 6?
27.
If f(x) = ax - b and f⁻¹(x + 1) = (1/2)x + 2, then what is the value of a and b?
28.
Which one of the following algebraic expressions is a rational expression?
29.
Which one of the following is the solution set of the equation (1 / (x - 2)) + (6x / (x² - 4)) = (3 / (x + 2))?
30.
What are the values of A, B, and C respectively so that (x - 1) / (x + x³) = A / x + (Bx + C) / (x² + 1)?
31.
The simplified form of the expression (1 - (1 / x)) / (1 - (1 / x²)) + (1 / (x + 1)) is equal to:
32.
Which of the following is the solution of the rational inequality (x² - 6x) / (x - 12) > 1?
33.
Which one of the following functions does not have a vertical asymptote?
34.
In a class, there are 8 more boys than girls. If the ratio of boys to girls is 4 to 3, what is the number of girls in the class?
35.
Which one of the following is true about the graph of f(x) = (1 - x²) / (x² - x)?
36.
Let A = [[3, a + b], [2, 4]] and B = [[8, 6], [2, a - b]]. If A = B, then the value of a is equal to:
37.
If the matrix [[y - 1, 4], [2, 1 - 3x]] + [[1 - x, 0], [1, 2y]] = [[0, 4], [3, 5]], then what is the value of x + y?
38.
Which one of the following matrices has no equal number of rows and columns?
39.
Which one of the following matrices is a symmetric matrix?
40.
What is the solution of the system of linear equations {x + y = 5, 2x - y = 1}?
41.
The inverse of matrix A = [[-2, -1], [3, 3]] is equal to:
42.
The perimeter of a triangle is 50m. The largest side of the triangle measures 20m more than the shortest side. The middle side is 3 times the measure of the shortest side. What is the length of the larger side of the triangle?
43.
What is the determinant of matrix A = [[1, -2, -3], [-1, 3, 4], [2, 5, 0]]?
44.
Let A and B be two invertible matrices of order 3. Suppose det(A) = 8 and det(B) = 16. What is det(A⁻¹B)?
45.
What is the value of x, so that matrix A = [[2, 3], [x, -2]] does not have an inverse?
46.
Which of the following relations holds for the sequence -8, -2, 4, 10, ...?
47.
Which of the following is neither arithmetic nor geometric sequence?
48.
What is the general term of the sequence Aₙ, if the 3rd term is 11 and the common difference is 4?
49.
What is the value of Σₙ₌₁¹⁰ (2n + 5)?
50.
How many terms of the sequence 3, 3/2, 3/4, 3/8, ... are needed to give the sum 93/16?
51.
The sum of integers from 1 to 100 that are divisible by 15 is equal to:
52.
The sum of the series 1 - 1/2 + 1/4 - 1/8 + ... is equal to:
53.
Which one of the following is a convergent sequence?
54.
A man accepts a position with an initial salary of Birr 12500 per year. If it is known that his salary will increase at the end of every year by Birr 250, what will be his salary at the beginning of the 12th year?
55.
Which of the following is the average rate of change of f(x) = x³ - 2x on the interval [1, 3]?
56.
What is the gradient (slope) of the function f(x) = x³ + √x at x = 1?
57.
Let f(x) = π² - 3, then the value of f'(2) is equal to:
58.
Let f(x) = kx² - 2x + 1 and f'(2) = 10, then what is the value of k?
59.
If f'(1) = 5, f(1) = 4, and g'(4) = 5, then (g ∘ f)(1) is equal to:
60.
What is the absolute minimum value of f(x) = x² + 2x on [-2, 2]?
61.
Which one of the following is the equation of the tangent line to the graph of f(x) = 3x² + 4x - 5 at (0, -5)?
62.
The volume of a spherical balloon is increasing at the rate of 24 cm³/sec. What is the rate of change of its surface area when its radius is 8 cm?
63.
What is the interquartile range (IQR) in statistics?
64.
What is the mean deviation from the mean for the data values: 5, 3, 7, 8, 4, 9?
65.
The number of days that students were missing from school due to sickness in one year was recorded:
