Welcome to your GRADE 12 MATHEMATICS SOCIAL MODEL EXAMINATIONS 2017
DIRECTIONS: FOR EACH OF THE FOLLOWING PROBLEMS, CHOOSE THE BEST ANSWER FROM THE GIVEN
ALTERNATIVES AND CAREFULLY BLACKEN THE LETTER OF YOUR BEST CHOICE ON THE SEPARATE
ANSWER SHEET PROVIDED.
1.
The mark that students scored in an examination is grouped in class intervals as shown in the following table for the f/f grouped data table below:
What is QD of the distribution respectively?
2.
What is the fractional form of the purely recurring decimal number 0.877?
3.
What is the normal line to the graph of a function f(x) = sqrt(20 - x^2) at the point (2, 4)?
4.
What is the slope of a secant line to the graph of the function f(x) = 2 + (x-1)ln(x) at x=1 and x=e?
5.
A theatre hall has 60 rows of seats. The first row has 40 seats, the second row has 44 seats, the third row has 48 seats, and so on. What is the seating capacity of the theatre hall?
6.
Which one of the following is the set of critical numbers of f(x) = sqrt(x^2 - 4)?
7.
Which of the following is the interval on which f(x) = x^3 + 3x^2 - 9x + 8 is strictly decreasing?
8.
The inverse of the matrix A = | 1 0 2 | | 2 -1 3 | | 4 1 8 | is:
9.
Which of the following is the product of AB of the two matrices A = | 13 -3 | | -4 1 | and B = | 1 3 | | 4 13 |?
10.
Suppose that A = | 1 0 1 | | -2 2 -1 | | 3 4 -3 | and B = | 0 1 3 | | 3 5 -1 | | 2 -2 4 | are given. If C = A^T B + B^T, then what is the entry of C_32?
11.
For any nxn square matrix A, which of the following is false?
12.
Which one of the following is the determinant of matrix A = | 1 3 5 | | 6 4 2 | | 9 7 0 |?
13.
Which one of the following is the arrow-reduced echelon form of the matrix | 1 1 1 | | 2 1 3 | | 4 -1 4 |?
14.
What is the solution set of the system of linear equations: x - 3y - 2z = 6 2x - 4y - 3z = 8 -3x + 6y + 8z = -5
15.
What are the domain and range of the function f(x) = x^-8 respectively?
16.
The solution set of the greatest integer |x - 2| = -3 is?
17.
Which one of the following is a false statement?
18.
The solution set of |7 - 2x| + |-2x + 7| = 6 is?
19.
If R = {(x, y): y ≥ -5 and -y ≤ x + 1}, then the domain of R^-1 is:
20.
Which of the following functions is not inverse to each other in their respective domain?
21.
The solution set of (x + 1)/(x - 1) + (x - 1)/(x + 1) = (2x - 2)/(1 - x^2) is:
22.
If (x - 1)/(x^3 + 3x + 4x^2) = A/x + B/(x + 1) + C/(x + 3), then what is the respective value of A, B, and C?
23.
If f(x) = (4 - x^2)/(x^2 - 2), then which of the following is TRUE about the function f?
24.
The simplest form of [(2/(x - 3)) * (1/(x + 2))] ÷ [(x + 7)/(x^2 - x - 6)], where x ≠ -7, -2, 3, is:
25.
The following is frequency distribution table of grouped data with variable x
For the f/f grouped data table below, what is standard deviation of the data?
What is the standard deviation of the data?
27.
Which of the following is not a rational function?
28.
Which one of the following is true about the range and interquartile range of the given data?
29.
If a 30% salt solution is to be mixed with a 20% salt solution to form a mixture of a 25% salt solution of 500 liters, how much of each is needed?
30.
Which one of the following is the inverse of the matrix A = | 4 2 | | 3 2 |?
31.
Suppose that A = | 1 0 2 | | 2 -1 3 | | 4 1 8 |. Then the result of (1/2)(A + A^T) is:
32.
A ball is dropped from a height of 40 meters. Each time it drops h meters, it rebounds 20% of the height. What is the total vertical distance traveled by the ball before it comes to rest?
33.
What is the instantaneous rate of change of f(x) = 6x^2 - 3 at x = 2?
34.
Which of the following is not a characteristic of a function?
35.
Which of the following statements is true about the relation R defined by R = {(x, y) | y = x^2}?
36.
A car rental service charges $20 per day plus an additional fee of $0.25 per mile driven. Which of the following best describes the total cost C in terms of the number of days d and miles m?
37.
Which of the following statements is true regarding the set of rational numbers?
38.
Which one of the following is not a rational number?
39.
If a = 3 + 2sqrt(2) and b = 3 - 2sqrt(2), then which one of the following is not true?
40.
The simplest form of [(3/(2sqrt(2) - 1) - (1/(sqrt(2) + 1))] ÷ [10 - sqrt(2)] is:
41.
The area of a square garden is 85 square meters. Estimate the side length of the garden.
42.
The numerical value of sqrt(176) - 2sqrt(275) + sqrt(1584) - sqrt(891) is:
43.
Which of the following is the simplest form obtained by rationalizing the denominator of (sqrt(5 + 2sqrt(6)) / (sqrt(5 - 2sqrt(6)))?
44.
What does Euclid's division algorithm primarily help to find for two integers a and b (where a > b)?
45.
When the expression (6/3 - 8/4) + sqrt(1/16 + 1/9) is simplified, it gives:
46.
The solution set of 3^x + 3^(x+3) = 28/9 is:
47.
Two students A and B bought exercise books and pens at the same time. Student A bought 10 exercise books and 3 pens for birr 92. Student B bought 12 exercise books and 2 pens for birr 104. If each exercise book had the same price as it did the pens, the price for each exercise book and each pen respectively is:
48.
If the system of equations is:
3x + ay = -12
4x + 8y = k
Determine the values of a and k so that the system has no solutions.
49.
The solution set of the equation |12 - |4x - 5|| = 13 is:
50.
Which of the following is not true about the quadratic equation x^2 + kx - 2k = 0?
51.
A rectangular swimming pool is 10m longer than its width. The pool is completely surrounded by a concrete deck that is 4m wide. The total area of the pool and the deck is 600m². The dimensions of the pool are:
52.
If (A \ B) ∪ B = A, then which of the following is always true?
53.
In a school of 150 students, 115 take Mathematics and 85 take Physics. How many students take Mathematics and Physics only?
54.
Which of the following statements is true regarding subsets and proper subsets?
55.
If A, B, and C are any three sets in the same universal set, then which of the following is not equal to A \ (B' ∪ C)?
56.
If A = {0, 1, 2, 3, 4, 5}, B = {0, 1, 2, 3, 4}, and R is a relation from A to B such that R = {(x, y): y = sqrt(x - 1)}, then what is the range of R?
57.
If A = {-2, -1, 0, 1, 2} and R = {(x, y): x ∈ A, y ∈ A, and x - y ∈ A}, then which of the following is not true?
58.
Which of the following is an arithmetic sequence?
59.
An arithmetic sequence has a constant difference between terms.
60.
Suppose a radioactive material loses one-third of its mass per year. If its current mass is 81 grams, how much will its mass be just after 3 years?
61.
What is the sum of the series ∑_{n=1}^{30} (-1)^n (1/n + 1/(n+1))?
62.
In a sequence {f_n}, let f_1 = 3, and f_{n+1} = n/(f_n^2) for n ≥ 1. Then f_4 is:
63.
What is the sum of the series ∑_{n=0}^{∞} 2^n * 3^{2-n}?
64.
Which one of the following describes the mechanical meaning of the derivative?
65.
Given f(1) = -1 and f'(1) = 1. If g(x) = (f(2x + 1) + 2)^2, then g'(0) = ?
66.
A right circular cylinder with a volume of 343π cm³ is to be constructed. The height h of the cylinder and the radius r of the base in order to use the minimum amount of material are:
