Welcome to your GRADE 12 MATHEMATICS SOCIAL MODEL EXAMINATIONS 2015
1.
If f(x) = { |x| if |x| ≤ 2
{ sgn(x) if x > 2 , then f(-1.3) + f(3) is equal to:
2.
If f(x) = 2x + 1 and (g∘f)(x) = x, then g(x) is equal to:
3.
Consider the graph of R below:
Which of the following is the graph of the inverse of R?
4.
The simplified form of the expression (1-x²)/(x²-2x+1) is:
5.
Which one of the following is true about the graph of f(x) = (x³ + x² + x)/(x² - x)?
6.
The distance from the line 3x + 4y - k = 1 to the point (0,1) is 2, then which one of the following is the possible value of k?
7.
The radius of a circle x² - 4x + y² = 0 is:
8.
The equation of parabola whose focus (3, -2) and directrix y = 0 is:
9.
The planet Venus travel around the sun in an elliptical path whose equation is approximately given by x²/25² + y²/24² = 1, where x and y are measured in millions of kilometers. The greatest possible distance between Venus and sun in millions of kilometers is:
10.
Let p, q and r be propositions such that (¬p ⇒ r) ∨ q is false. Then which one of the following propositions has truth value false?
11.
For real numbers x and y, which one of the following is NOT true?
12.
Given that p, q and r are propositions such that p = "There is an inflation", q = "Wages will increase" and r = "Cost of living will increase". Then which of the following is the correct symbolic representation and its validity for the argument: "Wages will increase if there is inflation. The cost of living will increase if there is inflation. Wages will never increase. Therefore, the cost of living increases."
13.
Which one of the following is quantitative data?
14.
The mean grade of ten students was 72. If two of the students with grade 53 and 75 were cancelled, then what should be the mean grade of the remaining students?
15.
What is the value of D₈ (decile 8) for the data set: 18, 2, 4, 6, 10, 7, 9, and 11?
16.
In a football championship 153 matches were played. Every team played one match with the other. The number of teams participating in the championship is ______.
17.
A bag contains 3 red, 4 blue, and 3 white balls. If three balls are drawn one after the other without replacement, then what is the probability of getting 3 red balls in a row (i.e. in the first, second and third draw)?
18.
In the expansion of (x - 2y)⁵, what is the coefficient of x²y³?
19.
If A = 
and B = 
, then find matrix C such that 2Aᵀ - 3C = 6B
20.
If A = 
is singular, then the value of k is:
21.
Let A = [ 3 2 1 ] and B = [ 0 ]. If |A| = 2 and X = [ x ], then what is the solution set of the system AX = B? [ a b 0 ] [ 4 ] [ y ] [ 1 2 2 ] [ 0 ] [ z ]
22.
If Aᵀ is the transpose of a square matrix A, then which one of the following is true?
24.
The multiplicative inverse (reciprocal) of (1+i)/(2+i) is:
25.
The principal argument of (1+i)/(i+√3) is ______.
26.
Which one of the following is the simplest form of |3 + 4i| + 3 + 4i?
27.
Which one of the following is the simplest form of |3 + 4i| + 3 + 4i?
28.
What is the maximum value of z = x + 2y, Subject to -x + y ≤ 0 x + y ≤ 10 x ≥ 0, y ≥ 0
29.
A small enterprise makes dresses and trousers. To make a dress requires 0.5 hour of cutting and 20 minutes of stitching. To make a pair of trousers requires 15 minutes of cutting and 0.5 hour of stitching. The profit on a dress is birr 20 and on a pair of trousers is birr 25. If the business can operate 8 hours per day for each activity (for cutting and for stitching), then how many dresses and trousers should the business made to maximize profit?
30.
The ratio of 12 meters to 200 centimeters is:
31.
In a school, 58% of the total number of students is boys. If the number of girls is 840, how many students are there in the school?
32.
Almaz deposits Birr 1000 at the end of every month into a saving account that pays an interest rate of 12% per year compounded monthly. How much money is in her account at the end of 5 years? (use (1.01)⁶⁰ = 1.8167).
33.
A machine costing Birr 38000 is estimated to have salvage value of Birr 6000. If the useful life time of the machine is 8 years, then depreciation per year using fixed installment method is:
34.
Which one of the following is an arithmetic sequence?
35.
If Σ_{k=1}^20 (k + x) = Σ_{k=5}^20 k, then x = ______
36.
The sum 1/5 - 2/5² + 2²/5³ - 2³/5⁴ + ⋯ is equal to ______.
37.
Suppose the population of Ethiopia is increasing at a rate of r% per year. If the population currently is p₀, then what will be the population after n years from now?
38.
Which one of the following is NOT monotonic sequence?
39.
The least upper bound of the sequence {(2n+1)/n} is:
40.
What is the value of lim_{x→∞} (√(x+3) - 5)/(4 - √x)
41.
Find the number b so that lim_{x→-2} (bx² + 15x + 15 + b)/(x² + x - 2) exists.
42.
Let f(x) = { 2x - 3, for x ≤ 1 { kx + 5, for x > 1 for what value of k does the graph of f(x) is continuous on (-∞, ∞)?
43.
lim_{x→∞} ((x+4)/(x-1))ˣ equals to
44.
The slope of tangent line to the graph of f(x) = √x at x = 4 is:
45.
If f(x) = xeˣ, then lim_{x→1} (f(x) - f(1))/(x - 1) is equal to:
46.
Let f(x) = 3x/(a - x), for what value of a is f'(-a) = 1
47.
Let F(x) = g(1 - x²). If g'(0) = 4, then F'(1) is equal to ______.
48.
If f(x) = 2x⁵ + 3x⁴ - 2x³ + x² + x - 1, then f⁽⁶⁾(x) is equal to:
49.
Which of the following is the set of all critical numbers of f(x) = √(1 - x²)?
50.
What is the maximum value of the function g(t) = t⁴ - 2t² on [-1, 1]?
51.
The graph below is the graph of f''(x) and f(x) has critical number at x = 2, then which one of the following is true?
52.
The total cost (in Birr) of producing x iron sheets per day is C(x) = 1000 + 100x - 0.5x², 0 ≤ x ≤ 100. What is the cost of producing 81ᵗʰ iron sheet?
53.
The radius of a circle is increasing at a rate of 2mm/sec. At what rate the area is increasing, when the radius is 3mm?
54.
Which one of the following is not true?
55.
What is the value of ∫ (1/(2x-1) + 1/(3-2x)) dx?
56.
What is the value of ∫₀¹ (x + 1)eˣ dx?
57.
Which one of the following functions is NOT integrable on [-1,1]?
