Nationwide Mathematics Competition Grade - 11 Student Name: 4th Round Time allowed: 1 hour School Name: Instruction I: Choose the best answer from the suggested options and write the letter of your choice on the answer sheet provided. 1. If x>0 and x(x+1)=6, what is the value of (x+1)(x+2)? A) 10 B) 12 C) 42 D) 48 2. A function f: IRIR satisfies f(10-x) = f(13+x) for all real number x. It is know that has exactly two roots. What is the sum of these two roots? A) -3 B) 3 C) 13 D) 23 3. If the domain of f is (0,1), then what is the domain of ƒ (e*) + ƒ (In|x|) ? B) (-e,0) C) (-1,0) x+1 = and f(a)=5, then f(2a) is equal to: x-1 A) (-e,-1) 4. If f(x)= A) 8 B) 6 5. If f(x)=√1+e, what is f'(x)? A) In(1-x) B) In(x³-1) C) 4 C) In D) (0,e) D) 2 D) (1+e³)³ 6. A rectangular area of 2500m² is to be fenced off. Two opposite sides of the fencing cost 3 birr per meter; the remaining two sides cost 2 birr per meter. If x represents the length of the sides requiring the more expensive fencing, what is the total cost of the fencing as a function of x? 1000 x 2500 x A) C(X)=6x+- B) C(x)=6x+ C) C(x)=3x+ 5000 1000 D) C(x)=3x+ x x 7. Let A=(a) be an nxn matrix with det(A) = 8 and a be a non-zero real number. If B=(aa), what is the determinant of B? A) 8a B) 8a" C) 8 D) 8a'j 8. Which one of the following points is collinear with the points (3,4) and (1,7)? A) (0,8) B) (2,5) 9. What is the area of the quadrilateral whose four vertices are given by A(-7,7), B(5,5),C(3,-4) and D(-5,-6)? A) 223 sq. units B) 113 sq. units C) (5,-1) D) (-1,10) C) 110 sq. units D) 76 sq. units A) -1 10. For what value of k the system B) 1 (x+ky=1 kx+y=1 has only one solution? C) -1 and 1 D) IR\{-1,1}