Grade 11 Mathematics Final Exam

If f = {0, 1, 2, 3, 5, 7, 8, 10} and g = {0, 3, 4, 4, 7, 10, 12, 20}, then gof = _______.

• {2, 3, 1, 12, 10, 20}

• {2, 7, 1, 12, 8, 20}

• {2, 3, 1, 0, 5, 7, 8, 10}

• {2, 7, 1, 12, 10, 20}

If relation R = {x | x = y + 36}, then which of the following is the inverse of R?

• {x | x = y - 2/3}

• {x | x = y - 3/2}

• {x | x = y + 2/3}

Which one of the following expressions is NOT rational expression?

• 2/3 + 3/(9x) + x

• 2/(42x) + 44/(xx)

• 32/(23910x) - x + 2

• 3/(2x) + 3/(21x) - 6

Which of the following is true?

• If A and B are invertible matrices, then the product AB is invertible and (ABB)^(-1) = B^(-1)A^(-1).

• If A and B are square matrices, then (AB)^(-1) = B^(-1)A^(-1).

• If A is a 3x4 matrix and B is a 4x3, then the product AB is a 4x4 matrix.

• If A and B are square matrices, then (AB)^2 = A^2B^2.

Which of the following matrices is in reduced echelon form?

• 1 0 0 0 2 0 0 0 1

• 0 0 1 0 1 0 0 0 0

• 0 0 0 0 0 1 0 1 0

• 1 0 0 0 1 0 0 0 0

For what value of k does the system of equations have no solution?

• k ≠ 1

• k ≠ -1

• k = -1

• k = 1

If A is a square matrix with A = [[1, 1, 2], [2, 4, 0], [6, 1, -1]], then what is the cofactor of a32?

• 4

• 1

• -1

• -3

Which of the following is one-to-one function?

• g(x) = y, where y is the father of x

• f = {(2, -2), (1, 3), (0, 1), (4, 1), (5, 6)}

• k(x) = x - 1

• f: x → x

Let A = 111 213 111 - (1/10) and B = 422 10 50 12 3 x. If B is the inverse of A, then ______x = ?

• 1

• 5

• 2

• 2

The solution of the equation 2x^2 + 3x + 5 = 0 is equal to:

• {1}

• {1, 0, -1}

• {0, 1}

• {1, -0}