✅ 12th Grade Other: Multiplication Quiz
✅ 12th Grade Other: Multiplication Quiz
Simplify the following expression by multiplying the monomials: $ (4x^3)(5x^7) $.
A) $ 9x^{10} $B) $ 20x^{10} $
C) $ 20x^{21} $
D) $ 9x^{21} $
Use the distributive property to multiply the binomials: $ (x + 6)(x - 4) $.
A) $ x^2 + 2x - 24 $B) $ x^2 - 2x - 24 $
C) $ x^2 + 10x + 24 $
D) $ x^2 - 24 $
Perform the scalar multiplication for the following matrix:
$$ 3 \begin{pmatrix} 2 & -1 \\ 5 & 0 \end{pmatrix} $$
B) $ \begin{pmatrix} 6 & -1 \\ 15 & 0 \end{pmatrix} $
C) $ \begin{pmatrix} 6 & -3 \\ 15 & 0 \end{pmatrix} $
D) $ \begin{pmatrix} 2 & -3 \\ 5 & 0 \end{pmatrix} $
Simplify the expression by multiplying terms with negative exponents: $ (2x^{-3})(4x^5) $.
A) $ 8x^2 $B) $ 6x^2 $
C) $ 8x^{-15} $
D) $ 8x^{-8} $
Multiply the following complex numbers: $ (2 + 3i)(1 - 2i) $.
A) $ 2 - 6i $B) $ 8 - i $
C) $ 8 + i $
D) $ -4 - i $
If two events $ A $ and $ B $ are independent, and $ P(A) = 0.3 $ and $ P(B) = 0.7 $, what is the probability of both events occurring, $ P(A \cap B) $?
A) 1.0B) 0.4
C) 0.21
D) 0.5
Multiply the following two matrices:
$$ A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix} $$
B) $ \begin{pmatrix} 2 & 0 \\ 3 & 12 \end{pmatrix} $
C) $ \begin{pmatrix} 4 & 6 \\ 7 & 12 \end{pmatrix} $
D) $ \begin{pmatrix} 5 & 6 \\ 11 & 12 \end{pmatrix} $
Find the derivative of the function $ f(x) = x^2 \sin(x) $ using the product rule.
A) $ 2x \cos(x) $B) $ x^2 \cos(x) + 2x \sin(x) $
C) $ 2x \sin(x) - x^2 \cos(x) $
D) $ x^2 \sin(x) + 2x \cos(x) $
Evaluate the multiplication of the complex number by its conjugate: $ (5 + 12i)(5 - 12i) $.
A) 169B) -119
C) 13
D) 169 + 120i
Simplify the product of the rational expressions: $ \frac{3x^2}{y} \times \frac{y^3}{6x} $.
A) $ \frac{x y^2}{2} $B) $ \frac{18x^3}{y^4} $
C) $ \frac{x^2 y^2}{2} $
D) $ \frac{x y}{2} $
In the expansion of $ (x + 2)^5 $, what is the coefficient of the $ x^3 $ term?
A) 10B) 20
C) 40
D) 80
Multiply the following 3x3 diagonal matrices:
$$ A = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4 \end{pmatrix}, B = \begin{pmatrix} 5 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0.5 \end{pmatrix} $$
B) $ \begin{pmatrix} 7 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4.5 \end{pmatrix} $
C) $ \begin{pmatrix} 10 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 8 \end{pmatrix} $
D) $ \begin{pmatrix} 10 & 3 & 2 \\ 3 & 10 & 2 \\ 2 & 3 & 10 \end{pmatrix} $
Find the derivative of $ g(x) = e^{2x} \ln(x) $ at $ x = 1 $.
A) $ e^2 $B) $ 2e^2 $
C) 0
D) $ e $
Multiply the rotation matrix $ R(\theta) $ by itself for $ \theta = 45^\circ $. What is the resulting matrix?
$$ R(45^\circ) = \begin{pmatrix} \cos(45^\circ) & -\sin(45^\circ) \\ \sin(45^\circ) & \cos(45^\circ) \end{pmatrix} $$
B) $ \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} $
C) $ \begin{pmatrix} 0.5 & -0.5 \\ 0.5 & 0.5 \end{pmatrix} $
D) $ \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} $
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