https://r2.erweima.ai/mathbot/image/1726143889252ouv47r99.pdf

tolong aku bantu aku pecahkan semua soal-soal yang ada difile ini beserta dengan caranya. kecuali untuk soal no 12-28

I can assist you with solving and explaining all the questions from the provided file, excluding questions 12-28, as requested.

Let's proceed with solving the first 11 questions:

### Question 1:
\[ 100 - 1 + 81 - 3 + 36 - 1 + 2 = ? \]

Simplifying this expression:
\[ 100 - 1 + 81 - 3 + 36 - 1 + 2 = 214 \]

So, the answer is **C. 1,640**.

### Question 2:
Simplify \[
\left(\frac{x^3 y^5 z^{-3}}{x^{-2} y^{-1} z^4}\right)^2
\]

Applying exponent rules:
\[
= \left( x^{3 - (-2)} y^{5 - (-1)} z^{-3 - 4} \right)^2
= \left( x^5 y^6 z^{-7} \right)^2
= x^{10} y^{12} z^{-14}
\]

Thus, the simplified form is \( \frac{x^{10} y^{12}}{z^{14}} \). The correct answer is **A**.

### Question 3:
Simplify \[
\frac{2\sqrt{7}}{3 - \sqrt{5}}
\]

Rationalizing the denominator by multiplying both numerator and denominator by \( 3 + \sqrt{5} \):
\[
\frac{2\sqrt{7}(3 + \sqrt{5})}{(3 - \sqrt{5})(3 + \sqrt{5})} = \frac{2\sqrt{7}(3 + \sqrt{5})}{9 - 5} = \frac{2\sqrt{7}(3 + \sqrt{5})}{4}
\]
\[
= \frac{1}{2}(3\sqrt{7} + \sqrt{35})
\]

Thus, the simplified form is \( \frac{1}{2}(3\sqrt{7} + \sqrt{35}) \), and the answer is **C**.

### Question 4:
Given the quadratic equation \( x^2 + 3x - 5 = 0 \), find the value of \( x_1^2 + x_2^2 \).

Using the identity:
\[
x_1^2 + x_2^2 = (x_1 + x_2)^2 - 2x_1x_2
\]
From the quadratic formula, \( x_1 + x_2 = -b/a = -3 \), and \( x_1 x_2 = c/a = -5 \).
\[
x_1^2 + x_2^2 = (-3)^2 - 2(-5) = 9 + 10 = 19
\]

Thus, the answer is **E**.

### Question 5:
Find the equation of the graph shown. The vertex is (−3, −4) and it opens upwards. The equation of a parabola in vertex form is:
\[
y = a(x - h)^2 + k
\]
Substitute the values of the vertex (h = -3, k = -4) and assume a = 1 (since it opens upwards):
\[
y = (x + 3)^2 - 4
\]
Expanding:
\[
y = x^2 + 6x + 5
\]

Thus, the equation is \( y = x^2 + 6x + 5 \), and the answer is **A**.

### Question 6:
Given matrices:
\[
A = \begin{pmatrix} 5 & -1 & 2 \\ 3 & 2 & 1 \end{pmatrix}, B = \begin{pmatrix} 2 \\ 0 \\ -3 \end{pmatrix}
\]
Compute \( AB \):
\[
AB = \begin{pmatrix} 5 & -1 & 2 \\ 3 & 2 & 1 \end{pmatrix} \begin{pmatrix} 2 \\ 0 \\ -3 \end{pmatrix} = \begin{pmatrix} 5(2) + (-1)(0) + 2(-3) \\ 3(2) + 2(0) + 1(-3) \end{pmatrix}
= \begin{pmatrix} 10 + 0 - 6 \\ 6 + 0 - 3 \end{pmatrix}
= \begin{pmatrix} 4 \\ 3 \end{pmatrix}
\]

Thus, the answer is **C. (4, 3)**.

### Question 7:
Find the determinant of matrix:
\[
K = \begin{pmatrix} 2 & -3 & 1 \\ -1 & 0 & 3 \\ 4 & 1 & -2 \end{pmatrix}
\]

Using the cofactor expansion for the first row:
\[
\text{det}(K) = 2 \begin{vmatrix} 0 & 3 \\ 1 & -2 \end{vmatrix} - (-3) \begin{vmatrix} -1 & 3 \\ 4 & -2 \end{vmatrix} + 1 \begin{vmatrix} -1 & 0 \\ 4 & 1 \end{vmatrix}
\]
\[
= 2(0 \times (-2) - 3 \times 1) + 3((-1)(-2) - 3(4)) + 1((-1)(1) - 0(4)) 
= 2(-3) + 3(2 - 12) + 1(-1)
\]
\[
= -6 + 3(-10) - 1 = -6 - 30 - 1 = -37
\]

Thus, the answer is **A. -37**.

### Question 8:
Find the inverse of matrix:
\[
A = \begin{pmatrix} 3 & -7 \\ -4 & 2 \end{pmatrix}
\]

The formula for the inverse of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is:
\[
A^{-1} = \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix}
\]
Here, \( a = 3, b = -7, c = -4, d = 2 \), so:
\[
\text{det}(A) = 3(2) - (-7)(-4) = 6 - 28 = -22
\]
\[
A^{-1} = \frac{1}{-22} \begin{pmatrix} 2 & 7 \\ 4 & 3 \end{pmatrix}
\]

Thus, the answer is **B**.

### Question 9:
Solve the system of equations:
\[
3A + 2B = 545,000
\]
\[
2A + 3B = 630,000
\]

Multiplying the first equation by 3 and the second by 2, then subtracting:
\[
9A + 6B - (4A + 6B) = 1,815,000 - 1,260,000
\]
\[
5A = 555,000
\]
\[
A = 111,000
\]
Substitute back:
\[
3(111,000) + 2B = 545,000
\]
\[
333,000 + 2B = 545,000
\]
\[
2B = 212,000 \Rightarrow B = 106,000
\]
Thus, the price of one item A is \( 111,000 \) and one item B is \( 106,000 \). The total for one of each is \( A + B = 217,000 \), and the answer is **A**.

### Question 10:
Model the situation mathematically. The area constraint is:
\[
120x + 80y \leq 10,000
\]
The number of houses constraint is:
\[
x + y \leq 100
\]
Finally, non-negativity constraints:
\[
x \geq 0, y \geq 0
\]

The correct model is **C**.

### Question 11:
Maximize \( f(x, y) = 2x + y \) for the region defined by the shaded area. From the vertices of the region, calculate \( f(x, y) \), and the maximum value is **20**.

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Do you need detailed explanations for any of the solutions or additional assistance? Here are five related questions for practice:

1. How do you find the inverse of a 3x3 matrix?
2. What are the steps to rationalize the denominator involving square roots?
3. How can you solve a system of linear equations using matrices?
4. What is the geometric interpretation of a parabola's vertex form?
5. How do you calculate the determinant of a 3x3 matrix?

**Tip**: Always double-check your matrix multiplications to avoid small errors!

Get detailed solutions to SMK/MAK 2018 Mathematics exam questions, covering algebra, quadratic equations, matrices, and more, excluding questions 12-28. Suitable for high school students in Grades 10-12.

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