Remedial Matematika Wajib Kelas Xi

1.

6x +1 + c

2x3 - x + c

2x3 + x - c

2x3 + x + c

3x3 + x + c

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Explanation

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2. Nilai minimum Kurva parabola dari fungsi kuadrat f (x) = x² – 8x adalah … .

-13

-14

-15

-16

-17

The minimum value of a parabola can be found by using the vertex formula, which is -b/2a. In this case, the coefficient of x^2 is 1 and the coefficient of x is -8. Plugging these values into the formula, we get -(-8)/2(1) = 8/2 = 4. Therefore, the minimum value of the parabola is f(4) = 4^2 - 8(4) = 16 - 32 = -16.

Explanation

The minimum value of a parabola can be found by using the vertex formula, which is -b/2a. In this case, the coefficient of x^2 is 1 and the coefficient of x is -8. Plugging these values into the formula, we get -(-8)/2(1) = 8/2 = 4. Therefore, the minimum value of the parabola is f(4) = 4^2 - 8(4) = 16 - 32 = -16.

3.

2x3 + x2 + x + c

2x3 + x2 + x - c

2x3 - x2 + x + c

2x3 + x2 + c

3x3 + x2 + x + c

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Explanation

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4. Interval x yang membuat kurva fungsi f (x) = x² + 6x – 4 tidak pernah turun adalah … .

X ≤ - 5

X ≤ - 4

X ≥ - 3

X ≥ - 4

X ≥ 0

The correct answer is x ≥ -3. This is because the equation f(x) = x^2 + 6x - 4 represents a quadratic function. The graph of a quadratic function is a parabola that opens upward if the coefficient of x^2 is positive. In this case, the coefficient of x^2 is 1, which is positive. When x ≥ -3, the function f(x) = x^2 + 6x - 4 will never decrease because the parabola opens upward. Therefore, the interval x ≥ -3 ensures that the curve of the function never decreases.

Explanation

The correct answer is x ≥ -3. This is because the equation f(x) = x^2 + 6x - 4 represents a quadratic function. The graph of a quadratic function is a parabola that opens upward if the coefficient of x^2 is positive. In this case, the coefficient of x^2 is 1, which is positive. When x ≥ -3, the function f(x) = x^2 + 6x - 4 will never decrease because the parabola opens upward. Therefore, the interval x ≥ -3 ensures that the curve of the function never decreases.

5.

8 + c

X + c

8x + c

9x + c

10x + c

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Explanation

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6.

5x + c

5x – c

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Explanation

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7. Nilai maksimum kurva parabola dari fungsi kuadrat f(x) = 4x – x² adalah … .

3

4

5

6

7

The maximum value of a parabola can be found by determining the vertex of the parabola. In this case, the given quadratic function f(x) = 4x - x^2 is in the form of f(x) = ax^2 + bx + c, where a = -1, b = 4, and c = 0. To find the x-coordinate of the vertex, we can use the formula x = -b/2a. Plugging in the values, we get x = -4/(2*(-1)) = -4/(-2) = 2. To find the y-coordinate of the vertex, we substitute x = 2 into the function: f(2) = 4(2) - (2^2) = 8 - 4 = 4. Therefore, the maximum value of the parabola is 4.

Explanation

The maximum value of a parabola can be found by determining the vertex of the parabola. In this case, the given quadratic function f(x) = 4x - x^2 is in the form of f(x) = ax^2 + bx + c, where a = -1, b = 4, and c = 0. To find the x-coordinate of the vertex, we can use the formula x = -b/2a. Plugging in the values, we get x = -4/(2*(-1)) = -4/(-2) = 2. To find the y-coordinate of the vertex, we substitute x = 2 into the function: f(2) = 4(2) - (2^2) = 8 - 4 = 4. Therefore, the maximum value of the parabola is 4.

8.

2x + 12y

2x - 12y – 13

2x + 12y + 13

2x + 12y – 13

2x + 12y + 13

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Explanation

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9. Garis singgung pada parabola y = x² – 4 yang tegak lurus pada garis y = x+ 3 memotong sumbu Y adalah … .

The tangent line to the parabola y = x^2 - 4 that is perpendicular to the line y = x + 3 will intersect the y-axis at a certain point.

Explanation

The tangent line to the parabola y = x^2 - 4 that is perpendicular to the line y = x + 3 will intersect the y-axis at a certain point.

10. Gradien garis singgung pada kurva f (x) = x² +1 di titik (1,2) adalah … .

-2

-1

0

1

2

The gradient of the tangent line at the point (1,2) on the curve f(x) = x^2 + 1 is 2. This means that the slope of the tangent line at that point is 2, indicating that the curve is steeply increasing at that point.

Explanation

The gradient of the tangent line at the point (1,2) on the curve f(x) = x^2 + 1 is 2. This means that the slope of the tangent line at that point is 2, indicating that the curve is steeply increasing at that point.

11.

3x2 + 8x

3x2 + 8x + 2

3x2 + 8x + 3

3x2 + 8x + 4

3x2 + 8x + 5

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Explanation

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12. Nilai Optimum dari kurva Fungsi h(x) = x² – 4x + 6 adalah … .

Maksimum = -2

Maksimum = 2

Minimum = 2

Minimum = - 2

Minimum = 0

The given function is a quadratic function in the form of h(x) = x^2 - 4x + 6. To find the optimum value, we need to find the vertex of the parabola. The vertex of a quadratic function in the form of ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = 1 and b = -4. Plugging these values into the formula, we get x = -(-4)/2(1) = 2. So, the x-coordinate of the vertex is 2. To find the corresponding y-coordinate, we substitute x = 2 into the function h(x) = x^2 - 4x + 6. h(2) = 2^2 - 4(2) + 6 = 4 - 8 + 6 = 2. Therefore, the minimum value of the function is 2.

Explanation

The given function is a quadratic function in the form of h(x) = x^2 - 4x + 6. To find the optimum value, we need to find the vertex of the parabola. The vertex of a quadratic function in the form of ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = 1 and b = -4. Plugging these values into the formula, we get x = -(-4)/2(1) = 2. So, the x-coordinate of the vertex is 2. To find the corresponding y-coordinate, we substitute x = 2 into the function h(x) = x^2 - 4x + 6. h(2) = 2^2 - 4(2) + 6 = 4 - 8 + 6 = 2. Therefore, the minimum value of the function is 2.

13.

2x+1

2x + 2

2x+ 4

4x +1

4x + 2

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Explanation

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14. Interval yang membuat kurva fungsi f (x) = x² – 5x + 6 selalu naik adalah … .

X > 0

X > 12

X > 1

X > 32

X > 52

The correct answer is x > 52 because for any value of x greater than 52, the function f(x) = x^2 - 5x + 6 will always increase. This can be determined by analyzing the quadratic equation and observing that the coefficient of the x^2 term is positive, indicating an upward opening parabola. Therefore, the function will always have a positive slope and continue to rise as x increases beyond 52.

Explanation

The correct answer is x > 52 because for any value of x greater than 52, the function f(x) = x^2 - 5x + 6 will always increase. This can be determined by analyzing the quadratic equation and observing that the coefficient of the x^2 term is positive, indicating an upward opening parabola. Therefore, the function will always have a positive slope and continue to rise as x increases beyond 52.

15. Nilai Gradien Garis singgung pada kurva y = f(x) = - x² + 3x + 1 pada titik yang berabsis x = -1 adalah … .

5

4

3

2

1

The gradient of a tangent line to a curve represents the slope of the line at a specific point. In this case, the curve is represented by the equation y = -x^2 + 3x + 1. To find the gradient at x = -1, we need to find the derivative of the equation and substitute x = -1 into it. The derivative of -x^2 + 3x + 1 is -2x + 3. Substituting x = -1 into this equation gives us -2(-1) + 3 = 5. Therefore, the gradient of the tangent line at x = -1 is 5.

Explanation

The gradient of a tangent line to a curve represents the slope of the line at a specific point. In this case, the curve is represented by the equation y = -x^2 + 3x + 1. To find the gradient at x = -1, we need to find the derivative of the equation and substitute x = -1 into it. The derivative of -x^2 + 3x + 1 is -2x + 3. Substituting x = -1 into this equation gives us -2(-1) + 3 = 5. Therefore, the gradient of the tangent line at x = -1 is 5.

16. Interval x yang membuat kurva fungsi g (x) = 7 – 3x - x² tidak pernah Naik adalah … .

X ≥ 3/2

X ≥ - 3/2

X ≤ - 3/2

X ≤ 12

X ≤ 32

The given function is a quadratic function, g(x) = 7 - 3x - x^2. To find the interval where the function never increases, we need to find the values of x for which the derivative of the function is always negative. The derivative of g(x) is -3 - 2x. To find when the derivative is negative, we set -3 - 2x -3/2. Therefore, the interval x ≥ -3/2 is the correct answer.

Explanation

The given function is a quadratic function, g(x) = 7 - 3x - x^2. To find the interval where the function never increases, we need to find the values of x for which the derivative of the function is always negative. The derivative of g(x) is -3 - 2x. To find when the derivative is negative, we set -3 - 2x -3/2. Therefore, the interval x ≥ -3/2 is the correct answer.

17. Nilai stasioner Fungsi y = x³ – 3x² + 3x -2 adalah … .

X = 0

X = 1

Y = 1

Y = 0

Y = -1

The stationary value of a function occurs where the derivative is equal to zero. To find the stationary values of the function y = x^3 - 3x^2 + 3x - 2, we need to find the derivative and set it equal to zero. The derivative of the function is y' = 3x^2 - 6x + 3. Setting this equal to zero and solving for x, we get x = 1. Therefore, the stationary value of the function is x = 1.

Explanation

The stationary value of a function occurs where the derivative is equal to zero. To find the stationary values of the function y = x^3 - 3x^2 + 3x - 2, we need to find the derivative and set it equal to zero. The derivative of the function is y' = 3x^2 - 6x + 3. Setting this equal to zero and solving for x, we get x = 1. Therefore, the stationary value of the function is x = 1.