Soal Matematika dan Statistika Kelas 12 no 6

 6. Persamaan grafik di samping adalah ...

Answer :

Soal Matematika dan Statistika Kelas 12 no 5

 5. Diketahui

f (x - 1) = (x - 1) / (2x -1) , x ≠ -1/2 dan f^-1 (x) adalah invers dari f(x). Rumus f^-1 (2x - 1) = ...

Answer :

Soal Matematika dan Statistika Kelas 12 no 4

 4. Diketahui fungsi f(x) = x^2 + 2x dan g(x) = x - 3. Fungsi komposisi (fog) (x) adalah ...

Soal Matematika dan Statistika Kelas 12 no 3

 3. Diketahui  ²log 3 = m dan ²log 5 = n. Nilai dari ²log 90 adalah ...

Soal Matematika dan Statistika Kelas 12 no 2

 2. Bentuk sederhana dari (1 + 3√2) - (4 - √50) adalah ...

Soal Matematika dan Statistika Kelas 12 no 1

 1. Bentuk sederhana dari

((2a^5 b^-5)/(32a^9b^-1))^-1

adalah ...

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART B NO.86 - 90

 86. The table shown gives value of the twice - differentiable function f and g and their derivatives f ' and g ' at selected values of x. What is 

lim x → 2 g(x^2) / (3x + f(x)) ?

Answer :

87. The velocity of a particle moving along the x - axis is given by v (t) = (1 - t^3) / (1 + t) for t ≥ 0 . Which of the following statements is true about the particle at time t = 1.5 ?

Answer :

88. The figure shows the graphs of the polar curves r = 4 (sin ( 2θ))^2 and r = 1 for 0 ≤ θ ≤ π/2. What is the area of the shaded region ?

Answer :

89. The graph of the function f shown consists of a semicircle centered at the origin and three line segments. If g(x) = _-2∫^x (f (t) +1) dt , then g (8) ?

Answer :

90. The position of a particle moving in the xy-plane is given by the parametric equation x (t) = 5 ln (t + 5) and y (t) = 5 sin (πt). At ant point on the curve, the slope of the line tangent to the path of the particle is given by dy/dx = π cos (πt) (t + 5). What is the value of d^2y / dx^2 at t = 1 ?

Answer :

 

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART B NO.81 - 85

81. A thin rectangular sheet of metal expands in a hot oven. At the instant when the width of the rectangular sheet of metal is 200 millimeters and the length is 300 millimeters, the width is increasing at a rate of 2 millimeters per minute, and the length is increasing at a rate of 3 millimeters per minute. What is the rate of change of the area, in square millimeters per minute, of the rectangular sheet of metal at that instant ?

Answer :

82. A particle travels along x-axis so that is velocity at time t ≥ 0 is given by dy/dx = sin (t^2) . What is the total distance the particle travels from t = 0 to t = 2.7 ?

Answer :

83. The function f is continuous on the closed interval [a,b] where a and b are constants and a < b . If f (a) < 0 < f (b) , which of the following statements must be true ?

Answer :

84. The alternating series

n = 1Σ ∞

(-1)^n+1 / (2n + 2)

converges to S. If the sum of the first six terms of the series is used to approximates S. What is the alternating series error bound ?

Answer :

85. The graph of a twice- differentiable function f is shown for 0 < x < 4 . The graph of f has a horizontal tangent at x = 2 and points of inflection at x = 1 and x = 3. On what intervals do f ' (x) and f '' (x) have the same sign ?

Answer :

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART B NO.76 - 80

 76. If f ' (x) = 1 + 2x - x^3 - √(x^4 + 1) , then f has a local minimum at x = ...

Answer :

77. 

The preceding figure shows the graph of g. If g(x) = ₁∫ ^x f (t) dt, which of the following could be the graph of y = f (x) ?

Answer :

78. The function f has derivatives of all orders for all real numbers. The table shown gives values of f and its first three derivatives at selected values of x. What is the value of _-1∫ ¹ f '' (x) dx ?

Answer :

79. On certain day, an industrial plant manufactures steel at a rate modeled by R (t) = 10 + 30e^-0,6t tons per hour, where t is measured in hours since the plant opened that day. What is the average rate at which the plant manufactures steel, in tons per hour, over the time interval 0 ≤ t ≤ 5 ?

Answer :

80. The power series

converges at x = 3. Which of the following must be true ?

Answer :

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.26 - 30

 26. Let f be function defined by f(x) = x^3 + x. If g is the reverse function of f, what is the slope of the line tangent to the graph of g at the point (2,1) ?

Answer :

27. 

The function f is continuous on the closed interval [0,5] and differentiable on the open interval (0,5). Selected values of f are given in the table shown. The value c = 4 satisfies the conclusion of the Mean Value Theorem for f on the closed interval [0,5]. What is the slope of the line tangent to graph of f at x = 4 ?

Answer :

28. Let f be a function with f(0) = 0 and derivative given by f'(x) = cos (x^2) . Which of the following is the Maclaurin series for f ?

Answer :

29. 

Let R be the region bounded by the graph of y = ln x , the vertical line x = e^2 , and the x-axis , as shown in the figure. Which of tthe following integrals are equal to the area of R ?

Answer :

30.

lim n →∞

k=1Σ n 

(3/n k)^2 (3/n) is ...

Answer :

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.21-25

 21. The function g has a continuous second derivative. If g (0) = 2 , g ' (0) = 4, g (3) = 5, and g ' (3) = 6, what is the value of ₀∫ ³ x . g''(x) dx ?

Answer :

22. The Maclaurin series for the function f is given below. What is the value of f⁽⁴⁾ (0) ?

Answer :

23. Let f be a differentiable function such that f (π) = 2 and f ' (π) = - 3. What is the slope of the line tangent to the polar curve r = f(π) at θ = π ?

Answer :

24. _{- ∞}∫ ¹ x^3 . 2^(x^3) dx is ...

Answer :

25.  ∫  dx / (x^2 + 4x + 5) = ...

2023 AP CALCULUS BC EXPLANATION SECTION 1 PART A NO.16 - 20

16. 

f(x) = x^2 - 2x for x≤ 4

f(x) = g(x) for x>4

let f be the function defined as shown. If f is differentiable, which of the following could define g(x) ?

answer :

17. The function y = f(x) satisfies the differential equation dy/dx = 2xy with the initial condition f(0) = 5. What is the value of f(2) ?

answer :

18. Which of the following gives the length of the curve y = tan x from x = - (π/4) to x = π/4 ?

answer :

19. If y = f(x) is a function such that dy/dx = (2x - y) / x , then d^2y / dx^2 = ...

answer :

20. Which of the following series converges to 1/e ?

answer :