代做G11 AI HL UNIT TEST REVISION-FUNCTIONS代做留学生SQL语言

G11 AI HL UNIT TEST REVISION-FUNCTIONS

1.The following diagram shows part of the graph of f with x-intercept (5, 0) and y-intercept (0, 8).

(a.i)Find the y-intercept of the graph of f(x) + 3.                                                                  [1]

(a.ii)Find the y-intercept of the graph of f(4x).                                                                    [2]

(b)Find the x-intercept of the graph of f(2x).                                                                       [2]

(c)Describe the transformation f(x + 1).                                                                             [2]

2.Let f(x) = xz  - 4x - 5. The following diagram shows part of the graph off.

(b)Find the equation of the axis of symmetry of the graph of f.                                            [2]

The function can be written in the form f(x) = (x - h)2  + k.

(c.i)Write down the value of h.                                                                                              [1]

(c.ii)Find the value of k.                                                                                                        [3]

(d)The graph of a second function, g, is obtained by a reflection of the graph of f in the y-axis, followed by a translation of 

Find the coordinates of the vertex of the graph of g.                                                                 [5]

3.The graph of the function f is given in the following diagram.

(a)Write down f(2) .                                                                                                                        [1]

(b)On the axes, sketch y = f-1(x).                                                                                             [2]

The function g is defined as g(x) = 3x - 1.

(c)Find an expression for g-1(x)                                                                                                                               [2]

(d)Find a value of x where f-1(x) = g-1(x) .                                                                             [2]

4.Three towns, A, B and C are represented as coordinates on a map, where the x and y axes represent the distances east and north of an origin, respectively, measured in kilometres.

Town A is located at (−6,  −1) and town B is located at (8,  6). A road runs along the perpendicular bisector of [AB]. This information is shown in the following diagram.


(a)Find the equation of the line that the road follows.                                                               [5]

(b)Town C is due north of town A and the road passes through town C.

Find the y-coordinate of town C.                                                                                       [2]

5.Consider the following function:  for x > 1.

(a) Find h-1(1) .                                                                                                                         [2]

(b)Find the domain of h-1(x).                                                                                                [2]

6.The strength of earthquakes is measured on the Richter magnitude scale, with values typically between 0 and 8 where 8 is the most severe.

The Gutenberg–Richter equation gives the average number of earthquakes per year, N, which have a magnitude of at least M. For a particular region the equation is log10 N = a − M, for some a ∈ R.

This region has an average of 100 earthquakes per year with a magnitude of at least 3.

(a)Find the value of a.                                                                                                              [2]

The equation for this region can also be written as 

(b)Find the value of b.                                                                                                               [2]

(c)Given 0 < M < 8, find the range for N.                                                                                  [2]

The expected length of time, in years, between earthquakes with a magnitude of at least M is N/1.   Within this region the most severe earthquake recorded had a magnitude of 7.2.

(d)Find the expected length of time between this earthquake and the next earthquake of at least this magnitude. Give your answer to the nearest year.                                                                           [2]

7.A scientist is conducting an experiment on the growth of a certain species of bacteria.

The population of the bacteria, P, can be modelled by the function P(t) = 1200 × kt , t ≥ 0, where t is the number of hours since the experiment began, and k is a positive constant.

(a.i)Write down the value of P(0).                                                                                                [1]

(a.ii)Interpret what this value means in this context.                                                                    [1]

3 hours after the experiment began, the population of the bacteria is 18 750.

(b)Find the value of k.                                                                                                                [2]

(c)Find the population of the bacteria 1 hour and 30 minutes after the experiment began.          [2]

The scientist conducts a second experiment with a different species of bacteria.

The population of this bacteria, S , can be modelled by the function S(t) = 5000 × 1.65t , t ≥ 0, where t is the number of hours since both experiments began.

(d)Find the value of t when the two populations of bacteria are equal.                                        [2]

It takes 2 hours and m minutes for the number of bacteria in the second experiment to reach 19 000.

(e)Find the value of m, giving your answer as an integer value.                                                      [4]

8.A cell phone starts charging at 07: 00. While being charged, the percentage of power, P, in the phone is modelled by the function P = 100 一 60 × a-t , where t is the number of hours after 07: 00.

(a)Find the percentage of power in the phone at 07: 00.                                                               [2]

The percentage of power in the phone reaches 75 % at 08: 00.

(b)Find the value of a.                                                                                                               [2]

(c)Draw the graph of P = 100 一 60 × a-t on the following set of axes.


[2]

(d)State a mathematical reason why the model predicts the percentage of power in the phone will never reach 100 %.                  [1]

9.Consider the function f(x) = ax2  + bx + c . The graph of y  = f(x) is shown in the diagram. The vertex of the graph has coordinates (0.5,  −12.5). The graph intersects the x-axis at two points,  (−2,  0) and (p,  0).

(a)Find the value of p.                                                                                                             [1]

(b)Find the value of

(i)    a.

(ii)   b.

(iii)  c .                                                                                                                             [5]

(c)

Write down the equation of the axis of symmetry of the graph.                                                 [1]

10.The pH scale is a measure of the acidity of a solution. Its value is given by the formula

pH = −log10  [H+], where [H+] is the concentration of hydrogen ions in the solution (measured in moles per litre).

(a)Calculate the pH value if the concentration of hydrogen ions is 0.0003.                                   [2]

The pH of milk is 6.6.

(b)Calculate the concentration of hydrogen ions in milk.                                                              [2]

The strength of an acid is measured by its concentration of hydrogen ions.

A lemon has a pH value of 2 and a tomato has a pH value of 4.5.

(c)Calculate how many times stronger the acid in a lemon is when compared to the acid in a tomato. [3]





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