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    GR 11 Worksheet Exponential

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    Ajneya .L
    This document contains 5 mathematics problems related to functions for an IB Math SL worksheet. The problems cover a range of topics including graph transformations, exponential and logarithmic functions, and modeling real-world scenarios involving population growth and bacterial growth over time. Students are asked to sketch graphs, find function values, rates of change, domains and ranges, areas under curves, and solve related equations. Neat working is required showing details like graph sketches and significant figures.

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    © All Rights Reserved
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    GR 11 Worksheet Exponential

    Uploaded by

    Ajneya .L
    166 views3 pages
    This document contains 5 mathematics problems related to functions for an IB Math SL worksheet. The problems cover a range of topics including graph transformations, exponential and logarithmic functions, and modeling real-world scenarios involving population growth and bacterial growth over time. Students are asked to sketch graphs, find function values, rates of change, domains and ranges, areas under curves, and solve related equations. Neat working is required showing details like graph sketches and significant figures.

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    Gr-11-worksheet-Exponential

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    This document contains 5 mathematics problems related to functions for an IB Math SL worksheet. The problems cover a range of topics including graph transformations, exponential and logarithmic functions, and modeling real-world scenarios involving population growth and bacterial growth over time. Students are asked to sketch graphs, find function values, rates of change, domains and ranges, areas under curves, and solve related equations. Neat working is required showing details like graph sketches and significant figures.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    166 views3 pages

    GR 11 Worksheet Exponential

    Uploaded by

    Ajneya .L
    This document contains 5 mathematics problems related to functions for an IB Math SL worksheet. The problems cover a range of topics including graph transformations, exponential and logarithmic functions, and modeling real-world scenarios involving population growth and bacterial growth over time. Students are asked to sketch graphs, find function values, rates of change, domains and ranges, areas under curves, and solve related equations. Neat working is required showing details like graph sketches and significant figures.

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    PATHWAYS WORLD SCHOOL: Mathematics Department

    Grade: 11 Level: SL Worksheet


    Topics: Functions Session-2017-2019
    • All the answers must be given to 3 sf, angle to 1 dp or the degree of accuracy specified in the question.
    • Show a neat sketch of the graph wherever needed with ALL NECESSARY DETAILS ON IT.

    1. Let f(x) = 3x2. The graph of f is translated 1 unit to the right and 2 units down.
    The graph of g is the image of the graph of f after this translation.

    (a) Write down the coordinates of the vertex of the graph of g. (2)

    (b) Express g in the form g(x) = 3(x – p)2 + q. (2)

    The graph of h is the reflection of the graph of g in the x-axis.

    (c) Write down the coordinates of the vertex of the graph of h. (2)
    (Total 6 marks)

    2. Let f(x) = Aekx + 3. Part of the graph of f is shown below.

    The y-intercept is at (0, 13).

    (a) Show that A =10. (2)

    (b) Given that f(15) = 3.49 (correct to 3 significant figures), find the value of k. (3)

    (c) (i) Using your value of k, find f′(x).

    (ii) Hence, explain why f is a decreasing function.

    (iii) Write down the equation of the horizontal asymptote of the graph f. (5)

    Let g(x) = –x2 + 12x – 24.

    (d) Find the area enclosed by the graphs of f and g.


    (6)
    (Total 16 marks)

    IB Questionbank Maths SL 1
    3. Consider the graph of f shown below.

    (a) On the same grid sketch the graph of y = f(–x). (2)

    The following four diagrams show images of f under different transformations.

    IB Questionbank Maths SL 2
    (b) Complete the following table.

    Description of transformation Diagram letter


    Horizontal stretch with scale factor 1.5
    Maps f to f(x) + 1
    (2)

    (c) Give a full geometric description of the transformation that gives the image in
    Diagram A.
    (2)
    (Total 6 marks)

    4. There were 1420 doctors working in a city on 1 January 1994. After n years the number of
    doctors, D, working in the city is given by

    D = 1420 + 100n.

    (a) (i) How many doctors were there working in the city at the start of 2004?

    (ii) In what year were there first more than 2000 doctors working in the city? (3)

    At the beginning of 1994 the city had a population of 1.2 million. After n years, the population,
    P, of the city is given by

    P = 1 200 000 (1.025)n.

    (b) (i) Find the population P at the beginning of 2004.

    (ii) Calculate the percentage growth in population between 1 January 1994 and 1
    January 2004.

    (iii) In what year will the population first become greater than 2 million? (7)

    (c) (i) What was the average number of people per doctor at the beginning of 1994?

    (ii) After how many complete years will the number of people per doctor first fall
    below 600?
    (5)
    (Total 15 marks)

    5. The number of bacteria, n, in a dish, after t minutes is given by n = 800e013t.

    (a) Find the value of n when t = 0. (2)

    (b) Find the rate at which n is increasing when t = 15. (2)

    (c) After k minutes, the rate of increase in n is greater than 10 000 bacteria per minute. Find
    the least value of k, where k  .
    (4)
    (Total 8 marks)

    IB Questionbank Maths SL 3

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