Modeling Revision Questions Set 1

Transcription

1 Modeling Revision Questions Set. In an eperiment researchers found that a specific culture of bacteria increases in number according to the formula N = 5 2 t, where N is the number of bacteria present and t is the number of hours since the eperiment began. Use this formula to calculate the number of bacteria present at the start of the eperiment; the number of bacteria present after 3 hours; (c) the number of hours it would take for the number of bacteria to reach The graph of = is shown on the aes below Draw the graph of = 5 on the same aes. Use our graph to find: (i) the values of when = 5 (ii) the value of that gives the minimum value of 2 2 3

2 3. The diagram shows the graph of = The graph crosses the -ais at the point A, and has a verte at B. A O B Factorise Write down the coordinates of each of these points (i) A; (ii) B. 4. The following diagram shows part of the graph of an eponential function f() = a, where. f () P What is the range of f? Write down the coordinates of the point P. (c) What happens to the values of f() as elements in its domain increase in value?

3 5. A function f is represented b the following mapping diagram Write down the function f in the form f() =, {the domain of f}. The function g is defined as follows g() = sin 5, { and < 4}. Complete the following mapping diagram to represent the function g. 6. Solve the equation =. Find the coordinates of the points where the graph of = intersects the -ais.

4 7. Diagram shows a part of the graph of = 2. Diagram Diagrams 2, 3 and 4 show a part of the graph of = 2 after it has been moved parallel to the -ais, or parallel to the -ais, or parallel to one ais, then the other Diagram 2 Diagram 3 Diagram 4 Write down the equation of the graph shown in Diagram 2; Diagram 3; (c) Diagram 4. 3

5 8. The graph below shows the curve = k(2 ) + c, where k and c are constants Find the values of c and k. 9. The diagram below shows a part of the graph of = a. The graph crosses the -ais at the point P. The point Q (4, 6) is on the graph. Q (4, 6) P O Find the coordinates of the point P; the value of a.

6 . The diagrams below show the graphs of two functions, = f(), and = g()..5 = f( ) = g( ) º 8º.5 8º 36º 2.5 State the domain and range of the function f; the function g.. The conversion formula for temperature from the Fahrenheit (F) to the Celsius (C) 5( F 32) scale is given b C =. 9 What is the temperature in degrees Celsius when it is 5 Fahrenheit? There is another temperature scale called the Kelvin (K) scale. The temperature in degrees Kelvin is given b K = C What is the temperature in Fahrenheit when it is zero degrees on the Kelvin scale?

7 2. The figure below shows part of the graph of a quadratic function = a c Write down the value of c. Find the value of a. (c) Write the quadratic function in its factorised form. 3. The graph of the function f () = is shown in the diagram below. Diagram not to scale A B C Factorize the epression Write down the coordinates of the points A and B. (c) (d) Write down the equation of the ais of smmetr. Write down the coordinates of the point C, the verte of the parabola.