Consider the function $f(x) = \ln(x^2 + 1). $</p><p>a) Use integration by parts to find the indefinite integral of$f(x)$.

The diagram shows an eyepiece graticule and cell viewed through a microscope. When the eyepiece graticule was calibrated at this magnification, the whole length of the graticule shown covered 12 divisions of a stage micrometer scale.

There were 100 divisions in 10 mm of the stage micrometer.

What is the actual length of the cell?

A 2.5 um

В 3.6 um

С 360 um

D 3mm

The photomicrograph shows the ultrastructure of part of a cell.

Which statement about the type of cell shown in the photomicrograph is correct?

A It is a plant cell because it has both chloroplasts and a nucleus.

B It is a plant cell because it has chloroplasts.

C It is an animal cell because it has a cell membrane.

D It is an animal cell because it has mitochondria.

A student examined a slide of human blood with a light microscope and made a careful drawing of the different cell types. The student used an eyepiece graticule so that the relative sizes of the different cell types were drawn accurately.

In the drawing:

• red blood cells were 7 mm in diameter

• lymphocytes were 6 mm in diameter

• neutrophils were 14 mm in diameter.

What is the linear magnification of the drawing?

A. x10

B. x40

C. x100

D. x1000

The diagram shows a graduated slide, with divisions of 0.1 mm viewed using an eyepiece graticule.

Pollen grains were grown in a sugar solution and viewed using the eyepiece graticule. Diagram 1 shows the pollen grains at the start. Diagram 2 shows the pollen grains after four hours.

What is the growth rate of the pollen tubes?

A. 5 μmh^-1

B. 10 μmh-¹

C. 5 mmh^-1

D. 10 mmh^-1

What is the definition of the resolution of a light microscope?

A. the degree of sharpness produced by the microscope

B. the greatest distance between two objects visible in the same field of view

C. the minimum distance that allows two objects to be viewed as separate

D. the size of the smallest object visible using the microscope

The electron micrograph shows a type of virus at a magnification of x30 000.

What is the length of the virus?

A. 2.2x10³nm

B. 2.2x10²nm

C. 2.2x10¹nm

D. 2.2x10⁰nm

A student was given a photomicrograph of a cell and told the magnification of the image. The student was asked to calculate the actual size of the cell. Which row in the table explains how to do this?

Which row shows the correct order of size of these cell structures?

1 width of a mitochondrion

2 width of a ribosome

3 width of a cell surface membrane

4 width of a chloroplast

The diagram shows a stage micrometer scale viewed through an eyepiece containing a graticule.

The small divisions of the stage micrometer scale are 0.1 mm

The stage micrometer scale is replaced by a slide of a plant cell.

What is the actual length of the nucleus in the plant cell?

A. 8 μm

B. 25 μm

C. 200 μm

D. 0.8 mm

The size of the measles virus, Morbillivirus, is approximately 150 nm.

The Mimivirus is approximately 4.5 times larger than Morbillivirus, whilst the Pandoravirus is approximately 1.5 times larger than the Mimivirus.

Which viruses can be seen using a light microscope with a maximum resolution of 0.25 μm and using an electron microscope?

The electron micrograph shows a type of virus at a magnification of x60 000.

What is the actual length of the virus?

A. 1.1 nm

B. 11 nm

C. 110 nm

D. 1100 nm

What are the appropriate units for measuring diameters of alveoli, diameters of white blood cells and the width of cell walls?

The actual diameter of a prokaryotic cell is 0.5 μm. An electron micrograph of the cell has a magnification of x50 000.

What is the diameter of the cell in the image?

A. 2.5 x 10^-1mm

B. 2.5x10⁰mm

C. 2.5x10¹mm

D. 2.5x10²mm

The diagram below was drawn from an electron micrograph of an animal cell.

Which diagram would represent the same cell seen under a simple light microscope, using daylight as the only light source?

The diameter of a red blood cell in a diagram was measured as 2.5 cm. The actual diameter of the red blood cell was 7 μm. Which calculation would give the correct magnification for the red blood cell in the diagram?

A. 7/25000

B. 2500/7

C. 25000/7

D. 25000/7000

The diagram shows a fin whale drawn to scale.

A student made three statements about the diagram.

1 The magnification is x0.006.

2 The ratio of actual size to diagram size is 1667:1 .

3 The fin whale has an actual length of 24 m.

Which statements are correct?

A. 1, 2 and 3

B. 1 and 2 only

C. 1 and 3 only

D. 3 only

A student was told that the actual length of a cell structure is 5 μm. The student was asked to state an equation that can be used to calculate the magnification of an electron micrograph of this cell structure. The student used some of the letters q to u in the equation.

q = the length of the cell structure image on the micrograph in centimetres

r = the length of the cell structure image on the micrograph in millimetres

s = 1000

t = 1/5

u = 5

Which is the correct equation to calculate the magnification?

A. q/s*u

B. q*s*t

C. r/s*u

D. r*s*t

The actual length of a cell structure is 8 μm. Which steps are used to calculate the magnification of an electron micrograph of this cell structure?

• step 1 measure the length of the cell structure image on the micrograph in centimetres
• step 2 measure the length of the cell structure image on the micrograph in millimetres
• step 3 divide the image length by 1000
• step 4 multiply the image length by 1000
• step 5 divide by 8
• step 6 multiply by 8

A. steps 1, 3 and 6

B. steps 1, 4 and 6

C. steps 2, 3 and 5

D. steps 2, 4 and 5

What is the typical resolution of a microscope using daylight as a light source with a x10 eyepiece lens and a x40 objective lens?

A. 0.20 nm

B. 200 nm

C. 100 μm

D. 400 μm

Which combination of lenses for a light microscope will give the greatest magnification?