Using Numbers and Graphics in Science

Harry wants to build a compound machine using two different simple machines. If order does not matter to Harry, how many different compound machines could he make?

Simple Machines

A simple machine is a mechanical device that changes the direction or magnitude of a force. The five types of simple machines are the (1) lever, (2) wheel and axle, (3) pulley, (4) inclined plane, and (5) screw.

Simple machines can be regarded as the elementary "building blocks" of which all more complicated machines (sometimes called "compound machines") are composed. For example, a bicycle is a compound machine that uses wheels, levers, and pulleys.

Source: https://en.wikipedia.org/wiki/Simple_machine

 

• 20

• 15

• 25

• 10

What is the spring constant for a spring that has been stretched 5 mm if the spring has an elastic potential energy of 200J?

Elastic Energy Formula

Elastic potential energy is the amount of potential energy that an elastic material possesses due to being stretched or compressed. A spring is a common example of an elastic material. The formula for the elastic potential energy of a spring is:

PEspring=1/2⋅k⋅x²

Where the elastic potential energy (PEspring) is measured in joules, the spring constant (k) is measured in newtons per meter (Nm), and the distance the spring is stretched or compressed compared to its rest position (x) is measured in meters.

• 16N/m

• 32N/m

• 80N/m

• 160N/m

A local construction company has access to seven different resources, but only has enough employees to extract three of these resources. How many ways can they choose which three resources to extract of the seven available? (Assume that the extraction of one resource does not affect the extraction of the other resources.)

Sustainable Resource Extraction

Sustainable resource extraction is using materials available in nature in a way that does not affect its balance. Usually, sustainability is based on some kind of cost-benefit analysis, where one has to accept some damage (or human-caused imbalance) to the ecosystem. Sustainability is the main concept that includes the use and disposal of materials, whereas extraction refers mainly to the process of actual harvest.

In resource extraction, sustainability is often achieved when the possible damages of it are minimized and the future of the ecosystem is ensured. One example of sustainable resource extraction is forestry when it tries to imitate nature's own processes and plant or seed the new forest.

Source: https://en.wikipedia.org/wiki/Sustainable_resource_extraction

• 21

• 210

• 35              

• 42

Nurse Becky at Victoria Elementary School found lice on seven of the children she sampled. She looked at their class schedules and noticed that all seven of them were in Mr. Hank’s morning mathematics class.

What should Nurse Becky do?

Lice Outbreak

Lice are tiny insects that live on humans and feed on their blood. As they feed on humans’ blood, they get larger but they harm the human on which they are living. This makes lice a parasite – it feeds off of a host and ultimately harms the host in the process.

Lice cannot fly or jump, but they can spread easily from one person to another when personal items are shared. Lice are often found in schools, where many students work closely together and share personal items.

• 
  Nurse Becky should automatically assume all the students in Mr. Hank’s morning mathematics class have lice and send them all home without checking.

• Nurse Becky should check every single first grade student, because she heard from a friend that first graders typically have lice more than any other grade level.

• Nurse Becky should check all the students in Mr. Hank’s morning mathematics class to determine if any of them have lice.

• Nurse Becky should check every single student at the school to determine if any students have lice.

Suppose Charles Darwin was able to count the populations of finches on three small islands and record his findings in a table.

If Charles Darwin wanted to select one finch from each island for future study, how many different ways would he be able to select these finches?

Allopatric Speciatio

Speciation is the evolutionary process by which biological populations evolve to become distinct species. The biologist Orator F. Cook coined the term speciation in 1906, but Charles Darwin was the first to describe the role of speciation in his 1859 book The Origin of Species.

There are four geographic modes of speciation in nature, based on the extent to which speciating populations are isolated from one another: allopatric, peripatric, parapatric, and sympatric. Allopatric is the most observed mode of speciation. During allopatric speciation, a population splits into two geographically isolated populations. The isolated populations then undergo genotypic or phenotypic divergence as they become subjected to dissimilar selective pressures and as different mutations arise. When the populations come back into contact, they have evolved such that they are reproductively isolated and are no longer capable of exchanging genes

The Galápagos Islands are particularly famous for their confirmation of allopatric speciation. During Charles Darwin’s five weeks on the Galápagos Islands, he noticed that finches differed from one island to another. When he returned to England, his speculation on evolution deepened after experts informed him that these were separate species, not just varieties. Darwin's finches are now one of the most well-known examples of adaptive evolution and allopatric speciation discussed in biology today.

Adapted from https://en.wikipedia.org/wiki/Speciation

• A. 3

• 1,200

• 1,200,000

• 60,000,000

) Sam has a mass of 68 kg. What is Sam’s approximate weight in newtons?

Mass vs Weight

Although the terms mass and weight are often used interchangeably, they are not the same. Mass is the measure of how much matter is present in an object. Weight takes into account the effect that gravity has on an object. The relationship between weight and mass is represented in the following equation:

w=mg

w is the weight of an object in newtons (1 N=1 kg⋅ms2)

m is the mass of an object in grams

g is the gravitational force acting on the object in meters per second squared (on Earth, g≈9.81m/s2

• 68 N

• 667 N

• 981 N

• A. 6,800 N

A fox is an animal that eats a wide variety of smaller animals. Suppose a fox has the opportunity to hunt two out of five animals for its meal. Assuming the order in which the fox hunts is important, how many ways can it choose two animals to hunt?

 

• 2

• 5

• 10                   

• 20

A group of agricultural researchers conducted an experiment to study the growth rates of plants at various temperatures. In their laboratory, they divided primrose, cucumber, and corn plants into a number of different groups. During the experiment, they kept the different groups of primrose plants at different but constant temperatures for twenty-four hours every day. They did the same for the corn and cucumber plants. The graph shows the growth rates that they recorded for the different groups of plants.

According to the graph, at what temperature did primroses grow best?

• 40 °F

• 50 °F

• 60 °F

• 80 °F

• 70 °F

A group of agricultural researchers conducted an experiment to study the growth rates of plants at various temperatures. In their laboratory, they divided primrose, cucumber, and corn plants into a number of different groups. During the experiment, they kept the different groups of primrose plants at different but constant temperatures for twenty-four hours every day. They did the same for the corn and cucumber plants. The graph shows the growth rates that they recorded for the different groups of plants.

Judging from the data in the graph, what sort of climate would favor the growth of cucumbers?

• cold nights, cold days

• cold nights, warm days

• very warm nights, very warm days

• warm, rainy days

• warm nights, cool days

The lightweight-materials content of the average car manufactured in the United States has increased sharply since the mid-1970s. The data shown in the graph are for an average passenger car produced by one major manufacturer and are typical of all U.S. automakers. Lightweight materials are shown in blue. Heavy materials are indicated in yellow.

Which of the following statements is a conclusion about cars made during the 1980s that can be drawn from the graph?

• Cars in the 1980s became increasingly expensive.

• Cars made during the 1980s weighed less than cars made during the 1970s.

• Cars made in the 1980s were more difficult to handle than those in the 1970s.

• Cars made during the 1980s weighed more than cars made during the 1970s.