1: Modules
- Page ID
- 56835
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- 1.1: Order of Operations
- To evaluate an expression means to simplify it and find its value.
- 1.2: Negative Numbers
- Negative numbers are a fact of life, from winter temperatures to our bank accounts. Let’s practice evaluating expressions involving negative numbers.
- 1.3: Decimals
- Decimal notation is based on powers of 10 : 0.1 is one tenth, 0.01 is one hundredth, 0.001 is one thousandth, and so on.
- 1.5: Accuracy and Significant Figures
- Every measurement contains some error. A standard sheet of paper is 8.5 inches wide and 11 inches high, but it’s possible that the actual measurements could be closer to 8.4999 and 11.0001 inches. Even if we measure something very carefully, with very sensitive instruments, we should assume that there could be some small measurement error.
- 1.6: Precision and GPE
- The precision of a number is the place value of the rightmost significant figure. For example, 100.45 is precise to the hundredths place, and 3,840 is precise to the tens place.
- 1.7: Formulas
- A formula is an equation or set of calculations that takes a number (or numbers) as input, and produces an output. The output is often a number, but it could also be a decision such as yes or no. The numbers in a formula are usually represented with letters of the alphabet, which are called variables because their values can vary. To evaluate a formula, we substitute a number (or numbers) into the formula and then perform the steps using the order of operations.
- 1.8: Perimeter and Circumference
- A polygon is a closed geometric figure with straight sides. Common polygons include triangles, squares, rectangles, parallelograms, trapezoids, pentagons, hexagons, octagons… The perimeter of a polygon is the distance around the outside. In general, to find the perimeter of a polygon, you can add up the lengths of all of its sides.
- 1.9: Percents Part 1
- Percent means “per one hundred”. A percent is a ratio or fraction with a denominator of 100 .
- 1.10: Ratios, Rates, Proportions
- A ratio is the quotient of two numbers or the quotient of two quantities with the same units. A rate is the quotient of two quantities with different units. You must include the units. A proportion says that two ratios (or rates) are equal.
- 1.12: Percents Part 2 and Error Analysis
- In this module, we will learn how to find the percentage rate and the base.
- 1.13: The US Measurement System
- This system used to be called the English system, but now the U.S. has the dubious honor of being associated with the system that uses inches, feet, miles, ounces, pounds, cups, gallons, etc. To convert from one unit to another, we often have to perform messy calculations like dividing by 16 or multiplying by 5,280.
- 1.14: The Metric System
- The metric system was first implemented following the French Revolution; if we’re overthrowing the monarchy, why should we use a unit of a “foot” that is based on the length of a king’s foot?
- 1.15: Converting Between Systems
- Converting between the U.S. system and metric system is important in today’s global economy; like it or not, the metric system is infiltrating our lives.
- 1.17: Angles
- Angle measurement is important in construction, surveying, physical therapy, and many other fields. We can visualize an angle as the figure formed when two line segments share a common endpoint. We can also think about an angle as a measure of rotation. A full rotation or a full circle is 360∘ , so a half rotation or U-turn is 180∘ , and a quarter turn is 90∘ .
- 1.19: Area of Polygons and Circles
- We have seen that the perimeter of a polygon is the distance around the outside. Perimeter is a length, which is one-dimensional, and so it is measured in linear units (feet, centimeters, miles, etc.). The area of a polygon is the amount of two-dimensional space inside the polygon, and it is measured in square units: square feet, square centimeters, square miles, etc.
- 1.20: Composite Figures
- Many objects have odd shapes made up of simpler shapes. A composite figure is a geometric figure which is formed by—or composed of—two or more basic geometric figures. We will look at a handful of fairly simple examples, but this concept can of course be extended to much more complicated figures.
- 1.21: Converting Units of Area
- Converting between units of area requires us to be careful because square units behave differently than linear units.
- 1.22: Surface Area of Common Solids
- In this module, we will look the surface areas of some common solids. (We will look at volume in a later module.) Surface area is what it sounds like: it’s the sum of the areas of all of the outer surfaces of the solid. When you are struggling to wrap a present because your sheet of wrapping paper isn’t quite big enough, you are dealing with surface area.
- 1.23: Area of Regular Polygons
- A regular polygon has all sides of equal length and all angles of equal measure. Because of this symmetry, a circle can be inscribed—drawn inside the polygon touching each side at one point—or circumscribed—drawn outside the polygon intersecting each vertex.
- 1.24: Volume of Common Solids
- The surface area of a solid is the sum of the areas of all its faces; therefore, surface area is two-dimensional and measured in square units. The volume is the amount of space inside the solid. Volume is three-dimensional, measured in cubic units. You can imagine the volume as the number of cubes required to completely fill up the solid.
- 1.25: Converting Units of Volume
- Just as we saw with area, converting between units of volume requires us to be careful because cubic units behave differently than linear units.
- 1.28: Mean, Median, Mode
- We often describe data using a measure of central tendency. This is a number that we use to describe the typical data value. We will now look at the mean, the median, and the mode.
- 1.29: Probability
- Probability is the likelihood that some event occurs. If the event occurs, we call that a favorable outcome. The set of all possible events (or outcomes) is called the sample space of the event. We will limit our focus to independent events, which do not influence each other. For example, if we roll a 5 on one die, that does not affect the probability of rolling a 5 on the other die.