Geometry Unit 1 Review Problems

The distance around a circle.

The space inside a circle.

The distance from the center of a circle to its edge.

A line segment that passes through the center of a circle and connects two points on the circle.

The ratio of a circle's circumference to its diameter; always approximately 3.14.

The formula used to calculate the circumference of a circle.

The formula used to calculate the area of a circle.

The relationship between two quantities where the ratio remains constant.

A scaled copy is a shape that has been enlarged or reduced by a certain factor. The ratio of corresponding side lengths is called the scale factor. All angles in the original figure and the scaled copy are the same. If two figures are scaled copies of each other, they are similar figures.

A scale drawing is a representation of a real-world object or place that is proportionally smaller or larger than the actual object or place. The scale factor tells us how much smaller or larger the drawing is than the original.

The area of a rectangle is found by multiplying the length and width. To find the area of a scaled copy of a rectangle, square the scale factor and multiply it by the area of the original rectangle. This is because both dimensions are multiplied by the scale factor.

The area of the park can be found by dividing the length of the park by the length of the drawing (330 yards / 11 inches = 30 yards/inch). This gives the scale factor for the drawing. To find the width of the park, multiply the width of the drawing by the scale factor (8 inches * 30 yards/inch = 240 yards). Then multiply the length and width of the park to find its area (330 yards * 240 yards = 79200 square yards).

A proportional relationship means that as one quantity increases, the other quantity increases at a constant rate. This can be represented by a straight line passing through the origin on a graph. The equation of the line will be in the form y = kx, where k is the constant of proportionality or the slope of the line.

In a proportional relationship graph, the slope of the line is the constant of proportionality. This constant represents the rate of change between the two quantities.

A relationship is proportional when the ratio between two quantities is constant. In other words, as one quantity increases, the other quantity increases at a constant rate.

A proportional relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, y changes directly with x.

In a proportional relationship, the graph is a straight line that passes through the origin (0,0).

In a proportional relationship, the unit rate is the constant of proportionality (k). It represents the amount of change in one quantity for every one unit change in the other quantity.

The constant of proportionality in a proportional relationship can be found by dividing any y-value by its corresponding x-value.

The point (1, k) is always on the graph of a proportional relationship, where k is the constant of proportionality. This point represents the unit rate.

A linear equation represents the relationship between two variables where the graph is a straight line. The equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

The slope of a line represents the rate of change between two variables. It is calculated as the change in y divided by the change in x.

The amount of space inside a circle.

It's a bit like 'perimeter' but for circles. It's the total distance around the circle.

It's about figuring out how much space is taken up inside the circle.

The distance from the center of a circle to its edge.

It's the line that goes straight across the circle through the center.

The percentage decrease in a population is calculated by finding the difference in population between two points in time, dividing that difference by the original population, and multiplying by 100%.

A discount represents a percentage reduction in the price of a product. To determine its price after a discount, we multiply the original price by the discount percentage and subtract the result from the original price.

A proportional relationship exists when the ratio between two quantities remains constant. In the context of discounts, the price after the discount is directly proportional to the original price; doubling the original price will also double the price after the discount.

A percentage increase represents a scaling up of a quantity. It is calculated by finding the difference between the original value and the increased value, dividing that difference by the original value, and multiplying by 100%.

A linear equation represents a direct relationship between two variables. In this context, the equation y = mx + c relates the cost of an item next year (y) to its cost this year (x). The slope (m) represents the percentage increase, and the constant (c) may represent a base price or other factors.