Geometry Unit 1 & 2 Review

Unit 1 Review Problems

• Problem 1: Identify scaled copies of a rectangle. Multiple rectangles are shown with dimensions. Determine which rectangles are scaled copies of a reference rectangle A.

• Problem 2: Polygon EFGH is a scaled copy of polygon ABCD. True statements include the scale factor from EFGH to ABCD is 3/1, and the length of segment BC is 2. Segment GH is three times as long as segment AB.

• Problem 3: A scale drawing of a rectangular park is 8 inches wide and 11 inches long. The actual park is 330 yards long. Calculate the area of the actual park. The answer is 2,640 square yards.

Unit 2 Review Problems

• Problem 1: Identify the graph that represents a proportional relationship. The correct graph is a straight line that starts at the origin (0,0).

Unit 2 (Additional Problems)

• Problem 2: The graph shows the cost of strawberries. The cost is proportional. Identify true statements regarding the cost of different quantities of strawberries. Identify the true statements.

• Problem 3: Abdullah walks to school at a constant speed. He walks 1 mile in 15 minutes. Identify the equation representing time (in minutes, t) as a function of distance (in miles, d). The equation is t = 15d.

• Problem 4: Two runners' distances are represented by two lines. Identify which runner ran more slowly. This problem requires a comparison of the slopes of the lines representing distance vs time.

Unit 3 Review Problems

• Problem 1: A circle has a radius of 40 centimeters. Which is closest to its circumference? The answer is approximately 251 centimeters.

Unit 3 (Additional Problems)

• Problem 2: A circle has a radius of 6 units. Order three student answers for the area of the circle from least to most accurate.

• Problem 3: Arjun measured the distance a wheel traveled in different numbers of rotations. Select true statements.

• Problem 4: Identify whether a quantity describes a circle's circumference or area. These include the amount of glass in a circular window, tiles needed to go around a circular pool, etc.

• Problem 5: Which measurement is always proportional to the diameter of a circle? The answer is Circumference.

• Problem 6: A figure consists of part of a circle and a rectangle. Calculate the perimeter and area of the figure. The perimeter is 16+4π or 28.56. The area is ≈32+8π or 57.12 square units

Unit 4 Review Problems

• Problem 1: A pencil is 120 millimeters long. A marker is 9% longer than the pencil. Calculate the length of the marker. The marker is 130.8 millimeters long.

• Problem 2: Kayleen mows a field. After mowing 1/8 of the field, she used 1/2 of a gallon of gas. Select all true statements. The statements are related to the amount of gas used mowing different portions of the field.

• Problem 3: The temperature in a room is 20.0°C. A thermometer measures the temperature as 20.8 °C. Find the percent error. The percent error is 4%.

• Problem 4: Identify if the price of the rug after a discount and sales tax is more or less than a stated amount or if it equals that amount (e.g., $50.00). Provide an explanation.

Intermediate Review Problems

• Problem 8: Determine if the relationship is proportional for height and running speed. Provide answers if available.

• Problem 8.1: Find the distance around the outside edge of the concrete sidewalk around a fish pond of a specified diameter and sidewalk width.

• Problem 8.2: Find the square meters of concrete needed to build a sidewalk around a fish pond.

• Problem 7.1: Find the number of boxes of tile needed to cover the bottom of a circular pool.

• Problem 7.2: Determine if the number of boxes of tile needed for Pool B is four times the number for Pool A, provide justification. (Using areas of the circles and the size of one box of tile)

• Problem 6.1 & 6.2: Determine if there is a proportional relationship between the original price, and the discounted price of an item.

• Problem 6.3: Calculate original price of a coat given the discounted price. 

• Problem 7.1: Calculate the expected cost of a new car considering a rate of increase.

• Problem 7.2: Calculate an equation that relates current year's cost of a car to next year's cost.

• Problem 7.3: Calculate the expected cost of another car considering a rate of increase in two years. 

• Problem (Unit 4): Helen is painting her room. After painting 20% of her room, Dalia has used 75% of a can of paint. Identify which of the provided statements is correct.