Semester One Comprehensive Exam

Transcription

1 TOPICS: Order of Operations o N.FL Solve problems involving operations with integers. o N.FL Add, subtract, multiply, and divide positive and negative rational numbers fluently. o A.FO Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) 5x + y, or x(x+2) and justify using properties of real numbers. Measurement o G.SR Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specific dimensions. Using Variables Inequalities Square and Cube Roots o N.MR Understand the concept of square root and cube root, and estimate using calculators. o N.ME Understand the meaning of a square root of a number and its connection to the square whose area is the number; understand the meaning of a cube root and its connection to a volume of a cube. o N.FL Estimate and solve problems with square roots and cube roots using calculators. o N.FL Find square roots of perfect squares and approximate the square roots of nonperfect squares by locating between consecutive integers, e.g., 130 is between 11 and 12. Basic Shapes Triangles, Quadrilaterals, Circles (Area, Perimeter/Circumference) o G.SR Understand the definition of a circle; know and use the formulas for circumference and area of a circle to solve problems. o G.SR Find area and perimeter of complex figures by sub-dividing them into basic shapes (quadrilaterals, triangles, circles). o G.SR Solve applied problems involving areas of triangles, quadrilaterals and circles. Volume & Surface Area (Prisms, Cylinders, Spheres) and Nets/Views o G.SR Know the volume formulas for generalized cylinders (V=Bh), generalized cones and pyramids ( V = Bh ), and spheres ( V =! r ) and apply them to solve problems. 3 3 o G.SR Understand the concept of surface area, and find the surface area of prisms, cones, spheres, pyramids, and circles. o G.SR Sketch a variety of 2-dimensional representations of 3-dimensional solids including orthogonal views (top, front, right side), picture views (projective or isometric), and nets; use such 2-dimensional representations to help solve problems. Probability/Relative Frequency o D.PR Compute relative frequencies from a table of experimental results for a repeated event. Interpret the results using relationship of probability to relative frequency. o D.PR Find and/or compare the theoretical probability, the experimental probability, and/or the relative frequency of a given event. o D.PR Understand the difference between independent and dependent events, and recognize common misconceptions involving probability, e.g., Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the fourth roll as she was on any previous roll. If-Then Statements (Always, Sometimes, Never) Unions & Intersections Classifying Shapes

2 Review Problems Chapter 2 Self Test Pg. 123 # 1, 6-8, Chapter 4 Self Test Pg. 269 # 7, 8, Chapter 11 Self Test Pg. 733 # 1, 3, 12 Chapter 7 Review Pg. 480 # 1, 3 L.5-8 Pg. 333 # 11, 13 L.3-8 Pg. 184 # 11, 15, 19 L.10-2 Pg. 626 # 5, 7, 9 (solve & check) L.10-4 Pg. 639 # 5, 7 (solve & checks) *All answers should be provided in the back of the book. Name Date Hour

3 Show all work. You may use your calculator for simple arithmetic, but you must show your steps. Remember, since you are using your calculator, no rounding should be done until you reach your final answers. 1. Lorena is planning to paint her house. The diagram on the last page of this test shows the right side of the house. She plans to paint this side (and only this side) red. Feel free to remove the last page from the rest of the test packet so you can look at it while answering all questions related to Lorena s house. a. Before she paints the side of the house, she needs to tape along the perimeters of the five windows. i. Find the circumference of the circular window. Round your answer to the nearest thousandth. ii. Find the perimeter of a single rectangular window. iii. What is the least amount of tape she will need? Round your answer up to the next whole foot. (Remember to account for all windows!) b. To ensure she buys the right amount of red paint, Lorena needs to find the area of the surface to be painted. Find this area to the nearest square foot. (Remember, Lorena doesn t paint the windows!)

4 c. Below is a rough sketch of the 3-dimensional view of Lorena s house. Draw the top, front, and right side views. d. Lorena wants to buy a protective film that filters out ultra-violet rays to cover the windows. i. Find the area of the circular window. Round your answer to the nearest thousandth. ii. Find the area of a single rectangular window. iii. What is the least amount of film she will need? Round your answer up to the next square foot. (Remember to account for all windows!)

5 e. When Lorena goes to the hardware store to purchase paint each gallon comes in a cylindrical container. The diameter of the base is 7 inches and the height of the can is 10 inches. Ignoring the thickness of the can, how much can the container hold? Round your answer to the nearest tenth. f. On her way home from the hardware store, Lorena pretends that she is an engineer for Behr (the paint manufacturer). Help Lorena determine how much plastic is required to make the paint can. Round your answer to the nearest tenth. g. Consider the following If-Then statement: If Lorena paints the right side of her house red, then she is happy. i. What is the hypothesis? ii. What is the conclusion? iii. Is the statement always, sometimes or never true? (Explain your answer!) iv. Write the converse of the statement. v. Is the converse always, sometimes or never true?

6 h. Use a ruler to measure the scaled drawing of the right side of Lorena s house. What is the width of the bottom of the house in centimeters? Round your answer to the nearest tenth. 2. Solve and check(s). a. 15x 40 = 23 8x " c b. + 9! 3 6 c. Graph the solution to question 2b.

7 3. Simplify. a. 72 is approximately equal to (Round to the nearest thousandth). b. 72 is between which two consecutive whole numbers? c. If the area of a square is 169 square units, what is the length of each side of the square? d. Extra Credit. Fill in the blanks. If the of a cube is 216 cubic inches, then the length of each edge is inches. In other words, the dimensions of the cube are x x. 4. Let A be all even prime numbers and B be the set {2, 6, 8, 11, 15, 18, 20.5, 22}. Hint: List all the even prime numbers before you answer the following questions! a. Find A! B b. Find A! B 5. Assume we are playing the dice game. Five of the dice count as scoring dice so far. You are trying to decide whether you should keep the score and end your turn, or if you should take a chance and roll the remaining die. What is the probability of you rolling a scoring die?

8 6. Match the appropriate terms with the definition or picture. The net for a cylinder A. A 3-sided polygon The net for a triangular prism B. Triangle C. A 10-sided polygon Pentagon D. Decagon E. A 5-sided polygon The net for a rectangular prism F. A 7-sided polygon Nonagon G. A 4-sided polygon Quadrilateral H. Octagon I. A 9-sided polygon Heptagon J. A 8-sided polygon

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