3. Here is a stem and leaf plot of the Weights of students in East Junior High Algebra I Class

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Eleanor Shields
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1 Test One Review Fall 06 Math If a student budgets her money as indicated by this pie graph, how much of her weekly $170 goes to food? Expenses misc. 10% housing 20% housing 2. The following box and whisker plot shows the scores of a history test. Which of the following statements are true about the scores? 120 students took the test. a. The mean score on the test was 60% b. The median score on the test was 60% c. The range of scores on the test was 70. d. About 25 % of the students scored 90 or better. e. About half the students scored between 30 and 60. f. About 60 students scored higher than 60% g. About 60 students scored below 50%. clothing 25% food 30% medical 15% medical food clothing misc Here is a stem and leaf plot of the Weights of students in East Junior High Algebra I Class a. The mean (or average) of this set of data is: b. The median of this set is: c. If one more value is added to this set say one student weights only 52 pounds how does this affect the mean and median of this set? Which is affected more? Why is this the case try to use the balance idea of mean to explain your ideas. d represents what? f. Do the mean and median have to be weights of students in the class? g. Explain what the mean represents or what it means. h. Create a box plot for the original data set. 4. If a student has $170 to spend per week, draw a pie chart for her weekly expenses. expenses percent degrees housing $ 34 medical $25.50 food $51 clothing $42.50 misc. $17 8

2 5. If a data set consists of 12, 15, 17, 17, 19, 19, 20, 20, 24 Find the mean for this set. Explain what it represents for the set of data try to do in two ways one of which includes the idea of a balance. If the value of 10 is now added to the set, what other value must be added in order to maintain the same mean. Find this value by using the balance idea (and not using the formula). 6. An experiment consists of drawing a ball from box A and then drawing another ball from box B. Where Y stands for a yellow ball and R stands for a red ball R1 just means red ball 1. a. What is the probability of drawing a yellow ball from Box A? b. What is the probability of drawing a yellow ball from Box B? box A box B c. Why are the probabilities in part a and part b not the same? d. Give the sample space for the experiment of drawing one ball from box A and then one ball from box B. e. Draw a tree diagram for all the outcomes. Show the associated probabilities on the tree branches. f. Explain how to find the following probabilities using both the tree diagram and the sample space, then find the probabilities. i. P( Y Y) = ii. P (R R) = iii. P (one red and one yellow any order) = iv. P(red first, yellow second) = v. P(at least one ball is red) = Y R Y R1 R2 7. How do we use tree diagrams to analyze this question from homework? Isaac and Gavin are going to make a game where they have a container and 5 balls one that is orange and four that are blue. They place the balls in the container. A person is going to draw twice from the container. The person wins $1 if they get an orange ball on either draw. Isaac wants the rules to be that after the first draw, the ball is replaced and the person draws again. Gavin wants the rules to be that after the first draw, that ball is not replaced and the person draws again. Isaac says they are going to have to pay out more money with Gavin s rule. Is Isaac right? Explain whether he is or is not using tree diagrams in your argument. 8. Redo problem 2 on the Probability Homework Handout. 9. a. A triangle that is obtuse and not isosceles. b. A concave polygon c. A kite with an interior angle that is a right angle.

3 d. A quadrilateral with exactly one line of symmetry and no rotational symmetry. e. A closed curve that is not a polygon. f. A figure with rotational symmetries of 90, 180, 270, and 360 (just those) that has no line of symmetry. g. parallelogram that is not h. a rhombus 10. Which of the geometric figures below are polygons. Explain what a polygon is and why those that are not are not. e. 11. Give a mathematical definition for: a. an angle d. parallelogram b. isosceles triangle e. rhombus c. equilateral triangle f. rectangle (if you already have the parallelogram defined) g. square 12. Following are some figures. Below write all the names that can be used to describe the figure using these names: parallelogram, rectangle, rhombus, kite, trapezoid, square. Note there is a name that is the MOST complete name but if a figure has the properties of other figures, it can also be one of those. (Like an equilateral triangle is an isosceles triangle or an actute triangle)

4 13. For each of the polygons (the first has congruent sides and right angles), draw in all lines of symmetry and give all angles of rotation. Use the symmetry of the first quadrilateral to discuss properties of its diagonals. 14. In each of the following: find the required properties if this is not possible explain why. a. Two properties that hold true for all rectangles but not for all rhombuses. b. Two properties hold true for all parallelograms but not for all squares. 15. Look over the writing problems you did related to the van Hiele levels and children sorting be able to answer those again I will want you to do explaining and writing on this test. 16. a. Write down a formula for finding the sum of the measures of the interior angles for any polygon. Explain what the numbers and letters in your formula represent. Be able to show two ways on a drawing of any polygon how we can use the fact about sum of interior angles of a triangle to find the sum of the interior angles of any polygon. You also need to explain the thinking that goes along with each method to develop a formula for finding the sum of interior angles of any polygon. Now show a second way of finding a formula for the sum of the interior angles and explain what the symbols and numbers mean. b. This figure is a regular polygon. Find the measures of the following angles (be sure to show all your work, do not use a protractor). i. m ( MLN) = ii. m( IJK)= c. What is the sum of the exterior angles for any polygon? N Be able to do problems like those from 12.4 using the various formulas to find measures of different angles. d. The sizes of five interior angles of a hexagon are 65, 72, 124, 116, and 150. Can we find the measure of the last angle? If so how, if not, why not. b. If the hexagon had been a regular hexagon instead, could we find the measure of one interior angle. If so how, if not why not. c. Polygon B is a B regular pentagon 7 8 M L J I K 17. Be able to identify or draw examples of all the types of triangles looked at. Look over work we have done each has a complete name as well as more general names. 18. Understand the hierarchies in the quadrilaterals be able to produce Venn diagrams. 19. Draw a Venn diagram that shows how all triangles are related.

5 20. Answer true or false,provide an example if a statement is false a. Any polygon with congruent sides must have congruent angles. b. Any polygon with congruent sides is a regular polygon. c. All squares are rectangles d. If all the sides of a quadrilateral are congruent, then the quadrilateral is a rhombus. e. Some rhombi are squares. f. All rhombi are kites g. some rectangles are parallelograms.

SOL 6.13 Quadrilaterals

SOL 6.13 Quadrilaterals 6.13 The student will describe and identify properties of quadrilaterals. Understanding the Standard: A quadrilateral is a closed planar (two-dimensional) figure with four sides