LEVEL 9 Mathematics Observation Student: Assessment Date: Grade in School: Concepts Evaluated Score Notes. Applying the concept of slope to determine rate of change Equation of a line: slope-intercept form. Finding length of one side of a right triangle from known sides Classifying triangles by side lengths, solving problems Ratio of perimeters and areas of figures having same shape. Graphing lines given equations in various forms Graphing of lines: slope and where the line crosses the y-axis Writing equation of a line given slope and point on line 4. Solving an equation or formula for one of its variables Calculating the volume of a pyramid and cone Operations with fractions and mixed numbers Director s Comments: Level 9 05 Sylvan Learning, Inc.
Start Time End Time Observation Exercises Grade 9+ Name Center Number Date. Determine the slope of each line. a. Line a passes through point (.5,.75) and point (4.0, 4.95). b. Line b is represented by the linear equation 4yx 6. c. Line c is graphed below. January 06 Sylvan Learning, LLC Page
. The figures below show two similar right triangles. a. Use the Pythagorean Theorem to determine the length of AB. b. Calculate the area of. c. Use a proportion to determine the length of EF. January 06 Sylvan Learning, LLC Page
d. Calculate the area of. e. Express the ratio of the areas of and in simplest form. f. What is the ratio of the perimeters of and? Explain how this ratio can be found without calculating the perimeters of the two triangles. January 06 Sylvan Learning, LLC Page
. Consider the linear equation y x 5. a. Graph the equation using the point-slope method. Explain each step. January 06 Sylvan Learning, LLC Page 4
b. Explain how the graph of the line through the given point will change if the slope is changed to.8. January 06 Sylvan Learning, LLC Page 5
4. The formula for calculating the volume of a rectangular pyramid is, where B is the area of the base of the pyramid and h is the height of the pyramid. a. Use the formula for the volume of a rectangular pyramid to write a formula that can be used to solve for h. b. Use this new formula to solve for the height of a pyramid with a volume of 78 ft. The base of the pyramid has a length of 4 feet and a width of feet. Express your answer as a mixed number. January 06 Sylvan Learning, LLC Page 6
Observation Exercises Grade 9+ Key. line a: 4 0.8 or 5, line b:, line c: 4 5 yy 4.95.75 4 a. line a: m 0.8 or x x 4.0.5 5 b. line b: 4yx 6 4y x6 y 4 m 4 x 4 c. line c: These skills are addressed in the following ILOs: A8-LF-5: Applying the concept of slope to determine rate of change A9-LF-9A: Equation of a line: slope-intercept form. a. AB 5 cm AB 5 This skill is addressed in the following ILOs: G9-8GE0: Finding length of one side of a right triangle from known sides G9-INTRO-6: Classifying triangles by side lengths, solving problems b. A 50 cm ABC A A bh A 50 change in y m change in x 5 AB AC BC AB AB c. EF cm possible proportion: 05 5 0 9 x 5x 9 0 x 5 0 5 Confidential January 06 Sylvan Learning, LLC Page
Observation Exercises Grade 9+ Key d. A 54 cm DEF A bh A 9 A 54 e. A A ABC DEF 50 5 54 9 f. P P ABC DEF 5 5 9 Possible explanation: The ratio of the perimeters of similar triangles is equal to the square root of the ratio of the areas. These skills are addressed in G8-8APV0R: Ratio of perimeters and areas of figures having same shape. a. Use the point-slope method: Step : Identify the point: x, y,5 Step : Identify the slope: m Step : Plot the point. Step 4: Use the slope to plot more points on the line. Confidential January 06 Sylvan Learning, LLC Page
Observation Exercises Grade 9+ Key b. Possible explanation: The line will rise at a steeper rate if the slope is changed to.8. These skills are addressed in the following ILOs: A8-LF-R: Graphing lines given equations in various forms A9-LF-8: Graphs of lines: slope and where the line crosses the y-axis A9-LF-9B: Writing equation of a line given slope and point on line 4. a. V h B V V Bh V B Bh h This skill is addressed in A8-LEI-4: Solving an equation or formula for one of its variables b. h 4 feet V h B 78 4 4 4 4 This skill is addressed in the following ILOs: G9-8APV0: Calculating the volume of a pyramid and cone N9-CA-5R: Operations with fractions and mixed numbers Confidential January 06 Sylvan Learning, LLC Page