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Geometry SOL Prep Verify solutions using your graphing calculator! The purpose of this document is to show students how to verify and check their answers. These are the calculator keystrokes that teachers can demonstrate to their students. The following problems are taken from the 2013 Released SOL test. Reasoning, Lines, and Transformations (SOL G.1, G.2, G.3, G.4) Store Key: One of the easiest ways to verify solutions is to use the Store key. Store a unique number greater than or equal to 10 for each variable and then type the problem and the different answer choices. Make sure to try all multiple choice answers. If two choices match, the simplified answer is the best solution. Keystrokes: Home screen: Fractions: Make the fractions look like the original problem and answers! This will prevent careless mistakes when entering problems into the calculator. Keystrokes: to select the n/d template Home screen: No calculator items on these SOLs. G.1a – Conditional Statements (#13) G.1b – Symbolic Form (#1) Numerical Checks for Multiple Choice Instructions! http://mathbits.com/MathBits/TISection/Algebra1/CheckNumerical.htm G.1c – Venn Diagram (#5 TEI) G.1d – Deductive Reasoning (#8) G.2a – Determine Parallel Lines Henrico County Public Schools - 2015 G.2b – Verify Parallelism (#3, 7, 15 TEI) Solving Equations Instructions! http://mathbits.com/MathBits/TISection/Algebra1/SolveEquations.htm #15 These angles are equal so enter it into Y= menu. Change your WINDOW settings so you can see the intersecting lines. Press [2nd][CALC][5] The x-coordinate is the solution. G.2c – Real World Problems with Parallel Lines (#9, 18) G.3a – Formulas (#10, 16) #16 Solve this problem as if it were a line of best fit. Step 1: Organize your points and create a table for x and y. Label your points x1, y1, x2, y2. Step 2: Enter the x values in L1 and the y values in L2. Step 3: Find the line of best fit by pressing Stat -> Calc, and the LinReg (4), Enter, and Calculate. Finding Slope Instructions! http://mathbits.com/MathBits/TISection/Algebra1/EquationsLines.htm Henrico County Public Schools - 2015 Step 4: For LinReg, the equation is shown on the screen as y = ax +b, where a is the slope (m) and b is the y-intercept. #10 Write the ordered pairs: (-1,8) and (7,-9), label the variables, and enter in the Home screen. G.3b – Application of Slope (#11 TEI) Writing Equations of Lines Instructions! http://mathbits.com/MathBits/TISection/Algebra1/EquationsLines.htm #11 Find the slope of the existing line described in SOL G.3a. Convert the slope (-.5) to a fraction on the Home screen. Apply “Rise over Run” to get additional points. Henrico County Public Schools - 2015 G.3c – Symmetry (#17) #17 To assist with the problem, graph both lines of symmetry. To graph the vertical line, turn on the Inequalz app and select X= in the top left corner. Transformations Instructions! G.3d – Transformations (#14) - None http://mathbits.com/MathBits/TISection/Geometry/Transformations.htm http://mathbits.com/MathBits/TISection/Geometry/Transformations2.htm G.4 – Constructions (#2, 4, 6, 12) - None Triangles (SOL G.5, G.6, G.7, G.8) G.5a – Triangle Inequalities (#24) G.5b – Triangle Inequalities Henrico County Public Schools - 2015 G.5c – Triangle Inequalities (#31) #31 Look at ALL 3 scenarios for EACH choice: G.5d – Triangle Inequalities (#21 TEI) #21 Type in the values on the Home screen. G.6 – Prove Congruent Triangles (#20, 23, 27, 30) #23 Identify the angle measures of EVERY angle in EACH triangle. Henrico County Public Schools - 2015 G.7 – Prove Similar Triangles (#26, 29, 32) #26 Identify which ratios are equal. G.8 – Right Triangles (#19, 22, 25, 28) SOH CAH TOA #19 cos 20 x 80 Make sure your calculator is set up in degree mode! Press [MODE] Working with Trig Ratios Instructions! http://mathbits.com/MathBits/TISection/Algebra1/TrigRatios.htm Here’s a trick. If you type the degree symbol, the calculator automatically switches to degrees! Type cos(20 and then [2nd][APPS] to get the degree symbol. #22 This can be done using truth tables. Type the equation on the Home screen. Press 2nd/Test to view the equal symbol. A value of 0 means it is FALSE. A value of 1 means it is TRUE. Henrico County Public Schools - 2015 #28 SOH CAH TOA sin 38 20 x Make sure your calculator is set up in degree mode! Press [MODE] Remember, if you type the degree symbol, the calculator automatically switches to degrees! Type[2nd][APPS] to get the degree symbol. Polygons and Circles (SOL G.9, G.10, G.11, G.12) G.9 – Quadrilaterals (#33 TEI, 39, 44) Type in the expressions for Y1 and Y1. #33 Change your window scale to view the intersections on the graph or Press [2nd][TRACE] and select Intersect [5]. #39 Label all of the angle measures in the diagram. Students must know the diagonals intersect to form right angles. Identify vertical and other congruent angles. Henrico County Public Schools - 2015 G.10 – Polygons (#34, 42, 47) #42 The polygon can be made by 4 triangles so the interior angles add up to 720 degrees (4 x 180). The two angles add to be 240 degrees. Each one is 120 degrees. #47 The octagon has interior angles that measure 135 degrees. The trapezoid has 2 angles that measure 250 degrees so each is 125 degrees. The remaining angle has to add with the others to equal 360 degrees. G.11a – Circles (#37) - none Henrico County Public Schools - 2015 G.11c – Circles (#41, 45) #41 C 2 (40) . The circumference is 251.33 ft. 70 The railing represents of the whole. 360 #45 A (5)2 . The area is 251.33 ft. 130 The shaded sector represents of the whole. 360 Graphing Circles Instructions! http://mathbits.com/MathBits/TISection/Algebra2/conicsCircle.htm G.12 – Equation of a Circle (#35, 40, 48 TEI) #40 To draw a circle, type [2nd][PRGM]. Select circle [9] from the list. It will start with an open parentheses. Type your X and Y values separated by a comma and your radius, then close the parentheses and press Enter. Ex: Circle (-4,1,3) where x=-4, y=1 and r=3. You should select [ZOOM][ZSquare] to draw the circle on a square axes. Press TRACE to check the different solutions. Henrico County Public Schools - 2015 #48 Draw the Circle as described on the previous problem. Make sure to switch the signs on the coordinates! Three-Dimensional Figures (SOL G.13, G.14) G.13 – Surface Area & Volume (#36, 43, 49) #36 Students need to remove the common side of the composite figure from each formula. #43 Henrico County Public Schools - 2015 #49 G.14a – Comparing Ratios (#38, 46 TEI, 50) #38 New Box (with height = 7.5) Henrico County Public Schools - 2015 #46 Ratio is cubed 27:125. Prove it is correct by comparing it to the ratio of the volumes. #50 Plug in values of 1 for the radius and height. The Volume = . Keeping the height the same measure, the formula for the new cylinder would be 4 r 2 (1) 4 r2 G.14b – Change in Dimension Affect - None G.14c – Affect on Dimension - None G.14d – Real World Problems - None Henrico County Public Schools - 2015