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Test Taking Tips

Test Taking Tips. Read each question carefully. Read the directions for the test carefully. For Multiple Choice Tests Check each answer – if impossible or silly cross it out. Back plug (substitute) – one of them has to be the answer For factoring – Work the problem backwards

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Test Taking Tips

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  1. Test Taking Tips

  2. Read each question carefully.

  3. Read the directions for the test carefully.

  4. For Multiple Choice Tests • Check each answer – if impossible or silly cross it out. • Back plug (substitute) – • one of them has to be the answer • For factoring – Work the problem backwards • Sketch a picture • Graph the points • Use the y= function on calculator to match graphs

  5. Do the Easy Ones First Then go Back and do the Hard Ones!

  6. Beware of the Sucker Answer Make sure you answer the question that is asked! Double check the question before you fill in the bubble!!

  7. Geometry FAQs

  8. X 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 4 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 6 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 7 0 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 8 0 8 16 24 32 40 48 56 64 72 80 88 96 104 112120 9 0 9 18 27 36 45 54 63 72 81 90 99 108117 126135 10 0 10 20 30 40 50 60 70 80 90 100 110 120130 140150 11 0 11 22 33 44 55 66 77 88 99 110121 132143 154 165 12 0 12 24 36 48 60 72 84 96 108120 132144 156168 180 13 0 13 26 39 52 65 78 91 104 117130 143156 169182 195 14 0 14 28 42 56 70 84 98 112 126140 154168 182196 210 15 0 15 30 45 60 75 90 105 120 135150 165180 195 210225 Factors Multiples Perfect Squares (6 ) (4 ) = 24

  9. C B A Geometry Basics A Point (Name with 1 capital letter) Line (Name with 2 capital letters, B • • ) A Ray (Name with 2 capital letter, ) • • A B Angle (Name with 3 letters. Middle letter is vertex C ) B A Line Segment (Name with two letters, AB) A • B Plane (Name with 3 non-collinear points, ABC)

  10. 90 • Complementary Angles • Right Angles • Symbol (┌ or ┐) • Perpendicular ┴ • A corner • 180 • Straight Angle (line) • Supplementary Angles • Half Circle • Sum of angles in a triangle GEOMETRY MAGIC NUMBERS Also called linear pair • 360 • Circle • Sum of angles in a 4 sided figure (quadrilateral)

  11. GEOMETRY MAGIC NUMBERS • Complementary Angles • Right Angles • Symbol (┌ or ┐) • Perpendicular ┴ • A corner 90

  12. GEOMETRY MAGIC NUMBERS 180 • Straight Angle (line) • Supplementary Angles • Linear Pair • Half Circle • Sum of angles in a triangle

  13. Supplementary Angles Two Angles are Supplementary if they add up to 180 degrees. HINT: S Straight or S Splits Thanks to http://www.mathsisfun.com/geometry/complementary-angles.html

  14. Vertical Angles Angles opposite each other when two lines cross They are called "Vertical" because they share the same Vertex (or corner point) vertex Vertical angles are congruent and their measures are equal: http://www.mathwarehouse.com/geometry/angle/interactive-vertical-angles.php

  15. Complementary Angles Two Angles are Complementary if they add up to 90 degrees (a Right Angle). HINT: C Corner or C looks like a corner Thanks to http://www.mathsisfun.com/geometry/complementary-angles.html

  16. Linear Pairs Angles on one side of a straight line will always add to 180 degrees. If a line is split into 2 and you know one angle you can always find the other one by subtracting from 180 A° 25° A° = 180 – 25° A° = 155°

  17. Right Angles A right angle is equal to 90° Notice the special symbol like a box in the angle. If you see this, it is a right angle. 90˚ is rarely written. If you see the box in the corner, you are being told it is a right angle. 90° 90° Notice: Two right angles make a straight line

  18. Properties of Equality • Addition Property: If a=b, then a+c=b+c • Subtraction Property: If a=b, then a-c=b-c • Multiplication Property: If a=b, then ac=bc • Division Property: if a=b and c doesn’t equal 0, then a/c=b/c • Substitution Property: If a=b, you may replace a with b in any equation containing a and the resulting equation will still be true.

  19. Properties of Equality Reflexive Property: For any real number a, a=a Symmetric Property: For all real numbers a and b, if a=b, then b=a Transitive Property: For all real numbers a, b, and c, if a=b b=c a=c a=c

  20. Conditionals & Bi-conditionals EXAMPLES: IFtoday is Saturday, THENwe have no school. “IF-THEN ” statements like the ones above are called CONDITIONALS. To make a bi-conditional, take off the IF and replace the THEN with “IF AND ONLY IF” Today is Saturday, IF AND ONLY IF we have no school.

  21. Conditionals Conditional statements have two parts… The part following the wordIF is the HYPOTHESIS The part following the word THEN is the CONCLUSION IFtoday is Saturday, THENwe have no school. Hypothesis: today is Saturday Conclusion: we have no school

  22. Converse The of a conditional statement is formed by exchanging the HYPTHESIS and the CONCLUSION. CONVERSE CONDITIONAL:IFit is snowing, THENwe will have a snow day. CONVERSE: IFwe will have a snow day, THEN it is snowing.

  23. Counterexample A Counterexample is an example that proves a statement false. Conditional Statement: IFan animal lives in water, THENit is a fish. * This conditional statement would be false. You can show that the statement is false because you can give onecounterexample. * Counterexample: Whales live in water, but whales are mammals, not fish.

  24. If-Then Transitive Property Given If Athen B, and if B then C. If sirens shriek, then dogs howl If dogs howl, then cats freak. You can conclude: If A then C. If sirens shriek, then cats freak.

  25. Quadrilaterals ( 4 sides ) Parallelogram Rectangle Rhombus Square Trapezoid Isosceles Trapezoid Kite

  26. Rectangle All angles are congruent (90 ˚ ) Congruent Sides Congruent Angles Parallel Sides Diagonals are congruent Congruent Sides Congruent Angles Parallel Sides Opposite sides Opposite sides parallel Parallelogram Opposite angles Diagonals bisect each other Consecutive angles are supplementary

  27. Rhombus Congruent Sides Congruent Angles Parallel Sides Congruent Sides Congruent Angles Parallel Sides Diagonals are perpendicular All sides are congruent Diagonals bisect angles Square Diagonals are perpendicular and congruent Diagonals bisect each other All sides are congruent All angles are congruent Angles = 90°

  28. Isosceles Trapezoid Congruent Sides Congruent Angles Parallel Sides Congruent Sides Congruent Angles Parallel Sides Diagonals are congruent Trapezoid Kite Diagonals are perpendicular

  29. Reflection Dilation Reflection Geometry in Motion Rotation Reflection Reflection Transformation

  30. A translation "slides" an object a fixed distance in a given direction.  The original object and its translation have the same shape and size, and they face in the same direction. Let's examine some translations related to coordinate geometry. In the example, notice how each vertex moves the same distance in the same direction. 6 units to the right

  31. Translations In this next example, the "slide"  moves the figure7 units to the left and 3 units down. There are 3 different ways to describe a translation

  32. When you reflect a point across the y-axis, the y-coordinate remains the same, the x-coordinate changes!

  33. When you reflect a point across the x-axis, the x-coordinate remains the same, and the y-coordinate changes!

  34. Examples of the Most Common Rotations Counterclockwise rotation by 180° about the origin: A is rotated to its image A'. The general rule for a rotation by 180° about the origin is (x,y) (-x, -y)

  35. Examples of the Most Common Rotations Counter clockwise rotation by 90° about the origin: A is rotated 90° to its image A'. The general rule for a rotation by 90° about the origin is (x,y) (-y, x)

  36. Dilations always involve a change in size. Dilations Dilations Dilations Dilations Dilations Dilations Dilations Dilations Dilations Dilations

  37. You are probably familiar with the word "dilate" as it relates to the eye.  The pupil of the eye dilates (gets larger or smaller) depending upon the amount of light striking the eye.

  38. Dilations - Example 1: If the scale factor is greater than 1, the image is an enlargement (bigger). PROBLEM:  Draw the dilation image of triangle ABC with scale factor of 2. OBSERVE: Notice how EVERY coordinate of the original triangle has been multiplied by the scale factor (2). HINT: Dilations involve multiplication!

  39. Dilations Example 2: If the scale factor is between 0 and 1, the image is a reduction (smaller). PROBLEM:  Draw the dilation image of pentagon ABCDE with a scale factor of 1/3. OBSERVE: Notice how EVERY coordinate of the original pentagon has been multiplied by the scale factor (1/3). HINT: Multiplying by 1/3 is the same as dividing by 3!

  40. Transversal Angles Parallel Lines Exterior 1 2 4 3 Interior 6 5 8 7

  41. Same Slope Parallel Lines y2 – y1 x2 – x1 Slopes are Negative Reciprocal Flip and Change Sign or Perpendicular slope y = mx + b lines

  42. Slope – Intercept Form y = mx + b Slope- directions Rise Run It’s a line address Example 2 To Graph: Example 1 y = -3X+0 y=-3X Starts at 0 rise/run =3/-1 Directions areup 3, over -1 y=2X+1 Starts at 1 Rise/run = 2/1 Directions areup 2,over 1 Thanks to http://www.mathsisfun.com/equation_of_line.html

  43. Linear Equations, Standard Form ax + by = c • Solving for y, It’s a football Game • Y VS Everybody Else • Follow football rules Play Football Lettersvs Numbers Example: Solve for Y 2x – 7y = 12 Just 3 easy steps 1. -7y = 12 – 2x X is offside, Penalty change signs 2. -7y = (12-2x) Huddle up ( ) 3. y = (12-2x) / -7Man on man defense Now you are ready to enter it into the calculator or graph it WATCH YOUR SIGNS!!

  44. Find Equation of the Line: y = mx + b To find m – Solve the equation for y and use m or use the y2 – y1 x2 – x1 formula I need slope (m) & the y-intercept (b) To find b - Plug x, y and m into the line equation and solve for b. MY ANSWER: y = x +

  45. Formulas Line Stuff Slope: m = ) Midpoint: (x, y) = ( , Distance: d = • Polygons: Sum of the interior measures: Sum of the exterior measures: 360° Measure of the interior angle in a regular polygon: Measure of the exterior angle in a regular polygon: 360°

  46. Sum of the Angles of a Polygon. Sum of Exterior Angles is 360

  47. Floor Rugs Area Floor Plan Examples of things you’d find the area of. Tiles or floors Acres

  48. Perimeter – Path around the Outside No Trespassing – Go all the way Around!

  49. Area Formulas h a b Area of Plane Shapes h h b b • b2 h r b1

  50. Perimeter Formulas a a b Area of Plane Shapes c a h b b b2 d a r b1

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