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Test Taking Tips

Test Taking Tips. Beware of the Sucker Answer. Make sure you answer the question that is asked!. Double check the question before you fill in the bubble!!. Do the Easy Ones First Then go Back and do the Hard Ones!. For Multiple Choice Tests

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Test Taking Tips

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  1. Test Taking Tips

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

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

  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. Read the directions for the test carefully.

  6. Read each question carefully.

  7. Algebra FAQs

  8. Number next to a Letter (variable) means Multiply 12a + -2b If a = 5, b = -3 Then substitute & multiply 12(5) + -2(-3) = 66 4x If x = -3 Then substitute & multiply 4(-3) = -12 So do numbers next to ( ) and letters next to letters x·y = xy 4(x) = 4x (-2)(a) = -2a a·b = ab 4·f ·g = 4fg

  9. Addition and Subtraction are snobs. They just combine with their own kind. They form cliques. 3x– 3a + 7 + 6x + 2a = 9x – a+ 7 4x² + 6x +9– 15x + 3x² + 10 = 7x² - 9x + 19 That’s Just How They Do. That’s How It Is. Deal With It! Multiplication and Division are party animals. They will do it with anyone! 2x · 4y = 8xy a· b·c = abc 12xy/4x = 3y Understanding Algebraic Culture is the Key to Success!!

  10. A Fraction is = 2 ÷ 3 A Division Problem

  11. Numbers come with Signs (+-) The sign is in front Remember: These are the same thing 5– 3 = 2 5 + - 3 = 2 Because Subtraction is Adding the Opposite If you are confused, Circle the number & the sign in front, then do the math! 2 – 56 + 7 – 8 – 10 = - 65

  12. ABSOLUTE VALUE The absolute value is always positive. The absolute value of │5│ is 5 The absolute value of │-5│ is 5 To solve, drop the bars and make the inside number positive Watch Out! -│6│ = - 6 because the negative is lurking outside the bars.

  13. ALGEBRA OPPOSITES • Opposite of Addition is Subtraction • 12 + 18 = 30 • 30 – 18 = 12 • Positive / Negative Numbers • The opposite of -5 is 5 • The opposite of 6 is -6 • Opposites add to zero • -4 + 4 = 0 • Opposite of Multiplication is Division • 25 * 4 = 100100 ÷ 4 = 25 Opposite of Squaring is Square Rooting = 25 = 5

  14. You can’t add FROGS & SMILEY FACES LETTERS & NUMBERS work the same. Algebra Truths UGLY numbers work the same as PRETTY Numbers • Simplifying is cleaning up your room, put all the FROGS together & all the SMILEY FACES together, then do the Math. Adding Negative numbers - Think MONEY $$$$$$, You won’t miss it.

  15. No Equal Sign????? Simplify It!! Combine Like Terms. Simplifying is like cleaning up your room, put all the FROGS (Variables) together and all the SMILEY FACES (Numbers) together, then do the Math. Don’t Forget Numbers come with Signs! 4x -5 +6x +21 -8x 4x +6x -8x -5 +21 -------------------------------------------------------------------------------------------------------------------------------- 4x+6x -8x -5 +21 4x +6x -8x -5 +21 -------------------------------------------------------------------------------------------------------------------------------- 2x +16 2x +16 You can’t add FROGS & SMILEY FACES, so you are finished. Good Job!

  16. WATCH YOUR SIGNS Adding or Subtracting **If signs are the same, add them and use the sign. 45 + 34 = 79, - 45 – 10 = -55 **If signs are different, subtract and use sign of larger number -18 + 8 = -10, 60 – 20 = 40 • –Positive number, dollars in your pocket. • Negative number, dollars borrowed Positive is warming up. • Positive - dirt in the hole. • Negative number -digging the hole. Negative is cooling off. • Think temperature Think Holes Think money

  17. WATCH YOUR SIGNS • Multiplying or Dividing • **If signs are the same, answer is positive. • 4 * 8 = 32, -63 / -7 = -9 • **If signs are different, answer is negative. • -6 * 7 = -42, -100 / 10 = -10

  18. Distribution Principle Multiply everything in parenthesis by number next to parenthesis FIRST THING!! THINK BIG MOUTH SHOUTING “DO ME, DO ME FIRST!!” EXAMPLE : 3( 6x – 3) = 18x- 9 3 (6x– 3)

  19. Distribution Principle Multiply everything in parenthesis by number next to parenthesis FIRST THING!! 3( 6x – 3) EXAMPLE : Get them off the bus So they can play football. 6x – 3 3 18x- 9

  20. Equation Solving??? Example: 2(10x – 3) = 6x + 2 Line of Scrimmage Get the Teams off the Bus 2(10x – 3) = 6x + 2 20x – 6 = 6x+ 8 Line up the Teams Penalty for off-sides – must change signs 20x – 6x = 8 + 6 Huddle up 14x = 14 14x = 14 14 14 Man on Man Defense X = 1 Think Football – Letters Vs. Numbers

  21. ≤ , ›, or ‹, or ≥ If the equation has an Inequality sign, follow the steps for solving equations with = signs. Play Football LettersVrs. Numbers Last Play of the Game If you have to MULTIPLY or DIVIDE by a negativenumber, Be sure to FLIP the Inequality. *****NOTICE***** UGLY NUMBERS WORK THE SAME AS PRETTY NUMBERS!!!

  22. UGLY Numbers Work the Same as PRETTY Numbers. If you can solve: 2X + 10 = 40 Play Football LettersVrs. Numbers Then you can solve: 5x + 1.93 = 4.56 I’m not afraid of Fractions. Have Calculator, Will Calculate! And you can solve: .5x + ⅝ = ⅓

  23. Clue Words for writing equations from word problems + Addition Word Sentence Algebraic Word Clue • 1 plus 5 • 6 is added to a number • The sum of 5 and a number • A number is increased by 10 • 15 is more than a number • 1+5 • 6+x • 5+x • x+10 • x+15 • Plus • added to • the sum of • increasing by • more than

  24. __ Clue Words for writing equations from word problems Subtraction Word Clue Word Sentence Algebraic • Minus • subtracted from • the difference of • decreased by • Less • less than • 6 minus 5 • 7 subtracted from a number • The difference of a number and 10 • A number is decreased by 20 • 5 less a number • 6 less than a number • 6-5 • x-7 • x-10 • x-20 • 5-x • x-6

  25. Clue Words for writing equations from word problems Multiplication Word Clue Word Sentence Algebraic • Times • Product • Doubled • Twice • Of (fractions and percents) • 7 times a number • Product of 8 and a number • A number doubled • Twice a number • 1/2 a number • 55% of a number • 7*x = 7x • 8x • 2x • 2*x = 2x • 1/2x • 0.55x

  26. Clue Words for writing equations from word problems ÷ Division Word Clue Word Sentence Algebraic • x÷7 • 10÷x • Quotient • divided by • The quotient of a number and 7 • 10 divided by a number *The first number written before the clue word will be the numerator

  27. Consistent and Inconsistent Systems • 1. Consistent – one or many solutions • 2. Inconsistent – No solution • 1. Independent – Only one solution • 2. Dependent – Has infinitely many solutions.

  28. 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

  29. Linear Equations, Standard Form ax + by = c Solving for y, Just 3 easy steps GreenismsMath Terms • 1.Move x term(Change sides, Change signs)Add/Subtract x term • 2.Give x side a hugParenthesis ( ) • 3.Divide by number next to the yCoefficient Example: Solve for Y 2x – 7y = 12 Just 3 easy steps 1. -7y = 12 – 2x (Move x term(Change sides, Change signs) 2. -7y = (12-2x) (Give it a hug) 3. y = (12-2x) / -7 (Divide by number next to the y) Now you are ready to enter it into the calculator and graph it WATCH YOUR SIGNS!!

  30. Linear Equations, Standard Form ax + by = c • Solving for y, It’s a Football Game • Y VS Everybody Else • Follow football rules Play Football Y vs everybody else 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 and graph it WATCH YOUR SIGNS!!

  31. Same Slope Parallel Lines y2 – y1 x2 – x1 Slopes are Negative Reciprocal (Flip & Change Sign) or Perpendicular slope y = mx + b l lines

  32. 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 +

  33. Exponents (Just follow the Rules) Exponent x² Base (x²a³g)(xa²g³) = (x³ g ) ( g³ y) ³ = a³k = x³

  34. Negative Exponents Just switch places and make exponent positive =

  35. X X ∙ X= X² X X² X times X is X squared

  36. Quadratics Multiplying Binomials – Draw the Face (x + 8) (x – 6) Multiply Watch your Signs x² +8x -6x -48 Simplify (Combine Like Terms, eat the buggers) x² + 2x -48

  37. Check This First The Math “F” Word “Factoring” 1. Is there a common factor (number or letter)? Yes Proceed with CGF NO. Proceed to question 2 Example 8x²y + 4x³ - 12x Factor each term • 8x²y 2 * 2 * 2* x * x * y • 12x 2 * 2 * 3 * x • 4x³ 2 * 2 * x * x * x Circle common terms • 8x²y 2 * 2 * 2* x * x * y • 4x³ 2 * 2 * x * x * x • 12x 2 * 2 * 3 * x Multiply circled numbers That’s your Common Factor Multiply leftovers, put in ( ) 4x ( 2xy + x²-3 )

  38. 2. Perfect squares on end & 3 terms ? x² - 10x + 25 NO, proceed to question 3 YES, SPLIT IT NICE x² - 10x + 25 Put out baggies to hold the answer. (parenthesis) ( x - 5 ) ( x-5 ) Split the second term nice. Place in baggies Split the first term nice Place in baggies Sign between is same as middle term ANSWER (x -5)²

  39. 3. Perfect squares on end & 2 terms? Yes, NO. proceed to question 4 Same as question 2 Except the signs are +,- Example x² - 64 Answer looks like this! ( x-8 ) ( x +8)

  40. 4. No perfect squares on end, 3 terms & startswithx²? YES, its quadratics in the morning NO, proceed to question 5 A M x² - 10x + 24 Put in the parenthesis (x-6) (x-4) Found it All Done!!

  41. 5. Is there a number in front of the x² & does it have 3 terms Yes, Jail Break Example 2x² + 7x + 3 NO! Then it is Prime (can’t factor) • 1. Steal the “a” and give it to the last term (Multiply) 1 x² + 7x + 6 (2*3) 2. Search and Seizure (quadratics in the morning)(See question 4) (x + 6) (x + 1) 3. Arrested and Caught - Divide last terms by “a” (x + 6/2 ) (x + 1/2 ) All Done!! 4. Beat it Down - (reduce fractions) (x + 3) (x + 1/2) (x + 3) (2x + 1) 5. Parole (kick denominator to the front)

  42. The Math “F” Word “Factoring” Summary Check This First Is there a common factor (number or letter)? Greatest Common Factor (GCF) • Factor each term • Circle common terms • Multiply common terms • Write it down • Put out baggie for leftover • Multiplyleftovers for each term • Put in baggie ( ) Example 8x²y+ 4x³-12x 4x ( 2xy+x²-3 ) Is there a Square on each End?? Perfect Squares • . Put out Parenthesis • . Split FIRST and LAST numbers nice • . Put in Signs 3 Different Kinds • A. x²- 16x +64 • (x–8) (x–8) • B. x²+ 18x +81 • (x+9) (x+ 9) • C. x²-36 • (x+6) (x–6)

  43. The Math “F” Word “Factoring” Summary No perfect squares and 3 terms and starts with x²? Quadratics in the Morning (AM) • Make a factor tree • Multiply to last number, add to middle number • Put out baggies (parenthesis) • Split first term nice • Drop in factors from tree Example x² +12x +32 (x+ 8) (x+ 4) Is there a number in front of the x² and does it have 3 terms? Jail Break • .Steal the “a” and give it to the last term (multiply) • .Search and Seizure (Quad in AM) • .Arrested and Caught (divide by “a”) • .Beat Down (reduce fractions) • .Parole (kick denominator to the front) • .Check it out. (FACE it) Example 2x² + 7x + 3 • x² + 7x + 6 • (x + 6) (x + 1) • (x + 6/2) (x + 1/2) • (x + 3) (x +1/2) • (x + 3) (2x + 1)

  44. Systems of Equations • Solve with Graphing Calculator • Solve each equation for y • (3 easy steps) • Use y= button and enter each equation • Use graph to eyeball answer • Or • Use to find where y1 and y2 are equal • Be sure answer is in (x, y) form To Solve by Graphing • Make an x, y Chart • Select any x, solve for y x 2x – 4 y 0 2(0) – 4 -4 1 2(1) – 4 -2 • Then graph the two points. • Do for both equations. • The answer is where they cross. • Be sure answer is in (x, y) form Y= 2nd TABLE

  45. 3y -2x = 11y + 2x = 9 Systems of EquationsSolve by Substitution(box & shove) • y + 2x = 9 • y = 9 – 2x • 3(9 - 2x) – 2x = 11 • 27-6x – 2x = 11 • 27 – 8x = 11 • - 8x = -16 • x = 2 • y = 9 – 2 (2) • y = 5 • (2, 5) • Solve one equation for x or y (change sides, change signs) • Box it • Rewrite other equation and shove box in • Solve for surviving letter • Distribute • Combine like terms • Solve • Send it back to box • Solve for other letter • Answer in (x,y) form

  46. 2x – y = 93x + 4y = -14 Systems of EquationsSolve by Elimination • Look for opposite signs • Multiply to create opposites • Add old and new equation together • Solve for surviving letter • Plug back into either equation(pick the easy one) • Solve for other letter • Answer in (x,y) format • 2x – y = 93x + 4y = -14 • 4(2x – y = 9) • 8x – 4y = 36 • 3x+ 4y = -14 • 11x = 22 • x = 2 • 2(2) – y = 9 • -y = 5 • y = -5 • (2, -5)

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