math 6-9

• chapter 6 WE7 - to convert to like fractions, the LCM is x-2. do you agree?

  The fraction … can be further simplified, before finding the LCM to convert to like fractions.

  Since … *make denominator x-2*

  thus, i agree.
• chapter 6 WE12 - explain if it is possible to have a value of y if x≤ -1/3

  If x = -1/3, 3x + 1 = 0 and 64/(3x=1) [from part a!!] will be undefined. If x < -1/3, then 3x + 1 < 0 and 64/(3x+1) < 0.

  Hence, no real solutions can be obtained for y!

  ∴ it is not possible to find a value of y.
• page 162 WE4 - is C directly proportional to n? use your graph to explain your answer.

  C is not directly proportional to n because the line does not pass through the origin.
• chapter 7 WE5 - state the two variables which are directly proportional to each other and explain your answer

  Since y=5x3, y/x3 = 5 is a constant, then y and x3 are directly proportional to each other!
• chapter 8 WE3 - are following triangles congruent?

  … *compare angles or sides*

  △STU does not have any right angle that corresponds to that in △DEF.

  ∴ △STU is not congruent to △DEF
• chapter 8 WE5 - similar or not similar?

  similar: Since all the corresponding angles are equal and all the ratios of the corresponding sides are equal, then △ABC is similar to △PQR

  not similar: Since not all the ratios of the corresponding sides are equal / not all corresponding angles are equal, then △DEF is not similar to △STU
• chapter 8 WE6 - start with this!

  Since △ABC is similar to △PQR, then all the corresponding angles are equal.

  or

  Since △ABC is similar to △PQR, then all ratios of the corresponding sides are equal
• chapter 8 WE9 - △A’B’C’ is an enlargement of △ABC with a scale factor of 2…

  △ABC is similar to △A’B’C’ under enlargement

  …
• chapter 8

  congruence: translation, rotation, reflection
• chapter 9 WE3 - does X lie closer to A or C?

  …

  Since length of CX < length of AX, X lies closer to C
• chapter 9 WE8 - determine if triangle is a right-angled triangle. (converse!)

  …

  Since AB² = BC² + AC², then by the converse of Pythagoras’ Theorem, △ABC is a right-angled triangle where ∠C=90°
• chapter 7 - formulas!

  directly proportional:

  • y1/x1 = y2/x2 OR y2/y1 = x2/x1
  • y = kx OR y/x = k where k is a constant

  inversely proportional:

  • x1y1 = x2y2
  • xy = k OR y=k/x where k is a constant
• chapter 7 - start with this!

  Since E is directly proportional to N,

  then E = kN, where k is a constant.
• ANGLES

  1. adj. ∠s on a str. line
  2. ∠s at a point
  3. vert. opp. ∠s
  4. ∠ sum of △
  5. corr. ∠s, PQ // RS
  6. alt. ∠s, PQ // RS
  7. int. ∠s, PQ // RS

  converse too…

  1. converse of corr./ alt./ int. ∠s

  TRIANGLES

  1. ∠s of equilateral △
  2. base ∠s of isos. △
• formulas for other shapes

  1. circle

  area: πr2

  circumference: 2πr

  2. parallelogram

  area: bh

  3. trapezium

  area: 1/2(a+b) x h