Variation Form 4 PDF

VARIATION Ms Octave Form 4  Variation Variation is where one variable is proportional to another variable by a constant proportion 𝑘. The symbol for Variation is ∝ Types of Variation: 1. Direct Variation 2. Indirect / Inverse Variation ...

VARIATION Ms Octave Form 4  Variation Variation is where one variable is proportional to another variable by a constant proportion 𝑘. The symbol for Variation is ∝ Types of Variation: 1. Direct Variation 2. Indirect / Inverse Variation  Direct Variation 𝑦 is directly proportional to 𝑥. If 𝑦 = 10 and 𝑥 = 2.5 Determine the value of: a. The constant proportion 𝑘. b. The value of 𝑥 when 𝑦 = 20 c. The value of 𝑦 when 𝑥 = 1.25  Direct Variation 1. Write the statement using the mathematical symbol for proportional 𝑦 is directly proportional to 𝑥. 𝒚 ∝ 𝒙. 2. Express statement above as an equation ; factoring the constant proportion 𝑘. The constant proportion 𝑘 is multiplied to the second variable. 𝒚 = 𝒌 × 𝒙.  Direct Variation 3. Determine the value of 𝑘, by using the value given at the beginning of the question for each variable that is 𝑦 = 10 and 𝑥 = 2.5. Every question will entail a value for each variable, so that the constant proportion 𝑘 is calculated. 𝒚=𝒌× 𝒙 𝟏𝟎 = 𝒌 × 𝟐. 𝟓 𝟏𝟎 =𝒌 𝟐. 𝟓 (a) The constant proportion is 𝒌 = 𝟒.  Direct Variation 4. Use the value of 𝑘 to substitute into the original formula 𝒚 = 𝒌 × 𝒙 to determine the value of 𝑥 𝑎𝑛𝑑 𝑦 𝑖𝑛 𝑏 𝑎𝑛𝑑 𝑐 𝑏𝑒𝑙𝑜𝑤. New equation: 𝒚 = 𝟒 𝒙 (b) The value of 𝑥 when 𝑦 = 20 𝒚=𝟒𝒙 𝟐𝟎 = 𝟒 × 𝒙 𝒙 = 𝟐𝟎/𝟒 𝒙=𝟓  Direct Variation (c) The value of 𝑦 when 𝑥 = 1.25 𝒚=𝟒𝒙 𝒚 = 𝟒 × 𝟏. 𝟐𝟓 𝒚=𝟓  Indirect/Inverse Variation A is varies inversely as the square of R. If A = 3 and R = 2 Determine the value of: a. The constant proportion 𝑘. b. The value of A when R = 4 c. The value of R when A = 12 Indirect/Inverse Variation 𝟏 𝑨∝ 𝑹² 𝟏 𝑨=𝒌× 𝑹² 𝒌 𝑨= 𝑹²  Indirect/Inverse Variation (a) Determining the value of 𝑘. If A = 3 and R = 2 𝒌 𝟑= 𝟐² 𝒌 𝟑= 𝟒 𝒌=𝟑×𝟒 𝒌 = 𝟏𝟐  Indirect/Inverse Variation 𝒌 𝑨= 𝑹² 𝒌 = 𝟏𝟐 𝟏𝟐 New equation is : 𝑨 = 𝑹² (b) The value of A when R = 4 𝟏𝟐 𝑨= 𝟒² 𝟏𝟐 𝑨= 𝟏𝟔 𝑨 = 𝟎. 𝟕𝟓  Indirect/Inverse Variation (c) The value of R when A = 12 𝟏𝟐 𝑨= 𝑹² 𝟏𝟐 𝟏𝟐 = 𝑹² 𝟏𝟐 𝑹² = 𝟏𝟐 𝑹² = 𝟏 𝑹= 𝟏 𝑹=𝟏