FORMULA CHAPTER
\mathrm{A}\propto\mathrm{B}\;\Rightarrow\;\mathrm{A}=\mathrm{kB}
Statement: Two quantities vary directly when their ratio remains constant.
\frac{\mathrm{A}}{\mathrm{B}}=\text{constant}
\mathrm{A}\propto\frac{1}{\mathrm{B}}\;\Rightarrow\;\mathrm{A}=\frac{\mathrm{k}}{\mathrm{B}}\;\Rightarrow\;\mathrm{AB}=\mathrm{k}
\mathrm{A}\propto\mathrm{BC}\;\Rightarrow\;\mathrm{A}=\mathrm{kBC}
\mathrm{A}\propto\mathrm{B}\;\Rightarrow\;\mathrm{A}=\mathrm{kB}
Question: A varies directly as B. If A = 12 when B = 3, find the relation between A and B.
Calculation: Use A = kB.
Step 1: k = A/B = 12/3 = 4.
Step 2: Therefore A = 4B.
Answer: The constant is 4 and A = 4B.
Statement: Two quantities vary directly when their ratio remains constant.
\frac{\mathrm{A}}{\mathrm{B}}=\text{constant}
Question: Test whether the pairs (A, B) = (6, 2) and (15, 5) show direct variation.
Calculation: Compare A/B for both pairs.
Step 1: 6/2 = 3.
Step 2: 15/5 = 3, so the ratio is constant.
Answer: A varies directly as B.
\mathrm{A}\propto\frac{1}{\mathrm{B}}\;\Rightarrow\;\mathrm{A}=\frac{\mathrm{k}}{\mathrm{B}}\;\Rightarrow\;\mathrm{AB}=\mathrm{k}
Question: A varies inversely as B. If A = 6 when B = 4, find the relation.
Calculation: Use AB = k.
Step 1: k = 6 × 4 = 24.
Step 2: Therefore A = 24/B.
Answer: The constant is 24 and A = 24/B.
\mathrm{A}\propto\mathrm{BC}\;\Rightarrow\;\mathrm{A}=\mathrm{kBC}
Question: A varies jointly as B and C. If A = 24, B = 3 and C = 2, find the relation.
Calculation: Use A = kBC.
Step 1: k = 24/(3 × 2) = 4.
Step 2: Therefore A = 4BC.
Answer: The constant is 4 and A = 4BC.
