Formulae: finding an unknown questions with answers

Questions

1. Question 1Substitute to find the subject

   The formula $v = u + at$ gives the speed of a moving object. Find the value of $v$ when $u = 11$, $a = 6$ and $t = 6$.

   Show the worked solution

   1. Step 1: Substitute the values you know$v = 11 + 6 \times 6$
   2. Step 2: Work it out: brackets first, then × and ÷, then + and −$v = 47$
2. Question 2Substitute to find the subject

   The perimeter of a rectangle is given by $P = 2(l + b)$. Find the value of $P$ when $l = 7$ and $b = 3$.

   Show the worked solution

   1. Step 1: Substitute the values you know$P = 2(7 + 3)$
   2. Step 2: Work it out: brackets first, then × and ÷, then + and −$P = 20$
3. Question 3The unknown is not the subject

   The cost, $$C$, of hiring a kayak for $h$ hours is given by $C = 15h + 8$. Find the value of $h$ when $C = 68$.

   Show the worked solution

   1. Step 1: Substitute the values you know$68 = 15h + 8$
   2. Step 2: Simplify, and get the term with the unknown on its own$15h = 60$
   3. Step 3: Divide both sides by the number in front of the unknown$h = 4$
4. Question 4The unknown is not the subject

   The cost, $$C$, of hiring a kayak for $h$ hours is given by $C = 15h + 8$. Find the value of $h$ when $C = 98$.

   Show the worked solution

   1. Step 1: Substitute the values you know$98 = 15h + 8$
   2. Step 2: Simplify, and get the term with the unknown on its own$15h = 90$
   3. Step 3: Divide both sides by the number in front of the unknown$h = 6$
5. Question 5Formulae with fractions

   The area of a trapezium is given by $A = \dfrac{1}{2}(a + b)h$. Find the value of $b$ when $A = 72$, $a = 9$ and $h = 8$.

   Show the worked solution

   1. Step 1: Substitute the values you know$72 = \dfrac{1}{2}(9 + b) \times 8$
   2. Step 2: Simplify, and get the term with the unknown on its own$4b = 36$
   3. Step 3: Divide both sides by the number in front of the unknown$b = 9$
6. Question 6Formulae with fractions

   A temperature of $C$ °C is $F$ °F, where $F = \dfrac{9C}{5} + 32$. Find the value of $C$ when $F = 140$.

   Show the worked solution

   1. Step 1: Substitute the values you know$140 = \dfrac{9C}{5} + 32$
   2. Step 2: Simplify, and get the term with the unknown on its own$\dfrac{9}{5}C = 108$
   3. Step 3: Divide both sides by the number in front of the unknown$C = 60$