3 - Higher Tier Questions
If you are sitting the Higher Tier GCSE maths exam paper, you may be required to form an equation for two quantities which are either directly proportional to, or inversely proportional to, one another:
(a i) - The cost of DVDs is directly proportional to the number of DVDs. It costs £8.40 for 5 DVDs. Form an equation connecting the cost of DVDs and the number of DVDs.
(a ii) - Use this equation to calculate the cost of 30 DVDs.
(a i) - As mentioned earlier, if the values 'a' and 'b' are in proportion, this can be written as a ∝ b.
If 'a' is the cost of DVDs and 'b' is the number of DVDs (a ∝ b) , you can write this as the equation:
a = k x b
Using the values in the question above, you can solve this equation to find the value of 'k' :
840 = k x 5
k = 840 ÷ 5
k = 168
As a result, you can form the equation:
a = 168b
(a ii) Using this equation, you can calculate the price for 30 DVDs by substituting 'b' with your specific value of 30:
a = 168 x 30
a = 5040
Therefore the cost of 30 DVDs is £ 50.40
(b) - The time taken to build a shed is indirectly proportional to the number of people building the shed. It takes 4 people 6 hours to build the shed.
(i) - Form an equation connecting the time ( t ), to the number of people building ( p ).
(ii) - Calculate how long would it take 8 people to build the shed
(b i) - The variables 't' and 'p' are indirectly proportional to one another. This can be written as:
t ∝ 1/p or t = k x 1/p
By placing the values mentioned in the question into this equation, you can find the value of 'k' :
t = k x 1/p
6 = k x 1/4
6 = k/ 4
k = 24
Therefore the equation connecting 't' and 'p' can be written as:
t = 24/p
(b ii) - Using your equation, you can calculate how long it would take 8 people to build the shed. If you substitute 'p' for your value of '8' :
t = 24/8
t = 3
Therefore, it would take 8 people 3 hours to build the shed.