Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Algebra 6
17 practice questions
Practice questions
11–17 of 17
Question 11
3 marks · Normal
Answer and see the solution →A factory produces widgets. The number of widgets, , produced is directly proportional to the number of workers, , employed.
(a)[1 mark]On a certain day, 50 workers produce 600 widgets. Write the formula connecting and .
(b)[1 mark]How many widgets would 90 workers produce?
(c)[1 mark]How many workers are needed to produce 960 widgets?
Question 12
2 marks · Normal
Answer and see the solution →Simplify the following expression, writing your answer as a power of only:
Question 13
2 marks · Normal
Answer and see the solution →It takes a bee 300 000 km to produce 2 kg of honey. The distance (km) travelled is directly proportional to the mass (kg) of honey produced.
How many grams of honey can the bee produce by flying 45 000 km? (Give your answer in grams.)
Question 14
4 marks · Hard
Answer and see the solution →The time, T seconds, for a chemical reaction is directly proportional to the square of the temperature, t °C. The reaction takes 32 seconds at 40°C.
a) Write down the formula for T in terms of t.
b) Calculate the time for the reaction at 70°C.
c) Find the temperature if the reaction takes 50 seconds.
(a)[1 mark]Write your answer in the form T = k t^2.
(b)[2 marks]Give your answer to 1 decimal place if necessary.
(c)[1 mark]Find t, the temperature, when T = 50.
Question 15
4 marks · Hard
Answer and see the solution →The cost, C dollars, of producing a metal sphere varies as the cube of its radius, r cm. A sphere of radius 5 cm costs $120.
a) Find the formula for C in terms of r.
b) What is the cost of a sphere with a radius of 7 cm?
c) A company wants to make a sphere for $405. Work out the radius of this sphere.
(a)[1 mark](b)[2 marks](c)[1 mark]Question 16
4 marks · Hard
Answer and see the solution →The cost of producing a metal container varies as the square of its base diameter and is inversely proportional to its height . When cm and cm the cost is £64.
(a)[1 mark]Write down a formula for in terms of and .
(b)[3 marks]Calculate the cost when cm and cm, giving your answer to 2 decimal places.
Question 17
3 marks · Hard
Answer and see the solution →Simplify the following using the rules of indices. Write your answer with positive indices only: