Additional Mathematics
Chapter 6: Coordinate Geometry II - Applications
Chapter Assessment
1
On separate diagrams, use shading to denote the following inequalities.
(i)
y5
[2]
(ii)
x + 2y  4
[3]
(iii) 2x  3y < 12
[3]
2
Write down the inequalities that define the region illustrated.
[5]
3
A factory produces two types of bicycle - the standard model and the deluxe model.
The factory buys in all the necessary parts and materials it needs, assembles the bicycles and
sells them on to a distributor.
A standard model takes 10 man-hours to assemble. A deluxe model takes 16 man-hours to
assemble. There are 800 man-hours available each week.
Bicycles must be completed at the end of the week - no bicycle assembly is started if it cannot
be finished by the end of the week. To satisfy distributors, at least 20 of each model must be
made each week.
Let x be the number of standard models made in a week and y be the number of deluxe
models made in a week.
(i)
(ii)
Express the information above as three inequalities and sketch a graph to illustrate
them.
[6]
The profit on a standard model is £50 and on a deluxe model is £60.
Find the number of bicycles that should be assembled each week to maximise the profit.
[6]
(iii) When more careful working practices are introduced the standard of the bicycles
improves and so they are sold for a greater price. The result is that the factory makes
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Additional Mathematics
£55 profit on a standard model and £95 on a deluxe model.
Should the factory now change its production to maximise the profit?
4
[4]
John wishes to buy some DVDs and Videos and has £200 to spend.
At a particular shop each DVD cost £15 and each Video cost £10.
He would like to buy at least 5 of each.
Let d be the number of DVDs that he buys and v be the number of videos that he buys.
(a)
Illustrate the region satisfied by the inequalities, using the horizontal axis for d and the
vertical axis for v.
[6]
(b)
Determine whether the following points (d, v ) satisfy the conditions. and show the
points on your graph to illustrate your answer in each case.
(c)
5
(i)
(6, 11)
[1]
(ii)
(8, 9)
[1]
(iii) (9, 5)
[1]
Show that there are two points which maximises the number of items that John can buy.
Comment on which one would be better.
[5]
A station carpark is to be laid out with spaces for small cars and large cars. A small car
requires 10 m2 of space and a large car requires 12 m2 of space. Not including driveways, the
entrance and exit, taxi rank and a small unmarked space for setting down and picking up
passengers, there is 600 m2 of available space to be marked out.
It is required to have at least 20 spaces for each type of car.
Let x be the number of small car spaces marked out and y the number of large car spaces
marked out.
(i)
(ii)
Write the information given above as three inequalities and illustrate them on a
graph.
[6]
With these constraints, maximise the number of spaces that may be marked out.
[4]
(iii) It is, in fact, required to have at least as many spaces for large cars as for small cars.
Write this as an inequality. Add it to your graph. Maximise the number of spaces that
may now be marked out.
[7]
Total: 60
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