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Subject Knowledge Enhancement: Mathematics
Subject Knowledge Audit: Self Study Questions
These tasks have been devised to help you to reflect upon your own subject
knowledge. They are intended to get you thinking: you may know the
techniques, but do you know why they work? We would encourage you to
look things up if you are unsure and to produce the fullest answers that you
can. You can annotate your work to show where you have done this and to
flag up questions that you found particularly challenging.
Please bring this work to the sessions during the first week as it will be used
to inform the subject knowledge audit process.
1. One way of calculating 1892 17 is to write 1892 in many different ways
‘keeping the value but changing the appearance’.
Which of the following is equivalent to the method of long division and
why?
(1000  800  90  2)  17
(1700  170  22)  17
(1700  170  17  5)  17
(850  850  85  85  17  5)  17
2. What is the value of 100?
How could you explain this result?
How might you explain negative indices?
3. Which is greater 3.78 or 3.7  108 and why?
4. Why do the following work?
5  4  5  14  54
3  12  3  2  6
1
2
 43  12  34  32
5. Check that 3+4+5=3x4 8+9+10=3x9 29+30+31=3x30
Write down a statement (in prose English) which generalises from
these three examples.
Express your generalisation using symbolic (algebraic) notation.
6. Which of the following statements is false and why?
(i)
(ii)
(iii)
(iv)
Kathryn Fox
The integer solutions of n  2  3 are n  6, 7,8 …
The only integer solutions of n 2  9 are n  0,1, 2,3
The integer solutions of 3  2n  1are n  0, 1, 2,...
2  n  6  10 can be written as 4  n  4
June 2010
Subject Knowledge Enhancement: Mathematics
7. Describe four different methods for solving quadratic equations such as
2 x 2  12 x  10  0 .
What happens when you try to solve the quadratic equation:
2 x 2  12 x  20  0 ?
8. Describe two distinct methods for solving simultaneous equations such
as
7x  5y  9
2x  3  y
Solve the following sets of equations commenting on your results:
y  x4
y  x4
2y  x  4
a)
b)
c)
yx7
yx7
y x  4 y
9. Sketch two graphs on the same set of axes to show the relationship
between the lengths of the sides (x,y) of a rectangle given that
a) the perimeter is 18 units
b) the area is 18 sq. units
y
x
10. Sketch a graph to show your height above the ground as a function of
time when travelling on the London Eye (or some other big wheel).
What has this got to do with trigonometry?
11. Is the following statement true?‘For a right angled triangle the area of
the semicircle on the hypotenuse is equal to the sum of the area of the
semicircles on the other two sides’.
Justify your answer.
12. “It is said that that the odds for each of the 49 lottery numbers coming
up are the same but you can’t prove that. The fact that the number 38
has come up much more often than the number 20 proves the exact
opposite”
Write one or two paragraphs setting out a response to the above pupil
comment.
Kathryn Fox
June 2010