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65 questions at your level
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Level 2
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Level 5
Proof by deduction
30 questions
Lesson
Not started
Mark as done
SECTION A: PURE MATHEMATICS
(a)
Disprove the following statement:
"
2
n
+
1
2^n + 1
2
n
+
1
is prime for all positive integers
n
n
n
." (2 marks)
(b)
Prove that the sum of the squares of any two consecutive odd integers is an even number that is not divisible by
4
4
4
. (3 marks)
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Level 2
5 marks
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Proof by exhaustion
8 questions
Lesson
Not started
Mark as done
Given that
a
a
a
,
b
b
b
and
c
c
c
are integers greater than 0 such that
c
=
2
a
−
1
c = 2a - 1
c
=
2
a
−
1
a
+
b
+
c
=
14
a + b + c = 14
a
+
b
+
c
=
14
prove, by exhaustion, that the product
a
b
c
abc
ab
c
is always a multiple of 6
You may use the table below to illustrate your answer.
You may not need to use all rows of this table.
a
a
a
b
b
b
c
c
c
a
b
c
abc
ab
c
(3 marks)
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●●●
Level 2
3 marks
Start
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Disproof by counter-example
14 questions
Lesson
Not started
Mark as done
A student writes the following two statements.
(a)
“For all positive integers
n
n
n
,
2
n
>
n
2
2^n > n^2
2
n
>
n
2
”
Prove by counter example that this statement is not true.
(2 marks)
(b)
“For all real numbers
x
x
x
, if
x
3
>
x
x^3 > x
x
3
>
x
then
x
>
1
x > 1
x
>
1
”
Prove by counter example that this statement is not true.
(2 marks)
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●●●
Level 2
4 marks
Start
→
Mark as done
SECTION A: PURE MATHEMATICS
(a)
Disprove the following statement:
"
2
n
+
1
2^n + 1
2
n
+
1
is prime for all positive integers
n
n
n
." (2 marks)
(b)
Prove that the sum of the squares of any two consecutive odd integers is an even number that is not divisible by
4
4
4
. (3 marks)
●●
●●●
Level 2
5 marks
Start
→