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Number Pattern
Questions on number pattern can be set in Paper 1 and Paper 2.
Number Pattern questions in Paper 2 are usually long and the "O" level examiners will always give a numerical example on the number pattern. Students are advised to study the example carefully and identify the pattern(s) based on the given numerical example. Next, questions will be asked based on the identified patterns.
Number Pattern questions in Paper 1 will be
(1) Write down the next two terms in the sequence
(2) Given the nth term formula, write down the first 4 terms
(3) Given the nth term formula, find the nth term eg 7th term.
(4)* Given the numerical sequence, find the nth term formula.
These are the common number patterns (nth term formula) that are set in the "O" level E.Maths exam.
Pattern 1
5, 7, 9, 11, 13, .....
Since the pattern is +2, + 2, the nth term formula will be 2n + a
n = 1, 2(1) + 3 = 5
n = 2, 2(2) + 3 = 7
So, the nth term forrmula is 2n + 3
Pattern 2
3, 5, 9, 17, 33, .....
Since the pattern is +2, + 4, + 8, ......,
ie +2^1, +2^2, +2^3
so the nth term formula will be 2^n + a
n = 1, 2^1 + 1 = 3
n = 2, 2^2 + 1 = 5
n = 3, 2^3 + 1 = 9
So, the nth term formula will be 2^n + 1
Pattern 3
4, 7, 12, 19, .....
Since the pattern is +3, +5, +7, the nth term formula will be
n^2 + a
n = 1, 1^2 + 3 = 4
n = 2, 2^2 + 3 = 7
n = 3, 3^2 + 3 = 12,
So, the nth term formula is n^2 +3.
Pattern 4
1, 3, 6, 10, ......
Since the pattern is +2, +3, +4, ...., the nth term formula will be
1/2[(n+a)(n+b)]
n = 1, (1/2)[(n+a)(n+b)] = 1/2[(1+0)(1+1)] = 1
n = 2, (1/2)[(n+a)(n+b)] = 1/2[(2+0)(2+1)] = 3
n = 3, (1/2)[(n+a)(n+b)] = 1/2[(3+0)(3+1)] = 6
n = 4, (1/2)[(n+a)(n+b)] = 1/2[(4+0)(4+1)] = 10
So, the nth term pattern will be (1/2)[(n)(n+1)]
PS : Students who have calculators with equation function eg Casio FX 95 MS or Sharp EL 509WS can make use its ability to solve for the 3 unknowns using the simultaneous equations mode for Patterns 1, 3 and 4 except pattern 2 to find the nth term formula
Paper 1 Exam Questions on Number Patterns
(1) Write down an expression, in terms of n, for the nth term
in this sequence 4, 9, 16, 25, ..... (Pattern ?)
(2) Write down an expression, in terms of n, for the nth term
in this sequence 2, 7, 12, 17, 22, ..... (Pattern ?)
(3) Write down an expression, in terms of n, for the nth term
in this sequence 4, 7, 10, 13, ..... (Pattern ?)
(4) Write down an expression, in terms of n, for the nth term
in this sequence 4, 7, 12, 19, 28, ..... (Pattern ?)
(5) Write down an expression, in terms of n, for the nth term
in this sequence 0, 3, 8, 15,..... (Pattern ?)
(6) Write down an expression, in terms of n, for the nth term
in this sequence 5, 9, 13, 17, 21,..... (Pattern ?)
(7) Write down an expression, in terms of n, for the nth term
in this sequence 1, 4, 7, 10, 13, .... (Pattern ?)
(8) Write down an expression, in terms of n, for the nth term
in this sequence 1, 3, 6, 10, 15, 21,..... (Pattern ?)
(9) Write down an expression, in terms of n, for the nth term
in this sequence 3, 6, 10, 15, 21,..... (Pattern ?)
(10) Write down an expression, in terms of n, for the nth term
in this sequence 1, 7, 17, 31, ..... (Pattern ?)
(11) Write down an expression, in terms of n, for the nth
term in this sequence 0, 3, 8, 15, 24, ..... (Pattern ?)
Students are advised to practise on these questions to familarize themselves with the different patterns asked in the "O" level Exam on E.Maths.
Thank you for your kind attention.
Regards,
ahm97sic
Edited by Ahm97sic 21 Oct `08, 8:49PM
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Originally posted by Garrick_3658:
I have it, but how?
Dear Garrick_3658,
Let us use Pattern 4 as an example
1, 3, 6, 10, ......
Use the general nth term formula an^2 + bn +c
n = 1, a(1)^2 + (1)b + c = 1
a + b + c = 1 ------------------------ (1)
n = 2, a(2)^2 + 2(b) + c = 3
4a + 2b +c = 3 --------------------- (2)
n = 3, a(3)^2 + 3(b) +c = 6
9a + 3b + c = 6 ------------------- (3)
We can solve these three simultaneous equations mathematically for a, b and c OR we can to make use of the equation mode in Casio FX 95 MS or Sharp EL 509WS to find a, b and c.
Using the equation mode in Casio Fx 95 MS to find the nth term formula
Press Mode twice
Press 1 for equation mode
Press 3 for 3 unknowns for 3 simultaneous equations a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3
Press 1 for a1
Press 1 for b1
Press 1 for c1
Press 1 for d1
Press 4 for a2
Press 2 for b2
Press 1 for c2
Press 3 for d2
Press 9 for a3
Press 3 for b3
Press 1 for c3
Press 6 for d3
Press =
x = a = 0.5
Press =
y = b = 0.5
Press =
z = c = 0
Since, a = 0.5, b = 0.5, c= 0,
the nth term formula an^2 + bn + c
= 0.5n^2 + 0.5n + 0
= 0.5n(n+1)
= (1/2)n(n+1)
Regards,
ahm97sic
Edited by Ahm97sic 23 Oct `08, 6:15PM
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Dear Garrick_3658,
When the n is a power, the general nth term forumla an^2 + bn + c cannot be used.
Until now ie 2007, "O" level examiners have not set nth term forumla with n^3. If it really comes out in 2008, you can use the nth term formula an^3 + bn^2 + cn + d to form 4 simultaneous equations to solve for a, b, c and d. However, this cannot be done using Casio FX 95 MS or Sharp EL 509WS. You will need a graphic calculator eg TI 84 Plus, Casio 9860 or Sharp 9900 to find the nth term formula.
Nevertheless, if n^3 really comes out in 2008 exam, it will probably be something like n^3 +2 in the sequence 3, 10, 29, 66, ......
For the topic LInear Law in add maths, many students have the difficulty to get the exact value of the gradient M and Y-intercept, C in the equation Y = MX + C where Y can be 1/y or lg y and X can be 1/x or lg x.
To get the exact value, we can make use of a topic known as linear regression (to be learnt in H2 and H1 Maths) which can help us to find the exact M and C. This is done using Casio FX 95 MS.
Press mode once
Press 3 for regression
Press 1 for linear regression
Input the X and Y data (not x and y data)
Press shift S-Var
Press right arrow three times
Press 1 for A = C
Press 2 for B = M
Regards,
ahm97sic
Edited by Ahm97sic 24 Oct `08, 1:05AM
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