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January 2011 Core 1 Paper ­ Question considered as challenging


Manipulation of terms

(a) find the value of 16 1/4
(b) Simplify x(2x 1/4) 4

Solution

= 16 1/4

= 1 / 416 = 1 / 2

= x (2x 1/4) 4

= x (16x 1)

= 16



Integration


(a)…

Page 2

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= 3/2(3) ­ ½



Arithmetic sequences

A sequence a1, a2, a3 . . . is defined by: a1 = 2 and an + 1 = 3a n ­ c

where c is a constant

(a) Find an expression for a2 in terms of c



Given that a i = 0…

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Arithmetic sequences
An arithmetic sequence had first term a and common difference d. The sum of the first 10
terms of this sequence is 162.

(a) Show that 10a + 45d = 162

Given also that the sixth term of the sequence is 17

(b) Write down a second equation…

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Integration
The curve with equation f(x) passes through the point (1, 0)

Given that, f'(x) = 12x 2 ­ 8x + 1

(a) Find f(x)

Solution
= f'(x) = 12x 2 ­ 8x + 1

= [12x 2+1 / (2 + 1)] ­ [8x 1+1 / (1 + 1)] +…

Page 5

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= k 2 + 2k ­ 3 = 0

= (k + 3) (k ­ 1) = 0

= k = 3 and 1

= f(x) > 0

=k < 3 and k > 1



Coordinate geometry
The line L1 has equation 2y ­ 3x k = 0, where k…

Page 6

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= 4 = 2/3 + c

= y = 2/3 x + 14/3

= 2x + 3y ­ 14 = 0

= B (7, 0)

= [(7 ­ 1) 2 + (0 ­ 4) 2]

= 52



Differentiation
The curve C has equation, y = x 3 / 2 9x…

Page 7

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= 8 = 8/7 + c

= c = 64 / 7

= y = 2x / 7 ­ 64 / 7

= 7y = 2x ­ 64

= 2x ­ 7y ­ 64 = 0






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