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CZ MAY 13
1. The first three terms ofa geometric series are

18,12 and p
respectively, where p is a constant.

Find

(a) the value of the common ratio of the series,
(1)

(b) the value ofp,
(1)

(c) the sum of the first 15 terms of the series, giving…

Page 2

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2. (a) Use the binomial theorem to find all the tems of the expansion of

(2 + 3;r)a

Give each term in its simplest form.


(b) Write down the expansion of

(2 - 3x)a
in ascending powers ofx, giving each term in its simplest fom.




15.-kl
' o b+ q6r--+Ll6*+…

Page 3

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J. f(x):2r3 5x2 + ar + 18

whereaisaconstant.

Given that (r - 3) is a factor of f(:r),

(a) show that a: 9
(2)

(b) factorise f(x) completely.
(4)

Given that

g(r,) - 2(3rr) - 5(34'1 9(3.) + 18
(c) find the values of ;r that satisfy g(v) : 0,…

Page 4

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5
,- 1*, + l.y



decimal places'
(a) Complete the table betow, giving the missing value of y to 3




Figure I

Figure 1 shows the region -R which is bounded by the curve with
equation y =:;'
(x' + 1)
the x-axis and the lines x = 0 and…

Page 5

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5-




0.64 rad / '.

Figure 2


Figure 2 shows a plan view of a garden'
The plan of the garden ,4BCuf'aionsists of
a lrt'anglre ABEjoined to a sectot BCDE of a
circle uith radius l2m and centre B' :23m and BC : 12m'
ifr" p"iti, A,, B andC lie…

Page 6

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6.




Figure 3

Figure 3 shows a sketch of part of the curve C with equation

y=x(x+$(x-2)
The curve C crosses the x-axis at the origin O and at the points I and B'

(a) Write down the x-coordinates of the points ,4 and B.
(1)

The finite region, shown…

Page 7

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7 . (i) Find the exact value ofx for which

logr(2x): logr(5x + 4) - 3
(4\

(ii) Given that

log,y + 31o9"2: 5


express in terms of a.
Jr'
Give your answer in its simplest fotm.
(3)




.-) 5 a+.t+ o 2-7 = 8 r) 5l-+ 1= J6r
LI…

Page 8

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8. (i) Solve, for -1 80" ( x < 180",

tan(,r - 40') = 1.5

giving your answers to 1 decimal place'
(3)


(ii) (a) Show that the equation
sitq tanq = 3cose + 2

can be written in the fotm

4cos2 0 * 2 cos0 - 1 :0 (3)…

Page 9

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9. The curve with equation

!:x2-32"'l(i +20, .r>o
has a stationary point P.

Use calculus

(a) to find the coordinates ofP,
(6)

(b) to determine the nature of the stationary point P.
(3)

Page 10

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10.




Figure 4


The circle c has radius 5 and touches the y-axis at the point (0, 9), as shown in Figure 4.

(a) Write down an equation for the circle C that is shown in Figure 4'
(3)

A line through the point P(8, - 7) is a tangent…

Comments

T


what board is this OCR model answers ??

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