If'
X100/301
NATIONAL
QUALIFICA
2004
FRIDAY,
TIONS
9.00 AM
21 MAY
-
10.10 AM
MATHEMATICS
HIGHER
Units 1, 2 and 3
Paper 1
(N on~calculator)
Read Carefully
1 Calculators may NOTbe used in this paper.
2
Fullcreditwill be givenonlywherethe solutioncontainsappropriateworking.
3 Answersobtainedby readingsfrom scaledrawingswill notreceiveany credit.
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SCOTTISH/'<"'"
QUALIFICATIONS
LIB
X100/301
6/26920
11I11111111111111111111111111111111111111111111111
AUTHORITY
@
.
1.
The
point
x + 3y + 1
p1.LL questions
should
A has coordinates
(7, 4).
=0
and 2x + Sy
=0
intersect
be attempted.
The
NI arks
straight
lines with
equations
at B.
3
(a) Find the gradient of AB.
(b) Hence show that AB is perpendicular
2. lex)
= x3 -
x2
5
to only one of these two lines.
- Sx - 3.
(a) (i) Show that (x + 1) is a factor off(x).
(ii) Hence or otherwise factorise lex) fully.
(b) One of the turning points of the graph of y
Write down the coordinates
of this turning
5
=lex)
lies on the x-axis.
1
point.
3. Find all the values of x in the interval 0 ~ x ~ 21t for which tan2(x) = 3.
4.
The diagram shows the graph of y
(a) Sketch the graph of y
= g(x).
4
11.
.7
= -g(x).
2
(b, 3)
(b) On the same diagram, sketch
the graph of y = 3 - g(x).
2
x
(a, -2)
5.
A, Band
C have coordinates
(-3, 4, 7), (-1, 8, 3) and (0,10,1)
(a) Show that A, Band Care collinear.
(b) Find the coordinates
6.
Given that y
= 3sin(x)
-7
of D such that AD
respectively.
2
3
+ cos(2x), find ~~.
[Turn over for Questions
[Xl00/301]
3
-7
= 4AB.
Page three
7 to lion
Page four
iV/arks
2
7.
Find
}0
8. (a) Write x2-10x
(b)
9.
10.
5
~4x + 1 dx.
Hence
show that the function
g(x)
= 1X3-
Solve the equation log2(x + 1) - 2Iog2(3)
In the diagram
angle DEC = angle CEB = x 0 and
angle CDE = angle BEA = 900.
CD = 1 unit; DE = 3 units.
By writing angle DEA in terms
of x 0, find the exact value of
cos(DEA).
11.
2
+ 27 in the form (x + b)2 + c.
4
Sx2 + 27x - 2 is always increasing.
4
= 3.
~~A
3
D
E
7
y'
The diagram shows a parabola passing
through the points (0, 0), (1, -6) and (2,0).
(a) The equation
of the parabola
form y = ax(x - b).
Find the values of a and b.
is of the
x
3
(b) This parabola is the graph of y = f'(x).
Given that f(1) = 4, find the formula
for f(x).
[END
[X100/301]
OF QUESTION PAPER]
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