Specimen Higher NAB Mathematics Unit 1
Outcome 1
1
A line passes through the points ( 6, 4 ) and ( 3, 2 ). Find the
equation of this line.
2
A line makes an angle of 25
with the positive direction of the
x-axis, as shown in Diagram 1.
2
y
The scales on the axes are equal.
25
x
Find the gradient of the line
giving your answer correct to 3
significant figures.
Diagram 1
2
3
A line L has equation y = 3x  4.
Write down the gradient of a line which is:
1
1
a. parallel to L
b. perpendicular to L
Outcome 2
4
The graph of a cubic y = f(x) is
shown in Diagram 2.
y
On separate diagrams sketch the
graphs of:
3
a. y = f(x)
b. y = f(x  4)
x
2
2
( 2, 4)
Diagram 2
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Specimen Higher NAB Mathematics Unit 1
5
The graphs with equations y = 2x
and y = ax are shown in Diagram
3.
y = ax
y
If the graph with equation y = ax
passes through the point ( 1, 5 ),
find the value of a.
y = 2x
( 2, 4 )
x
Diagram 3
6
The graphs of y = 10x and its
inverse function are shown in
Diagram 4.
yy =
1
10x
Write down the equation of the
inverse function.
1
x
1
Diagram 4
1
7
Functions f and g are defined on suitable domains by f(x) = ( x + 2 )2
and g(x) = x  1.
Obtain an expression for f(g(x)).
2
Outcome 3
8
Given y 
3
dy
.
x  0, find
2
dx
x
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2
Specimen Higher NAB Mathematics Unit 1
9
A sketch of the curve with
equation y = x2  6x + 8 is
shown in Diagram 5.
y
P
A tangent has been drawn at the
point P ( 4, 5 )
x
Find the gradient of the tangent
at P.
Diagram 5
10
1 3
x  x 2  15 x  7 . Using
3
differentiation, find the coordinates of the stationary points on this
curve and determine their nature.
3
A curve has equation y 
6
Outcome 4
11
Ted the mechanic has an old car. Its engine loses oil at the rate of
20% per week. The engine contains 5 litres of oil immediately after
being filled. The engine will be irrepairably damaged if the volume
of oil in the engine drops below 3.5 litres. Ted tops up the engine
each week with 0.5 litres of oil.
There are un litres of oil in the engine at the start of a particular
week.
a. Write down a recurrence relation for un+1, the amount of oil
in the engine at the start of the following week.
b. Find the limit of the sequence generated by this recurrence
relation as n   .
c. Will the engine be irrepairably damaged?
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