Download Unit Assessment 1 – Set 1

Unit Assessment 1 – Set 1
Outcome 1
y
1. Find the gradient of the line shown
in the diagram.
74º
x
2. Find the equation of the line passing through the
point (2,-1) and parallel to the line y – 2x – 4 = 0.
3. Find the equation of the line through the point (0,4) and
perpendicular to the line x + y + 1 = 0
Outcome 2
4. If f(x) = 2 – 3x and g(x) = x – 1 find the values of
a) f(g(x)) b) g(f(x))
Solve the equation f(g(x)) – g(f(x)) = 6x.
5. The diagram shows the graph of a function
y = f(x). On separate diagrams sketch the
graphs of
a) 2 + f(x)
b) -f(x)
c) f(x-3)
d) 4 - f(x)
Outcome 3
6. If f(x) = (1 – 2x)2 , find f (-2)
7. Find y in each example
a) y =
2x  1
5 x
b) y = 3 x ( x  2)
8. Find the equation of the tangent
to the curve y = (x-1)(x-2) at the
point A(3,2). The tangent is shown in
the diagram.
9. Find the stationary values of the function
f(x) = 4x3 – 9x2 + 6x
and determine their nature.
Outcome 4
10. There are 40 tons of pollution in a
loch. Each week the council remove
38% of the pollution in the loch and at
the end of the week a local factory is
allowed to deposit 9 tons of waste in the
loch.
a) Set up a recurrence relation.
b) Find the amount of pollution in each
of the first five weeks.
c) Determine the long term state of the
loch.