1)
2)
3)
4)
5)
6)
If tan(φ)=0,5 and π<φ<3π/2 calculate
Sin φ
cos φ
sin 2φ
cos (π-φ)
cos(π+φ)
2) Show that the series 𝑙𝑜𝑔2 𝑥 + 𝑙𝑜𝑔4 𝑥 + 𝑙𝑜𝑔16 𝑥 + ⋯.
is geometric and find the sum of the series for infinite
terms
3) Let f ( x) = 3 ( x + 1)2 −12 .
(a)
(b)
(i)
(ii)
(iii)
(iv)
(c)
Show that f ( x) = 3x2 + 6x − 9 .
For the graph of f
write down the coordinates of the vertex;
write down the equation of the axis of symmetry;
write down the y-intercept;
find both x-intercepts.
Hence sketch the graph of f .
4) Let x = 6.4 ×107 and y = 1.6 ×108 .
Find
a)
𝑥
𝑦
b)
y − 2 x , giving your
answers in the form a ×10k where 1 ≤ a < 10 and k ∈ Z .
5) The graph of the function f ( x) = 3x − 4 intersects the
x-axis at A and the y-axis at B.
(a)
Find the coordinates of
(i)
A
(ii)
B.
(b) Let O denote the origin. Find the area of triangle
OAB.
6) Let a = log x , b = log y , and c = log z . Write
log(
𝑥 2 √𝑦
𝑧3
)in terms of a, b and c.
7) (a) Let logc 3 = p and logc 5 = q . Find an expression
in terms of p and q for
(i) log c 15 ;
(ii) log c 25.
(b) Find the value of d if log d 6= 1/2
8) i) Two weeks after its birth, an animal weighed 13kg.
At 10 weeks this animal weighed 53kg. The increase in
weight each week is constant.
(a) Show that the relation between y, the weight in kg,
and x, the time in weeks, can be written as y=5x+3.
(b) Write down the weight of the animal at birth.
(c) Write down the weekly increase in weight of the
animal.
d) Calculate how many weeks it will take for the animal
to reach 98kg.
9) Solve
8 (4x) – 9 (2x) + 1 = 0