Additional Mathematics Practice Assessment
Term 3 - Reinforcement & Review
Total Marks: 39
Time Allowed: 60 minutes
1. (a) Solve the equation 7v−2 = 15, giving your answer correct to 2 decimal places.
[2]
1
1
(b) Solve the equation y 2 − 6y 4 + 8 = 0.
2. (a) Write 2 lg x − lg(5x − 4) as a single logarithm to base 10.
(b) Hence solve the equation 2 lg x − lg(5x − 4) = 0.
[3]
[2]
[4]
3. Variables x and y are such that when ln y is plotted against x, a straight line passing
through (2, 5) and (5, −1) is obtained. Find y as a function of x.
[5]
1
4. (a) A 4-digit number is to be formed from the seven digits 0, 1, 2, 4, 5, 7, 8. Each
digit can be used at most once in any number and the number does not start
with 0.
(i) Find the number of ways in which this can be done.
[2]
(ii) Find how many of these 4-digit numbers are odd.
[3]
(b) A committee of 6 people is to be selected from a group of 8 teachers and 5
students. Find the number of different committees that can be selected which
include at least 2 students.
[3]
n
1
n
(c) Show that
+
= n(n + 1) for n ≥ 2.
2
2
1
[3]
5. A function f is such that f (x) = e3x−1 , for x ∈ R.
(a) Write down the range of f .
[1]
(b) A function g is such that g(x) = 2x + 4, for x ∈ R. Find the exact solution of
the equation f g(x) = 10.
[3]
2
6.
(i) Show that
cos θ
1 + sin θ
+
= 2 sec θ.
cos θ
1 + sin θ
(ii) Hence solve the equation
1 + sin θ
cos θ
+
= 4, for 0◦ ≤ θ ≤ 360◦ .
cos θ
1 + sin θ
3
[4]
[4]