1.
A population of bacteria is growing at the rate of 2.3% per minute. How long will it take for the
size of the population to double? Give your answer to the nearest minute.
Working:
Answer:
.
(Total 4 marks)
2.
The diagram shows three graphs.
y
A is par
1.
(a)
2
x 3x 10 = (x 5)(x + 2)
(C2)
(M1)(A1)
2
(b)
x 3x 10 = 0 (x 5)(x + 2) = 0
x = 5 or x = 2
(C2)
(M1)
(A1)
[4]
1
(a) p = 2 , q = 2
(C2)
or vice versa
2.
(b)
(A1)(A1)
By symmetry C is midway between p, q
Note: This (M1) may be gained by implication.
(
1.
t
1.023 = 2
ln 2
t = ln 1.023
= 30.48.
30 minutes (nearest minute)
Note: Do not accept 31 minutes.
(M1)
(M1)(A1)
(A1) (C4)
[4]
2.
(a) C has equation x = 2
ie y = log2 x (A1)
OR
(b)
y
(A1)
(C2)
Equation of B is x = log2y
Therefore equation of C is y =
1.
(a)
(b)
2
Factorize x 3x 10.
2
Solve the equation x 3x 10 = 0.
Working:
Answers:
(a) .
(b) .
(Total 4 marks)
2.
The diagram represents the graph of the function
f:x
(x p)(x q).
y
1
2
2
x
C
(a)
Write down the values of p and q.
(b)
The function has a m
1.
3
2
Consider the function f(x) = px + qx + rx. Part of the graph of f is shown below.
The graph passes through the origin O and the points A(2, 8), B(1, 2) and C(2, 0).
(a)
Find three linear equations in p, q and r.
(4)
(b)
Hence find the value of p, o
1.
(a) attempt to substitute points into the function
3
2
e.g. 8 = p(2) + q(2) + r(2), one correct equation
8 = 8p + 4q 2r, 2 = p + q + r, 0 = 8p + 4q + 2r
N4
(b)
attempt to solve system
e.g. inverse of a matrix, substitution
(M1)
A1A1A1
(M1)
p = 1, q = 1