IFYMB002 Mathematics Business 2020-21
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IFYMB002 Mathematics Business
Examination
2020-21
Section A
Answer ALL questions. This section carries 45 marks.
Question A1
The line with equation 5
+ 3
− 
= 0 crosses the 
− axis at point X and the 
− axis at point Y.
The area of triangle OYX, where O is the origin, is 120 square units.
Find the values of 
. [ 4 ]
Question A2
The probability that it rains on a given day is 0.4.
Find the probability that it does not rain for 7 consecutive days.
Give your answer as a decimal to 3 significant figures.
In this question, 1 mark will be given for the correct use of significant figures.
Question A3
A quadratic equation is defined as 
2 + 9
+ 3 = 0 where 
is an integer. Find the largest possible value of 
if the equation has two real distinct roots.
Question A4
In the expansion of (
+ 4
)8 the coefficient of the 
3 term is 112 .
Find the value of 
.
Question A5
(a) Write 2 log 
( 
) + log 
( 
) − log 
( 
) as a single logarithm.
You are given the value of the expression in part (a) is equal to 1 . (b) State the value of 
.
Question A6
Solve sin( 
) = −0.966 (0° ≤ 
≤ 360°)
Question A7
If 
= 56
2 + 3 ln 
− 4
4
, find the exact value of 
when 
= 
.
Question A8
Find
∫ (10
2 − 3)2 
.
Question A9
Eight readings are shown below in ascending order (smallest to largest).
−1, 0, 2, 
, 10, 15, 17, 23.
(a) Write down the mean in terms of 
.
You are given the median is 8.
(b) Find the standard deviation.
Question A10
The probability a student has blue eyes is 
.
Five students are selected at random.
Write down, in terms of 
, the probability that exactly 3 or exactly 4 of the students have blue eyes.
Give your answer in the form 5
3 (
− 
)(
− 
) where 
and 
are integers. [ 4 ]
Question A11
A curve has equation 
= ln(tan 
)
Write down 
and hence find its value when 
= 
. [ 3 ]
|
Question A12
A curve has equation |
|
1 − |
to find 
and hence find the coordinates of the stationary [ 5 ]
Section B
Answer 4 questions ONLY. This section carries 80
marks.
Question B1
(a) Solve the equations 3
− 5
= 5 [ 4 ]
9
+ 10
= 0
All working must be shown: just quoting the answers, even the correct ones, will score no marks if this working is not seen .
|
.
ii.
(c) i.
ii.
(d)
. |
The expression
Write down the remainder in terms of
You are given the remainder is −3 and
Find the possible values of
Factorise 63
Hence, or otherwise, solve the inequality 63
Give your critical values in the form
An arithmetic series has first term
Show that |
The sum of the first 40 terms is 5000.
ii. Find the value of 
and the value of 
.
(e) A geometric series is defined as 
+ 
2 + 
3 + …
Write down the 
ℎ term in terms of 
in its simplest form.
Question B2
(a) The variables 
and 
are connected by the formula
= 22
− 12(2
) + 40.
ii. Find the values of 
when 
= 8. [ ]3
iii. What happens to 
when 
becomes large and negative? [ 1 ]
(b) 
(where 
≠ 0) is a real number.
i. Prove that 
0 = 1. [ 1 ]
ii. Find the value of 
if
30
8 − 6
8 1
× 4
= 72 [ 3 ]
(c)
NOT TO SCALE
60 cm
65 cm
Figure 1
Figure 1 shows the acute-angled triangle 
with 
= 65 cm and 
=60 cm. The area of triangle 
is 1800 cm2 .
i. Find the value of sin 
, giving your answer in the form are integers.
ii. Show that cos 
= 
.
iii. Find the length of 
. Give your answer in the form 5√
where 
is an integer.
iv. Find angle 
.
v. Find the shortest distance from 
to 
. Show your working.
vi. Find the shortest distance from 
to 
using a different method. Again, show your working.
|
Question B3 (a) |
|
4
|
NOT TO SCALE |
||||||
Figure 2
Figure 2 shows a rectangular field which has a smaller rectangle removed from one side. All measurements are in metres.
The perimeter of the field is 408 metres.
ii. Show that the area of the field, 
, is given by [ ]3
= 2040
− 136
2
iii. Use calculus to find the value of 
which makes the area a maximum. [ ]3
iv. Use calculus to confirm your value of 
gives a maximum. [ ]3
v. Find this maximum area. [ 1 ]
∫ (12 − 8
)
2
.
2022-06-05