!st Semester Final Review part 4
1. (a) Represent the function y = 2x2 – 5, where x  {–2, –1, 0, 1, 2, 3} by a mapping diagram.
x
y
(b)
List the elements of the domain of this function.
(c)
List the elements of the range of this function.
2. An atlas gives the following information about the approximate population of some cities in the
year 2000. The population of Nairobi has accidentally been left out.
City
Population in Millions
Melbourne
3.2
Bangkok
7.2
Nairobi
Paris
9.6
São Paulo
17.7
Tokyo
28.0
Seattle
2.1
The atlas tells us that the mean population for this group of cities is 10.01 million.
(a)
Calculate the population of Nairobi.
(b)
Which city has the median population value?
!st Semester Final Review part 4
3. A survey was conducted of the number of bedrooms in 208 randomly chosen houses. The results
are shown in the following table.
(a)
Number of bedrooms
1
2
3
4
5
6
Number of houses
41
60
52
32
15
8
State whether the data is discrete or continuous.
(1)
(b)
Write down the mean number of bedrooms per house.
(2)
(c)
Write down the standard deviation of the number of bedrooms per house.
(1)
(d)
Find how many houses have a number of bedrooms greater than one standard
deviation above the mean.
4. Annie is starting her first job. She will earn a salary of $26000 in the first year and her salary
will increase by 3 every year.
(a)
Calculate how much Annie will earn in her 5th year of work.
(3)
Annie spends $24800 of her earnings in her first year of work. For the next few years,
inflation will cause Annie’s living expenses to rise by 5 per year.
(b)
(i)
Calculate the number of years it will be before Annie is spending more than she
earns.
(ii)
By how much will Annie’s spending be greater than her earnings
in that year?
5. Let A = 4.5 × 10–3 and B = 6.2 × 10–4. Find
(a)
AB;
(b)
2(A + B).
Give your answers in the form a × 10k, where 1 ≤ a < 10 and k 
.
!st Semester Final Review part 4
1.
(a)
–2
–1
0
1
2
3
2.
3.
–3
–5
3
13
(b)
x  {–2, –1, 0, 1, 2, 3}
(c)
y  {–3, –5, 3, 13}
(a)
=
(A2) (C2)
3.2  7.2  x  9.6  17.7  28.0  2.1
= 10.01.
7
Hence 67.8 + x = 10.01 × 7 = 70.07.
x = 70.07 – 67.8 = 2.27 (accept 2.27 or 2.3 million).
(b)
Median is the middle value which is 7.2.
Bangkok.
(a)
Discrete
(b)
2.73
(M1)
(A1)(M1)
(M1)(A1)
(M1)(A1)
(A1)
(C2)
4.
(c)
1.34
(A1) (C1)
(d)
23
(a)
tn = arn-1 t5 = 26000(1.034)
= $29263.23 (29263 or 29300)
3
(b)
(i)
26000(1.03)n−1 = 24800(1.05)n−1
(M1)
So a total of 3.46 years after she starts work.
Note: Allow 3 or 4 years.
(ii)
24800(1.05)3 – 26000(1.03)3
= $298.20
5.
(a)
2.79 × 10–6
(b)
1.024 × 10–2 (Accept 1.02 × 10–2)
(A
(M1)(A1)