Question 1

A rectangle has length $2.6$ x $10^4 m$ and width $1.9$ x $10^4 m$. 
Find the area of the rectangle in $dam^2$

Accepted Answer

$4.94$ x $10^6 dam^2$

Answer

$4.94$ x $10^{7} dam^2$

Answer

$4.94$ x $10^6 dam^3$

Answer

$4.94$ x $10^8 dam^2$

Question 2

Given $x = 2.6$ x $10^4$ and $y = 5.0$ x $10^{-8}$.

(b)	Which of the following statements about the nature of $x$ and $y$ above is incorrect?
(i)	$x$ belongs to $\mathbb{N}$  			
(ii)	$y<x$	
(iii)	$y$ belongs to $\mathbb{Z}$ 			
(iv)	$x + y$ belongs to $\mathbb{R}$ 	
(v)	$x$ belongs to $\mathbb{Q}$

Accepted Answer

iii

Answer

v

Answer

iv

Answer

i

Question 3

A National Lottery is offering prizes in a new competition. The winner may choose one of the following.
	
	Option one:	250 in the first week, 450 in the second week, 650 in the third week, increasing by 200 each week for a total of 10 weeks.

Option two:	10 in the first week, 20 in the second week, 40 in the third week
	continuing to double for a total of 10 weeks.

Calculate the amount of money the winner will receive in the tenth week if option one is selected.

Accepted Answer

2050

Answer

2000

Answer

2250

Answer

2150

Question 4

A National Lottery is offering prizes in a new competition. The winner may choose one of the following.
	
	Option one:	250 in the first week,  450 in the second week, 650 in the third week, increasing by 200 each week for a total of 10 weeks.

Option two:	10 in the first week, 20 in the second week, 40 in the third week
	continuing to double for a total of 10 weeks.

Calculate the amount of money the winner will receive in the tenth week if option two is selected.

Accepted Answer

5120

Answer

5210

Answer

10420

Answer

10240

Question 5

A National Lottery is offering prizes in a new competition. The winner may choose one of the following.

Option one:    250 in the first week, 450 in the second week, 650 in the third week, increasing by $200 each week for a total of 10 weeks.

Option two:	10 in the first week, 20 in the second week, 40 in the third week
	continuing to double for a total of 10 weeks.

Calculate  how much more money will the winner will get in total for the 10 weeks, if option one is selected instead of option two.

Accepted Answer

1270

Answer

6390

Answer

2270

Answer

3070

Question 6

The annual fees paid to a school for the school years 2000, 2001 and 2002 increase as a geometric progression. The table below shows the fee structure.

Year	Fees (USD)
2000	8000.00
2001	8320.00
2002	8652.80

If  the fees continue to increase in the same ratio. Find the fees paid for 2006, correct to two decimal places

Accepted Answer

10122.55

Answer

9733.22

Answer

9733.20

Answer

10122.60

Question 7

Daniel wants to invest $25 000 for a total of three years. There are two investment options.
Option One:	pays compound interest at a nominal annual rate of interest of 5 %, compounded annually.
Option Two:	pays compound interest at a nominal annual rate of interest of 4.8 %, compounded monthly.

Calculate how much many he will have at the end of the three years for both options.

Accepted Answer

Option one: 28940.63 
Option two: 28863.81

Answer

Option one: 25313.80
Option two: 28863.81

Answer

Option one: 28036.81
Option two: 25301.20

Answer

Option one: 28940.63 
Option two: 25301.20

Question 8

The first term of a geometric sequence is 18, the second term is 6.
Find the common ratio of this sequence

Accepted Answer

$\frac{1}{3}$

Answer

$3$

Answer

$12$

Answer

$0.3$

Question 9

Write the following number in standard form:
12569500.67

Accepted Answer

$1.26$ x $10^7$

Answer

$1.25$ x $10^7$

Answer

$1.26$ x $10^{-7}$

Answer

$1.26$ x $10^9$

Question 10

1The mass of a soccer ball is 430 g measured to the nearest unit. Find the bounds on the mass.

Accepted Answer

$429.5 g \leq$ $x<430.5g$

Answer

$429.5 g \leq$ $x\leq430.5g$

Answer

$429 g \leq$ $x<431g$

Answer

$429 g \leq$ $x \leq431g$

Question 11

Marcela wants to buy a house, so she needs to save money first before asking for a loan. She must have at least $25000 at the end of december 2030. So she will start an annuity in december 2020. The account pays 4.8% of annual interest, compounded monthly. How much money she will have to save monthly in this account in order to have the initially amount of money proposed?

Accepted Answer

162.73

Answer

156.34

Answer

245.33

Answer

208.33

Question 12

Find the series of the sequence (see image).

Accepted Answer

40

Answer

0

Answer

27

Answer

120

Question 13

The monetary value of a land, increases 5.5% each year. It was bought in 1999 for $15000. Find out what would be its monetary value in 2030.

Accepted Answer

$78871.03

Answer

$76920.52

Answer

$119226.80

Answer

$74759.27

Question 14

The fifth term of an arithmetic sequence is 32 and the fifteenth term is 72. Find out the common difference of this sequence.

Accepted Answer

4

Answer

3.5

Answer

It is not possible to find the common difference without having the first term of the sequence.

Answer

3

Question 15

Andrés asks for a loan in a bank. The amount of money he needs is $5000. The bank offers him two options for the loan:

Option 1:     11.5% annual interest, compounded monthly for 5 years.

Option 2:     6.8% annual interest, compounded monthly for 10 years.

Calculate how much more interest in total would Andrés pay if he selects option 2 instead of option 1.

Accepted Answer

$307.04

Answer

$235.00

Answer

$52.42

Answer

$525.02

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