Republic Polytechnic
A113 Mathematics
Problem 06 - Practice questions
1 Find the area under the curve in Figure 1.
10
10
40
50
Figure 1
2 Find the area under the curve in Figure 2.
20
10
20
25
35
40
Figure 2
3 Estimate the area under the following graph g

Republic Polytechnic
A113 Mathematics
Worksheet 09: Player Selection
Factors
1. As the team captain of the air rifle club, how would your choice of the player be
affected if:
a. one of the potential players has just sprained his left wrist?
b. one of the

Republic Polytechnic is
sending a representative
to participate in an air rifle
competition.
This competition will have
one representative from
each polytechnic in
Singapore.
The contestant who scores
the highest in the
competition wins.
There are four po

Republic Polytechnic
A113 Mathematics
Practice Questions P09
1. The following data shows the test marks (1 10) obtained by a group of students:
6
7
7
1
3
2
8
6
8
2
4
4
9
10
2
6
3
1
6
6
9
8
7
5
7
10
8
1
5
8
Draw a frequency table for the data.
2. Find the

Republic Polytechnic
A113 Mathematics
Practice Questions P10
1. A student has 3 comic books and 4 story books.
a. How many ways can he arrange the 3 comic books on the first level of his
book shelf?
b. How many ways can he arrange the 4 story books on the

Republic Polytechnic
A113 Mathematics
Problem 10: Guess My Choice
Designing the pricing of the tokens
1. Referring to Scenarios 1, 2 and 3 mentioned in the problem statement,
a. Which scenario is most likely to happen? Explain your choice.
Position1:
1/5

Republic Poly is organizing a funfair to collect funds for
charity. Your friend has been assigned to be in charge
of a game named Guess My Choice.
In the game, 5 balls of different colours will be handed
to the player. The player will have to pick 3 balls

Republic Polytechnic
A113 Mathematics
Practice Questions P11
1. Which statement(s) describe the distribution used in this problem?
a.
There are only two possible outcomes for each of the trial.
b.
The number of trials, n, is fixed.
c.
All trials must be d

Republic Polytechnic
A113 Mathematics
Worksheet 11: Hack-a-Shaq
Dallas Mavericks versus Phoenix Suns
1. Discuss with your classmates to make sure everyone understands the
problem statement. What are some of the considerations which you should
make to tack

Date on which score was taken:
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 1
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 2
Day 3
Day 3
Day 3
Day 3
Day 3
Day 3
Day 3
Day 3
Day 3
Day 3
Day 4
Day 4
Day 4
Day 4
Day 4
Day 4
Day 4
Da

Republic Polytechnic
A113 Mathematics
Worksheet 8: Making Sense of Things
Case Study 1: Quiz show
1. If you are the contestant taking part in the quiz show, would you switch your
initial choice of the box? Why or why not?
Yes. Because Wins after change de

Republic Polytechnic
A113 Mathematics
Worksheet 06: Internet Download
Factors Affecting Download Speed
1. Discuss and list down some factors which affect how fast a file can be
downloaded from the Internet.
Type of connection
2. It is often observed that

Figure 1. A download window
A typical file download window can be seen in Figure 1
above. In this window, you can find information such as the
estimated time left for the download to complete and the
amount of data downloaded.
Figure 1. A download window

Republic Polytechnic
A113 Mathematics
Worksheet 07: Everyday Statistics
What is statistics?
1. What is your understanding of the words statistics and statistic?
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or

Republic Polytechnic
A113 Mathematics
Problem 07 - Practice questions
1 Suppose the average monthly wage in USA is $6,000 while the average
monthly wage in Bolivia is $3,000. Which of the following are good ways to
represent the monthly salary of the resp

We come across charts and data in newspaper articles
everyday like the ones in Newspaper.docx.
Examples of statistics-backed articles include:
1. General statistical information for the purpose of public
education
2. Agenda-based marketing through statist

Republic Polytechnic
A113 Mathematics
Practice Questions P08
1.
Which of the following event(s) is/are unlikely to have an effect on the yield of
the farmers crops during the harvesting season?
Event A: The weather is very bad during the harvest season.
E

Explore the following case studies and try to make sense of things.
Case Study 1: Quiz Show
On a quiz show held by a local TV station, the contestant is asked to
choose one of the three boxes. One of the boxes contains $1,000
cash. The other two boxes are

Among the star players in the NBA tournament, Shaquille
ONeal (also known as Shaq) of the Phoenix Suns is notorious
for his low free-throw shooting percentage.
His career average of 52.8% is very low compared to the
typical range of 70-90% for other playe

Republic Polytechnic
A113 Mathematics
Practice Questions P12
1. If a fair die was tossed four times in a minute, how many times would you expect
even numbers to show up in a 15-minute interval?
2. In one week, the meteorological station estimated that the

Republic Polytechnic
A113 Mathematics
Worksheet 12: Whales
Considerations
1. What factors would you consider when signing up for a whale-sighting trip?
2. What do you think could possibly influence your chance of sighting a whale during
a trip?
Making Sen

Data collected by Group A students (in ml)
314
340
305
309
334
342
343
306
352
334
351
326
318
331
324
330
309
324
312
322
319
332
321
305
300
349
347
303
330
342
Data collected by Group B students (in ml)
334
344
339
339
339
346
311
342
332
321
328
339
3

Republic Polytechnic
A113 Mathematics
Problem 15 - Practice questions
1 A sugar packing company claimed that the average mass of each packet of
sugar is 1 kg.
Adrian bought one packet of sugar.
He found the mass to be 0.975 kg.
Ben bought 30 packets of su

Republic Polytechnic
A113 Mathematics
Problem 15: Making a strong case
Presumed innocent until proven guilty
1.
The earth was originally known to be flat. However around 200 BC, the
Greek scholar Eratosthenes came up with the idea that the earth is in fac

A soft drink manufacturer claims that the average
volume of soda per can is 330 ml.
Two groups of students suspected that the actual
average volume of soda in a can is lesser than the
manufacturers claim. They conducted their own
studies to check the manu

Equation of a Straight Line ( y = mx + c )
x
y
2.1
10
3
4
-6.67
m=
24.00
y-intercept =
3.60
x-intercept =
Hence, y = -6.67 x +24.00
m = gradient, c = y-intercept
Given y = mx + c and
5
m=
( y y1 )
m 2
3
c=
( x 2 x1 )
8
If x =
43
then y =
If 2 lines are pe

P10 LEO Quiz Solutions
Q1. Find the mean, median and mode for the following list of values:
23, 16, 12, 17, 19, 15, 11, 20, 12, 19
mean =
23:16:12:17:19:15:11:20:12:19
10
Re-arrange in ascending order:
= 16.4
middle
11, 12, 12, 15, 16, 17, 19, 19, 20, 23

P07 LEO Quiz Marking
Q1a. (Speed of bus at 80 s) = 9
b. (distance travelled by the bus from 30 s to 120 s) = 9 90 = 810
c. (distance travelled by the car from 30 s to 120 s) = 25 90 = 2250
(additional distance travelled by the car compared to the bus) = 2

School of Engineering
A113 Mathematics
Quiz for Problem 04: Barbecue
1. 2 apple pies and 2 chicken burgers cost $8.40. 2 apple pies and 1 chicken burger
cost $5.40. What is the cost of a chicken burger?
A
B
A-B
apple pies
2
2
0
chicken burgers
2
1
1
total

P11
Dice and Tosses
6th Presentation
A113 Mathematics
Probability
Probability is the likelihood or chance of an event (E)
occurring, which takes a value in the range of 0 to 1
(inclusive).
For example, the chance of a fair coin falling on its Head
is 0.5

P07
Internet Download
6th Presentation
A113 Mathematics
Download Speed of Internet Data
The download speed can be affected by many
factors such as the type of connection (e.g.
ADSL, cable, optic fiber) and end-user traffics.
The time taken to download a

School of Engineering
A113 UT2 Revision Worksheet
Give your answers in 2 decimal places, where applicable.
Rate of Change
1. A bus travels at a constant speed of 80 km/h for half an hour along a straight
road. Then it stopped for a 20 minutes break and co

School of Engineering
A113 UT1 Revision Worksheet
Algebraic Manipulation
Sequence of Operations
Without using calculator, evaluate the following expressions:
1)
(5 + 4 2) 3
2)
32 + 4 (23 + 32) 100
Algebraic Expressions
Simplify the following expression:
3

P03
Pushcart
6th Presentation
A113 Mathematics
Mathematical modeling
Many real-life situations can be modeled using
mathematical functions, which can be expressed
in terms of graphs or equations.
For example, in todays problem, we modeled
the projected