MEDTEC School Admission Test: Section 1: Mathematics
MEDTEC School Admission Test: Section 1: Mathematics
MEDTEC School Admission Test: Section 1: Mathematics
Admission Test
Instruction for answers sheet reading
A,B,C,D,E The green letter indicates the correct answer
Section 1: Mathematics
Question #1
1000 is the product of three numbers suitably chosen among 2, 4, 16, 25, 125.
What is the sum of the three numbers?
A 131
B 45
C 21
D 133
E 143
I omit the answer
Question #2
A 26
B 27
4
C 28
D 29
E 27
I omit the answer
Question #3
On a series of 20 shots in the basket, Bob had a 55% success rate. After 5 more shots, the rate
dropped to 52%. How many of the last 5 shots were successful?
A 2
B 0
C 1
D 3
E 4
I omit the answer
Question #4
Let a, b, c, d be real numbers such that a ≤ b and c ≤ d. Which of the following inequalities is
certainly true?
A ac2 ≤ bc2
B a−c≤b−d
C a+d≤c+b
D ac ≤ bd
E ac2 ≤ bd2
I omit the answer
Question #5
A 44
44
B
x−3
C 0
D 15
E 4x + 15
I omit the answer
Question #6
In the real number field the solution set for the inequality
x3 − 3x2 > 3 − x
is
A (3, +∞)
C (−∞, −1) ∪ (1 , 3)
D (−∞, 3)
E (−∞, +∞)
I omit the answer
Question #7
we have
A a<b<c
B a<c<b
C b<c<a
D c<b<a
E b<a<c
I omit the answer
Question #8
10x = x3 − x
has
Question #9
y = f (x) = √x (x + 3) (x − 2)
is the set
A −3 ≤ x ≤ 0 or x ≥ 2
B x≥0
C −3 ≤ x ≤ 2
D x ≤ 0 or x ≥ 2
E −∞ < x < +∞
I omit the answer
Question #10
You have two cubes of side L made by the same homogeneous material. Inside the first cube, a
cubic hole of side L / 3 has been cut, while the second cube has no holes inside. What is the ratio
of the weight of the first cube to that of the second cube?
A 26 ⁄ 27
B 2⁄3
C 8⁄9
D 19 ⁄ 27
E The ratio depends on the side L
I omit the answer
Question #11
In the Cartesian coordinate plane let r be the line of equation y = −3 x + 7. Then the straight line
symmetric to r with respect to the line y = 4 has equation
A y = 3x + 1
B y = 3x − 7
E y = 3x − 1
I omit the answer
Question #12
As shown in the figure below, the angle formed by a horizontal line (the "ground") and the line of
sight to an object above the horizontal line is called the angle of elevation.
Suppose that observing the top T of a vertical tower BT, an observer has measured the elevation
angles of 30° and 60° respectively from the positions P and Q on the ground. We know that the
distance between point P and base B of the tower is equal to p meters and that point Q is q meters
closer to B than point P. Then the ratio q/p is
A 2/3
B 1/2
C 1/3
D 3/4
E dependent on the height of the tower
I omit the answer
Question #13
In the Cartesian coordinate plane Oxy, the equation of the circle centered at (3, 5) and passing
through the point (−1, 2) is
A x2 + y2 − 6x − 10y + 9 = 0
B x2 + y2 + 6x + 10y + 9 = 0
C x2 + y2 + 6x + 10y − 19 = 0
D x2 + y2 − 6x − 10y − 19 = 0
E x2 + y2 − 6x − 10y + 29 = 0
I omit the answer
Question #14
If the claim "All students in my class speak at least three different languages" is false, then it is
certainly true that in my class
Question #15
Liam and Tom are friends. Nevertheless, Liam always lies, while Tom always tells the truth. Which
sentence did both Liam and Tom say?
Question #16
Ann, Bob, Edith, Sam and Tom are friends. You ask Ann, Edith and Tom about their birthdays. Tom
says that he was born in the same month as Edith but 9 days after her, and that his friends'
birthdays are on March 20, April 23, April 24 and May 24. Ann and Edith say that they celebrate
their birthdays on the same day of the week.
So Ann's birthday is
A April 24
B March 20
C March 27
D April 23
E May 24
I omit the answer
Question #17
The following table shows the distribution of the wrong answers in a test with 10 questions given to
a class of 25 students:
wrong
0 1 2 3 4 5 7
answer
numbers
of 2 7 6 3 4 2 1
students
A 2.44
B 61
C 0.88
D 3.5
E 4
I omit the answer
Question #18
Grouped data on the systolic blood pressure (in mmHg) of 160 female students (F) and 150 male
students (M) are given in the following table:
It follows that
the male students with systolic blood pressure at most equal to 115 mmHg are
A 75% of the female students with systolic blood pressure at most equal to 115
mmHg
at most 60% of male students has systolic blood pressure greater than 120
B
mmHg
half of the male students have systolic blood pressure greater than 120
C
mmHg
the percentage of female students with systolic blood pressure greater than
D 120 mmHg is larger than the percentage of male students with systolic blood
pressure greater than 120 mmHg
more than 80 female students and more than 78 male students have systolic
E
blood pressure equal to 129 mmHg
I omit the answer
Question #19
Four boys (M) and eight girls (F) signed up for a dance class. If the pairs of dancers are chosen at
random, then the statistical frequencies of the couples FF (two girls), FM (one girl and one boy)
and MM (two boys) are:
Question #20
A strange (but regular) dice has 1 dot on three faces, 2 dots on two faces and 3 dots on one face. If
you roll the dice twice, what is the probability of getting two odd numbers?
A 4/9
B 2/3
C 1/4
D 1/9
E 3/5
I omit the answer
Question #1
One of the rules of sales is that an advertisement only has to catch the attention of a possible
customer. It does not have to actually say anything about a product itself in order to increase sales.
Getting people to simply remember a product is more important for advertising than getting them to
know anything about the product.
Potential customers will remember a product even if they do not know much
A
about it
B Telling the truth about products would decrease sales
C It is not difficult to catch a possible customer's attention
D Advertisers lie more often than they tell the truth
E People who advertise products know very little about them
I omit the answer
Question #2
Twentieth-century cities are experiencing a period of radical transformation shown by the large
building projects that are redesigning entire parts of cities, from high-speed railways to
expressways. Throughout the world, cities are looking to the future, skylines all look the same, and
speed and movement are the key words.
Which of the following statements best describes the main concept expressed in the argument
presented above?
In the twentieth century, cities across the world are undergoing a great change
A
aimed at making travel quicker
B The key words for the public transport of the future are innovation and speed
Cities across the world have similar configurations because they are designed
C
using the same concept of growth
The change to twentieth-century cities is determined by their function and not
D
their configuration
The change to cities, in the twentieth century, is linked to the population
E
moving from the countryside to urban centres
I omit the answer
Question #3
3D printing shops are springing up here and there in capital cities across the world, even though
demand for objects is still limited at the moment. In the future, each district of each city will have its
own "local factory" to meet its residents' specific needs.
Question #4
In the face of a crisis that has led to the closure of some eleven European refineries in the last five
years, ENI has decided to convert the Porto Marghera plant: an investment of 100 million euros,
compared with the 600 needed to build a new plant. This is the first case in the world of the green
conversion of a traditional refinery.
Which of the following statements best describes the main concept expressed in the argument
presented above?
ENI has decided to invest in restructuring one of its plants to prevent its
A
possible closure
ENI has decided to invest in restructuring one of its plants to save 400 million
B
euros
C Green conversion is the main thrust of European ecological policies
D Other market operators will also convert their facilities to become green
E Porto Marghera is the trail-blazing project of ENI's new ecological policy
I omit the answer
Question #5
Despite being universal, gossiping at work is seen as unprofessional and can compromise career
progression chances, damage the reputation of individuals or groups or the organisation itself and
lead to lower productivity or the departure of the best employees.
Which of the following statements, if true, would greatly strengthen the argument presented above?
The Minister for Employment has declared that firms that supported the
"internal and external privacy management" project last year, implementing
A
policies aimed at controlling gossip, recorded higher productivity than
companies that showed no interest in the project
The annual employee productivity assessment by management is a legal
B
obligation that not all small and medium-sized companies fulfil
Some international firms devote two or three training days on evaluating and
C countering gossip at work, based on the findings of company surveys of
organisational well-being
Checking that there are no conflicts of interest among the management of
D public companies is a legal obligation that is fulfilled every three years at
ministerial level
The "employee of the year" award is a way for firms to acknowledge the work
E carried out by the employee and usually involves giving the winner a financial
reward
I omit the answer
Question #6
In the last decade, investment in research and development in Italy increased modestly, reaching
1.25% of Gross Domestic Product in 2018. But this level is way below that of technologically
advanced countries, confirming the current trend towards specialisation in hand-crafted rather than
high-tech products.
Which of the following statements can be deduced from the argument presented above?
Question #7
Which of the following statements best summarises the conclusion of the argument presented
above?
Question #8
Eight people -- four drivers: Edward, Rachel, Michael, and Alice; and four passengers: Charles,
Sarah, John, and Harry -- are being assigned to four cars, numbered 1 to 4.
Each person is assigned to exactly one car, and exactly two people are assigned to each car.
Assignments of people to cars must conform to the following conditions:
If Charles is assigned to car 2 and Sarah is assigned to car 4, which one of the following must be
true?
Premature babies that are regularly massaged are more active than premature babies that are not
massaged. For the same daily milk intake, babies that are massaged gain more weight than babies
that are not massaged. This appears strange because usually more active babies require more
calories to gain weight.
Which of the following statements, if true, would explain the apparent inconsistency described in
the argument presented above?
Question #10
Vampire bats fly over a much larger area than other similar-sized bats. The reason for this is that
the animals they feed on are not very common in the forests where they live and this scarcity of
prey forces them to fly further to find food.
Which of the following statements, if true, would greatly strengthen the argument presented above?
Vampire bats fly over a much larger area only if they are in regions where
A there is not much food for them; this is not true if they are in regions where
such food is plentiful
Vampire bats fly over an area eight times larger than the area over which
B
similar-sized bats fly
After babies are born, vampire bats must look for food more often to feed
C
themselves and their offspring
D Vampire bats sometimes fly over a small area for many weeks
E For similar living conditions, vampire bats eat less than other bat species
I omit the answer
Question #1
Which periodic table group contains elements in three states of matter at standard ambient
pressure and temperature?
A Halogens
B Noble gases
C Alkaline earth metals
D Alkali metals
E Carbon group
I omit the answer
Question #2
A CH3CH2CH2OH
B CH3CH(OH)CH3
C CH3OCH3
D CH3COCH3
E CH3CH2CHO
I omit the answer
Question #3
Question #4
which of the following represents the Brønsted-Lowry bases for this reaction?
Question #5
If 20.0 mL of 1.0 M HBr are diluted to a total volume of 60.0 mL, what is the molar concentration of
the HBr in the resulting solution?
A About 0.33 M
B 0.25 M
C 1.0 M
D 0.50 M
E About 0.66 M
I omit the answer
Question #6
A 50 W lightbulb is plugged into a standard 100 V outlet. Assume that the electrical energy is
provided as in the case of a direct-current circuit. What is the resistance of the bulb filament?
A 200 Ω
B 100 Ω
C 400 Ω
D 20 Ω
E 2Ω
I omit the answer
Question #7
An ideal fluid flows from left to right at a steady rate through a tube segment. The cross-sectional
areas of the tube are A1= 100 cm2 on the left side and A2 = 50 cm2 on the right side. The fluid
speed is v1 = 20 cm/s on the left side. What is the fluid speed v2 on the right side?
A 40 cm/s
B 5 cm/s
C 80 cm/s
D 320 cm/s
E 10 cm/s
I omit the answer
Question #8
A block is placed at rest on a plane inclined at an angle α to the horizontal. The coefficient of static
friction between block and plane is μs = 1. Determine the maximum angle of incline to keep the
block from sliding.
A 45°
B 60°
C 15°
D 30°
E 1°
I omit the answer
Question #9
A transverse circular wave propagates on a plane surface without energy dissipation. If the wave
amplitude is 2 cm at a distance of 10 cm from its centre, what is the wave amplitude at a distance
of 40 cm from its centre?
A 1 cm
B 0.5 cm
C 2 cm
D 0.25 cm
E It cannot be answered without knowing the wave frequency
I omit the answer
Question #10
An ideal gas is confined into a cylinder with a movable piston and is in equilibrium at 20 °C and 1
atm. Then the temperature is raised to 40 °C while we keep the pressure of the gas constant.
Which of the following statements is correct?
Section 4: Biology
Question #1
Question #2
Phagocytosis means
Question #3
Which of the following combinations would you expect to find in a person's blood after a rich meal?
Question #4
A sensitive
B mixed
C only sympathetic
D motor
E motor and sympathetic
I omit the answer
Question #5
A micrometre
B millimetre
C nanometre
D dalton
E angstrom
I omit the answer
Question #6
A fix CO2
B adapt to appropriate environments
C resist disease
D reproduce
E breathe
I omit the answer
Question #7
An allele is
Question #8
A 7
B 3
C 12
D 8
E 5
I omit the answer
Question #9
A anaphase
B prophase
C interphase
D metaphase
E telophase
I omit the answer
Question #10
A Escherichia coli
B Erythroblast
C Amoeba proteus
D Tripanosoma brucei
E Syncytium
I omit the answer
Question #1
All mammals
Question #2
A mm Hg
B pascal
C atm
D mm air
E neutrons/m2
I omit the answer
Question #4
Question #5
X-rays are
A electromagnetic waves
B very fast free electrons
C elastic waves with a lot of energy
D very penetrative nucleons
E a bundle of neutrons
I omit the answer
Question #6
A impossible
B possible, if induced
C rare, but possible
D frequent
E normal
I omit the answer
Question #7
reaches the same level in all receptacles (if these receptacles are not
A
capillary)
reaches a level proportional to the specific weight of the liquid in the various
B
receptacles
C reaches the same level in all receptacles, with no exception
D reaches different heights in the various receptacles, according to their size
E none of the answers shown is correct
I omit the answer
Question #8
Question #9
All living beings are classified with two terms that indicate
Question #10
Electrolysis of water is a process in which the passage of an electric current causes the
decomposition of water into