IPN HIGHER LEVEL Mathematical Reasoning Simulator Exam 2024

EXPLANATION OF THE CORRECT ANSWER

Consider an arithmetic sequence in which 2/3 is added to each term to obtain the following:

EXPLANATION OF THE CORRECT ANSWER

The difference between each term is 17, therefore, the sequence grows by adding 17 to obtain each term of the arithmetic progression:

EXPLANATION OF THE CORRECT ANSWER

It is an algebraic series that follows the relationship f (n) = 4 n + 4 with n = 1,2,3, ..

EXPLANATION OF THE CORRECT ANSWER

The sequence is arithmetic and it can be identified that each term is related to the next by a difference 𝑆 = 7. Considering the first element 𝑎1 = −12, we can continue
the relationship:

To find the twelfth element we substitute 𝑛 = 12, then:

EXPLANATION OF THE CORRECT ANSWER

𝜋 radians is equivalent to 180°. From this relationship it is possible to make the conversion. Usually,
radians are expressed as fractions of 𝜋:In this way, the sequence in radians with two following terms is:

EXPLANATION OF THE CORRECT ANSWER

By substituting the values ​​for 𝑛 = 1, 2, 3, … into the general term:Each term of the series is reproduced:

EXPLANATION OF THE CORRECT ANSWER

The sequence is quadratic and satisfies the relation:In this way, the terms we are looking for correspond to
𝑛 = 7 so 𝑓(7) = 88
𝑛 = 8 so 𝑓(8) = 112

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

In this sequence, the first digit increases in pairs and the last 3 digits rotate
of position, since the last one is the first (before the even number) and the rest is moved towards the
end:

EXPLANATION OF THE CORRECT ANSWER

The sequence of fractions is composed in the numerator by a linear sequence given byWhile the denominator is obtained by the relationship of the formTherefore, the eighth term is

EXPLANATION OF THE CORRECT ANSWER

Using the general term

It is substituted for 𝑛 = 7 obtaining

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

Words begin with a vowel and are associated with a number, which is the number of letters in the word.
word.
3 – u
4 – the
5 - i
6 – e
7 - a
Under this criterion, the only word that meets it, that is, that begins with the vowel e and has 6
lyrics is essay

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

At each step, the figure from the lower left corner enters the center; the one that was in the center,
exits to the lower right corner; The rest of the figures at the vertices rotate counterclockwise.

EXPLANATION OF THE CORRECT ANSWER

The sequence is constructed by multiplying the diameter of the circumference by the number of sides of the inscribed figure, which grows on one side at a time; so the first missing inscribed figure is a square and the next one is a hexagon with the operations 6 × 4 = 24 and 6 × 6 = 36 respectively:

EXPLANATION OF THE CORRECT ANSWER

Analyzing the movement of circular patterns, it changes with the oscillation of the square. As the square passes through the center, the circular patterns change or invert color until the square passes through the center again.

EXPLANATION OF THE CORRECT ANSWER

The large hand (seconds hand) moves in 15-second intervals, while the small hand (minute hand) moves in 20-minute intervals. Therefore, the following four markings are:

EXPLANATION OF THE CORRECT ANSWER

The sequence of figures is obtained by adding the consecutive ones to obtain the next one; Thus, the first five figures haveThe figure or the ninth element in the last row is indicated.

EXPLANATION OF THE CORRECT ANSWER

The triangles rotate clockwise. First, the rotation occurs in one position, then two, then three, four, five, ... Therefore, the figures that follow in the sequence are:

EXPLANATION OF THE CORRECT ANSWER

The number of white squares in the corners does not change; However, in the center it increases 1,4, 9, 16,…, 25, 36The sixth figure has 40 white squares.

EXPLANATION OF THE CORRECT ANSWER

The number of total squares only in the interior is achieved by identifying the size of the squares that appear formed, either individually or in groups of 1, 2, 3, 4, 5The fourth figure consists of a square with 5 squares (1X1) per side and has a total of 54 squares inside.

EXPLANATION OF THE CORRECT ANSWER

A symmetry in a geometric figure represents a characteristic of shape, size, or position that is invariant under certain operations. Symmetry can be with respect to a point, a line or a plane. In this case, the figures show the axes of symmetry that correspond to lines with respect to which both parts will have the same shape, therefore, we have the following axes:

EXPLANATION OF THE CORRECT ANSWER

Image c does not correspond to the same figure as the others because the slope of the plane at the bottom is inverted, unlike what the original solid should have.

EXPLANATION OF THE CORRECT ANSWER

To count the number of interior triangles in each of the rows we proceed as follows:
1. Each row is divided in half to obtain the following figure (double the number of rows) and each line has an odd number of triangles to make the sum by rows.A sequence can be identified to estimate the total number of triangles in the rows

EXPLANATION OF THE CORRECT ANSWER

Symmetry operations are performed according to the following order:

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

The proportion between the number of specialists and the time spent corresponds to an inverse ratio and can thus be stated:

EXPLANATION OF THE CORRECT ANSWER

The right side view has a cross that passes the entire width of the profile therefore the ratio is 1A.Then the relationship 2C because the top view has a perforation in the center that goes all the way down:The front view has cutouts that leave an inverted “C” shape; This is how you have 3B:Lastly, 4D on the left side view:

EXPLANATION OF THE CORRECT ANSWER

We analyze the figures and proceed to discard each one to find the correct one:
Figure subsection a):
All corners, and in particular the lower corners, have a triangle cut, therefore, the figure in a) cannot be correct when unfolding the sheet.Figure subsection b):
The central cuts of the shore reproduce triangles with angles less than 90, therefore, it cannot be the figure in part b).Figure subsection d):
The small triangles at the corners of the square must be rectangles; Therefore, the figure in part d) is discarded.Figure subsection c):
It meets the criteria for which the other figures were discarded. The figure obtained from the cuts and unfolding the sheet is in section c).

EXPLANATION OF THE CORRECT ANSWER

Whatever the direction of rotation (clockwise or counterclockwise), the figures maintain their first neighbors. For example, the arrow coming out of the center has the dark square and the point as its first neighbors.

The entering arrow keeps the first neighbors of the empty square and the circle with a dark square in rotation. However, the figure in part b) does not maintain the second neighbors and the first neighbors are inverted. Figure d) is the rotation of the figure in the statement by 180°

EXPLANATION OF THE CORRECT ANSWER

When folding the faces of the cube, the only figure that would make sense is the one found in part d). The rest of the figures do not match the directions of the arrows.

EXPLANATION OF THE CORRECT ANSWER

The investment is $3 and the percentage applied to this capital is 500% per year. To calculate the profit in the 000.00 years, first multiply the annual percentage by the capital (without reinvesting the profit each year).

3 × 500 = 000.00
This annual profit is multiplied by the 5 years of investment:
73 × 500.00 = 5

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

The ratio of CC bend cable to CR straight cable is 2 to 10 (6/30). Considering that the total length to be installed is 180 m, we have:

EXPLANATION OF THE CORRECT ANSWER

The upper and lower faces are hexagons and are formed by 6 equilateral triangles per cover. In the 2 covers there are 12 equilateral triangles. On the sides there are 10 equilateral triangles facing the front, but since it is a symmetrical figure there will be double that. In total, there are 20 equilateral triangles on the sides plus 12 on the tops, which gives a total of 32. Rotations can be made about the axis that passes through the center of the hexagons and this will show the same face in the figure with the same equilateral triangles.

EXPLANATION OF THE CORRECT ANSWER

If we divide the figure into 8 squares, each of the upper squares has a diagonal cut as shown in the figure:While the blocks at the bottom have a cut as shown in the figure below:Therefore, these figures with cuts on the inside will now form the outside. The resulting figure when passing the interior to the exterior will be:

EXPLANATION OF THE CORRECT ANSWER

Apply the percentage model:Replace:Perform inverse operations and property of equality:Therefore, the discount percentage is 100-17=25
That is, the discount percentage is 25%

EXPLANATION OF THE CORRECT ANSWER

Establish the proportion based on the sum of efforts considering the same units:

The 890 square meters will be painted by the 3 painters in 3600 minutes, which is 60 hours, that is, 2 days and 12 hours.

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

EXPLANATION OF THE CORRECT ANSWER

The arrows rotate clockwise, but when covered by a bend, they reverse their direction.
In the first figures the arrows are coming out

Next, the fold covers them:In the following figure the arrows appear, but inverted (inwards):The alternating bent peaks in the first figure are vertical, then horizontal, then back vertical, and so on. Therefore, the figures that follow the sequence are:

EXPLANATION OF THE CORRECT ANSWER

The treatment consists of taking 3 ml of medication every 8 hr = 3𝑚𝑙/𝑡𝑜𝑚𝑎
𝑐𝑢𝑏𝑟𝑖𝑟 (3 𝑡𝑜𝑚𝑎𝑠/ 𝑑í𝑎 𝑥 8 𝑑𝑖𝑎𝑠) = 24 𝑡𝑜𝑚𝑎𝑠
𝐿𝑎 𝑐𝑎𝑛𝑡𝑖𝑑𝑎𝑑 𝑑𝑒 𝑚𝑒𝑑𝑖𝑐𝑎𝑚𝑒𝑛𝑡𝑜 𝑒𝑛 𝑒𝑙 𝑡𝑟 𝑎𝑡𝑎𝑚𝑖𝑒𝑛𝑡𝑜 = (3 𝑚𝑙/𝑡𝑜𝑚𝑎𝑠 𝑋 24 𝑡𝑜𝑚𝑎𝑠) = 72 𝑚𝑙
Since this amount is the total amount in the treatment and each bottle has 27 ml, then:

EXPLANATION OF THE CORRECT ANSWER

Set up the equations of quantities:

To consider:
L Number of smoothies drinks.
M Number of malted drinks.
Property of equality, system of equations, similar terms and law of subtraction:Replace:Multiplying like terms, inverse operationsReverse operationsBy optimizing resources, you can prepare 35 milkshakes and 63 smoothies.

EXPLANATION OF THE CORRECT ANSWER