In this question, you need first to create equivalent expressions in the equation that have equal bases.
Choice 𝐴 is correct – The equation 3^{𝑥 + 3} = 243 can be written as:
3^{𝑥 + 3} = 3⁵
Since the bases are the same, then their exponents are equivalent:

Substituting 𝑥 by 2 in 5^{x - 1} = 5^{2 - 1} = 5¹ = 5

Compare the real parts alone, then the imaginary parts.
Choice 𝐷 is correct – Comparing the real parts in this question:
𝑥 + 2𝑦 = 7
Comparing the imaginary parts:
-8 = 2𝑥 + 8𝑦
-4 = 𝑥 + 4𝑦
𝑥 + 4𝑦 = -4
Therefore, we will have a system of two equations:

Subtracting both equations to eliminate 𝑥:
-2𝑦 = 11
𝑦 = - 11 / 2 = -5.5
Substituting 𝑦 by -5.5 in the first equation: 𝑥 + 2𝑦 = 7
𝑥 + 2(-5.5) = 7
𝑥 - 11 = 7
𝑥 = 18

This question is related to composition of functions.
Choice 𝐵 is correct – First, let’s find the value of 𝑔(2):
𝑔(2) = 3√7 as there are no 𝑥 in 𝑔(𝑥) to substitute it by 2.
Then: ℎ(3√7) = (3√7)² - 3 = 60
Hence: 𝑓(60) = -3 cos⁡ 60 = -3 ( 1 / 2) = - 3 / 2 = -1.5

The area of a semi-sphere is given by 𝐴 = 2π𝑟² with 𝑟: the radius of the sphere.
Choice 𝐸 is correct – If we need to find the area of a shaded region in this semi-sphere, then it should be smaller than or equal to the total area of the semi-sphere, then 𝐴₁ < 𝐴 = 2π𝑟²
However, choice 𝐴 is incorrect, as 4π𝑟 will not result the numerical value of the area.
In choice 𝐵, 5 / 2 π𝑟² > 2π𝑟² as 5 / 2 > 2, therefore it is incorrect.
In choice 𝐶, as 7 / 2 > 2, we have 7 / 2 π𝑟² > 2π𝑟², and this choice is incorrect.
In choice 𝐷, as 4 > 2, we have 4π𝑟² > 2π𝑟², and this choice is incorrect.
In choice 𝐸, 4 / 3 < 2, then 4 / 3 π𝑟² < 2π𝑟². This can be the area of the shaded region in the semi-sphere.

To solve this question, simply before solving the rational inequality, check the conditions, check the answers if you could find the condition as a choice. If not, solve the inequality.
Choice 𝐷 is correct – The excluded values for this inequality are:
𝑥 + 1 ≠ 0, so 𝑥 ≠ -1
and 𝑥 + 3 ≠ 0, so 𝑥 ≠ -3.
Then choice 𝐷 which is -1 cannot be a value for 𝑥.

The distance between two points in a 3D-coordinate plane can be found using the formula: √(𝑥₂ - 𝑥₁)² + (𝑦₂ - 𝑦₁)² + (𝑧₂ - 𝑧₁)².
Choice 𝐵 is correct – Applying the formula in our question:

Multiply vector 𝑉^→   by 5, and add the result to the product of 𝑀^→   by 2:
Choice 𝐵 is correct – The result of 5𝑉^→   is:
5(2𝑖^→   + 7𝑗^→   ) = 10𝑖^→   + 35𝑗^→
While 2𝑀^→   = 2(-3𝑖^→   + 𝑗^→   ) = -6𝑖^→   + 2𝑗^→
The addition of both results:
10𝑖^→   + 35𝑗^→  + (-6𝑖^→   + 2𝑗^→  ) = 4𝑖^→   + 37𝑗^→

An obtuse angle has a measurement greater than 90°. In this question, the obtuse angle is ∠𝐵 (facing the largest side).
Choice 𝐸 is correct – To find the value of this obtuse angle, use the laws of cosines:

Remember the logarithm rules:
𝑎^{log_𝑎 ⁡𝑘} = 𝑘 and log_𝑎⁡ 𝑎^𝑘 = 𝑘
Choice 𝐴 is correct – In our question:
2^{log₂ ⁡𝑥} = 𝑥 using the logarithm rules.
In addition, log₃⁡ 3^4𝑥 = 4𝑥 using the logarithm rules.
Hence, the equation will be: 𝑥 + 4𝑥 = 25
5𝑥 = 25
𝑥 = 5

Choice 𝐶 is correct – In this question, we need to work on combinations. However, we might have different options of selections.

1. John can select 7 questions (the maximum number) from paper A, and 5 from paper 𝐵. Therefore: ₇C₇ × ₁₁C₅ = 462
2. He can select 6 questions from paper A, and 6 from paper 𝐵. Therefore: ₇C₆ × ₁₁C₆ = 3234
3. He can select 5 questions from paper A, and 7 from paper 𝐵. Therefore: ₇C₅ × ₁₁C₇ = 6930
4. He can select 4 questions from paper A, and 8 from paper 𝐵. Therefore: ₇C₄ × ₁₁C₈ = 5775

He is obliged to choose at least 4 questions from each paper, then he cannot choose 3 questions from paper 𝐴.
Adding all the results:
462 + 3234 + 6930 + 5775 = 16401

Choice 𝐷 is correct – We know that sin ⁡( π / 2 - θ) = cos⁡ θ.
Thus, cos⁡ θ = 0.8, and then θ = cos^-1⁡ 0.8 = 36.87°.
Consequently, sin⁡ θ = 0.6.
Finding cot⁡ θ = 1 / tan θ⁡ = 1 / sin ⁡θ / cos ⁡θ = cos θ / sin⁡ θ = 0.8 / 0.6 = 4 / 3
Therefore: sin⁡ θ × cot ⁡θ = 0.6 × 4 / 3 = 4 / 5 = 0.8
Or:
Choice 𝐷 is correct – We know that sin ⁡( π / 2 - θ) = cos θ
Thus, cos⁡ θ = 0.8
sin⁡ θ × cot⁡ θ = sin⁡ θ × cos θ / sin⁡ θ = cos θ = 0.8

The standard deviation refers to as the measure of how spread out numbers are. To find it out, we need to search for the square root of the variance, which is the average of the squared differences of the mean.
Choice 𝐵 is correct – The mean of the numbers in the set is:
6 + 19 + 14 + 13 + 7 + 11 / 6 = 35 / 3
Subtracting 35 / 3 from each number in the set, and then finding its square:

The average of the sum of these results is:

The standard deviation will then be: √ 173 / 9 = 4.38

Choice 𝐴 is correct – The cube of a binomial (𝑎 - 𝑏) is a³ - 3𝑎²𝑏 + 3𝑎𝑏² - 𝑏³.
In our case, 𝑥 = 4(2𝑖 - 3), then 𝑥³ = [4(2𝑖 - 3)]³ = 64(8𝑖³ - 3(4𝑖²)(3) + 3(2𝑖)(9) - 27)

Using the units given, you need to find the time of each interval, then find the average speed of Wassim’s trip.
Choice 𝐷 is correct – The distance is in kilometers (k𝑚), while the speed is in kilometers per hour (k𝑚/ℎ𝑟). Then, to find the time, we need to divide the distance by the speed:
k𝑚 ÷ k𝑚 / ℎ𝑟 = k𝑚 ∙ ℎ𝑟 / k𝑚 = ℎ𝑟
For the first part: 50 k𝑚 at 65 k𝑚 per hour:
50 / 65 = 10 / 13 ℎ𝑟
For the second part: 50 k𝑚 at 80 k𝑚 per hour:
50 / 80 = 5 / 8 ℎ𝑟
For the third part: the rest (104 - 50 - 50 = 4 k𝑚) at 54 k𝑚 per hour:
4 / 54 = 2 / 27 ℎ𝑟
The total time for this trip is: 10 / 13 + 5 / 8 + 2 / 27 = 1.47 ℎ𝑟.
Therefore, the average speed of this trip is: 104k𝑚 / 1.47ℎ𝑟 = 70.8 k𝑚/ℎ𝑟

In an arithmetic sequence, the difference between the consecutive terms is always alike.
Choice 𝐶 is correct – To find 𝑘, simply create an equation in which you respect the rule of consecutive terms in an arithmetic sequence:

Choice 𝐶 is correct – The roots of (𝑥 - √2)² (2𝑥 - √2)(𝑥 + √2) = 0 are:
𝑥 - √2 = 0 (double)
𝑥 = √2
or 2𝑥 - √2 = 0, then 2𝑥 = √2
𝑥 = √2 / 2
or 𝑥 + √2 = 0, so 𝑥 = -√2
The sum of the roots: √2 + √2 + √2 / 2 + (-√2) = 3√2 / 2

To tackle this question, you need to understand the type of the equation given. It is a vertical hyperbola of a general form: (𝑦 - 𝑘)² / 𝑎² - (𝑥 - ℎ)² / 𝑏² = 1.
The equation of the asymptotes are:
𝑦 = ± 𝑎 / 𝑏 (𝑥 - ℎ) + 𝑘
Choice 𝐵 is correct – In our hyperbola, we know that 𝑘 = 3.
We have: 𝑎² = 16, thus 𝑎 = 4.
𝑏² = 25, thus 𝑏 = 5.
Factoring 𝑥² - 14𝑥 + 49 using perfect squares will result: (𝑥 - 7)². It means ℎ = 7.
The asymptotes could be 𝑦 = ± 4 / 5 (𝑥 - 7) + 3
Taking the negative answer:
𝑦 = - 4 / 5 (𝑥 - 7) + 3 = - 4 / 5 𝑥 + 28 / 5 + 3 = - 4 / 5 𝑥 + 43 / 5 = -4𝑥 + 43 / 5

Remember that cos²⁡ 𝑥 + sin²⁡ ⁡𝑥 = 1.
Choice 𝐵 is correct – In our question, cos⁡ 𝑥 = 0.24, then cos²⁡⁡ 𝑥 = 0.0576.
Hence, 0.0576 + sin²⁡ 𝑥 = 1
sin²⁡ ⁡𝑥 = 1 - 0.0576 = 0.9424

Choice 𝐵 is correct – In rectangle 𝐴𝐵𝐶𝐷, segment 𝐴𝐶 is considered to be the hypotenuse in triangle 𝐴𝐵𝐶, right at 𝐵.
Since m∠𝐵𝐴𝐶 = 25°, then we can use the trigonometric ratios to find the length of 𝐴𝐵^— and 𝐵𝐶^—.
For ∠𝐵𝐴𝐶, 𝐵𝐶^— is its opposite. Thus, sin⁡ 25° = 𝐵𝐶 / 5 ⟹ 𝐵𝐶 = 2.11.
For ∠𝐵𝐴𝐶, 𝐴𝐵^— is its adjacent. Thus, cos⁡ 25° = 𝐴𝐵 / 5 ⟹ 𝐴𝐵 = 4.53.
The perimeter of triangle 𝐴𝐵𝐶 is equal to 5 + 2.11 + 4.53 = 11.64 cm.

The given equation represents an ellipse such that its general form is (𝑥 - ℎ)² / 𝑏² + (𝑦 - 𝑘)² / 𝑎² = 1, and then it is a vertical ellipse. To find the foci, we need to find 𝑐 such that c² = 𝑎² - 𝑏².
Choice 𝐴 is correct – Finding c:

The coordinates of the foci in a vertical ellipse are: (𝑏, ±𝑐).
Hence, (3, ± 2√10) are the coordinates of the foci.

The oblique asymptote of a rational function will exist if the degree of the denominator is one less than the degree of the numerator.
To find it out, and if the degree of the denominator is equal to 1, you need to divide the numerator by the denominator using long division, synthetic division, or by factoring if possible.
Choice 𝐶 is correct – Applying long division in our case:

(𝑥 - 3) 5𝑥 + 15 / 5𝑥² + 0𝑥 - 2

- 5𝑥² - 15𝑥
- 15𝑥 - 2
15𝑥 - 45
43

The result of the division will be the equation of the oblique asymptote (without taking into consideration the remainder):
𝑦 = 5𝑥 + 15

To solve this question, we need to use permutations. It is an arrangement of numbers or options into a linear order.
Choice 𝐴 is correct – We have 8 as the total number of greeting cards, and 5 as the number of friends selected.
Then ₈𝑃₅ = 6720

As both circles touch/intersect each other internally, and the small circle passes through point 𝐴, which is the center of the big circle, then the radius of the small circle is half the radius of the big circle.
Choice 𝐸 is correct – The radius of the small circle is 6 / 2 = 3 𝑚.
Then its area is 𝐴_𝑠 = π𝑟² = π(3)² = 9π 𝑚².
The area of the big circle is A_𝑏 = π𝑅² = π(6)² = 36π 𝑚².
The area of the shaded region can be found by subtracting the area of the small circle from the area of the big circle:
𝐴 = 𝐴_𝑏 - 𝐴_𝑠 = 36π - 9π = 27π 𝑚² = 84.823001 𝑚²
Options 𝐴 and 𝐵 are incorrect. Therefore, we need to convert our area into 𝑐𝑚². It is by multiplying the numerical value we have by 100².
The result is: 848230 𝑐𝑚².

Choice 𝐷 is correct – The function 𝑦 = -3^𝑥 is an exponential function of a general form 𝑦 = a^𝑥, and exponential functions are always continuous. Since a = -3 < 0, then it is decreasing. Therefore, (𝐼) is correct.
As a < 0, then the range is {𝑦 | 𝑦 < 0}. Then, (𝐼𝐼𝐼) is correct.
Substituting 𝑥 by 0, will result: 𝑦 = -3⁰ = -1, but substituting 𝑥 by -1 will result: 𝑦 = -3^-1 = - 1 / 3 ≠ 0, then (𝐼𝐼) is incorrect.

Find the area of the rectangle, then find the area of each unshaded shape, and subtract the result from the total area.
Choice 𝐵 is correct – The area of the rectangle 𝐴 can be found by 𝐴 = 𝐿 ∙ 𝑤 with 𝐿 its length, and 𝑤 its width.
𝐴 = 8 × 4 = 32.
The first unshaded shape is a trapezoid. Its area 𝐴' can be found by 𝐴' = 1 / 2 ℎ(𝑎 + 𝑏) with ℎ being its height, 𝑎 its small base, and 𝑏 its big base.
𝐴' = 1 / 2 (4)(2 + 8) = 20.
𝐻𝐷𝑇 is a right angled triangle at 𝐷 with 𝐻𝑇 = 4.9 and 𝐷𝑇 = 4. Using Pythagorean theorem:
𝐻𝑇² = 𝐷𝐻² + 𝐷𝑇²
4.9² = 𝐷𝐻² + 4²
24.01 = 𝐷𝐻² + 16
𝐷𝐻² = 8.01
𝐷𝐻 = 3√89 / 10
The area 𝐴'' of triangle HDT can be found by 𝐴'' = 1 / 2 𝑏ℎ with 𝑏 its base and ℎ its height.
𝐴'' = 1 / 2 ( 3√89 / 10 )(4) = 3√89 / 5
The area 𝐴_𝑠 of the shaded region: 𝐴_𝑠 = 𝐴 - 𝐴' - 𝐴'' = 32 - 20 - 3√89 / 5
𝐴_𝑠 = 6.34

Using trigonometric identities, and specifically double-angle identities, we have: cos⁡ 2θ = 1 - 2sin² ⁡θ.
Choice 𝐵 is correct – Since 1 - 2sin²⁡ θ = - 1 / 3 , then cos ⁡2θ = - 1 / 3 .
Using 1 - 2sin² θ = - 1 / 3 , and solving for sin θ :
-2 sin²⁡ θ = - 1 / 3 - 1
sin² ⁡θ = 2 / 3
sin⁡² = √6 / 3
Thus, sin⁡ θ / 2cos ⁡2θ = √6 / 3 / 2(- 1 / 3 ) = - √6 / 2 = -1.2

Choice 𝐶 is correct – To find the number of people who joined the boxing team, add the values in the ratio, divide the total number of people by the sum you found, then multiply the quotient by the amount of the boxing team in the ratio.
Adding the amounts in the ratio: 9 + 10 + 8 = 27
243 ÷ 27 = 9
Multiply 9 by the amount of the boxing team in the ratio (10):
9 × 10 = 90

Two lines are perpendicular if the product of their slopes is equal to -1.
Choice 𝐵 is correct – Write –𝑥 / 3 + 7𝑦 / 2 = -1 in the form of 𝑦 = 𝑚𝑥 + b:
7𝑦 / 2 = 𝑥 / 3 - 1
𝑦 = 2 / 21 𝑥 - 2 / 7
The slope of this line is m = 2 / 21 . The slope m' of the line perpendicular to the given line can be found by applying 𝑚 ∙ 𝑚' = -1
2 / 21 𝑚' = -1
𝑚' = - 21 / 2

Choice 𝐵 is correct – Arrange the numbers in the set from lowest to greatest:
5, 10, 10 , 20, 25, 30
There are even number of data. The median will be the average of the middle two numbers: 𝑀 = 10 + 20 / 2 = 15.
The mode is the number that occurs the most: 𝑚 = 10.
The average of 𝑀 and 𝑚: 𝑀 + 𝑚 / 2 = 15 + 10 / 2 = 12.5

To find the domain of the rational function, find the conditions of this rational function (the denominator cannot be equal to zero).
Choice 𝐸 is correct – Find the conditions:
𝑥² - 5𝑥 - 14 ≠ 0
Factorizing 𝑥² - 5𝑥 - 14 will result: (𝑥 - 7)(𝑥 + 2).
Then: (𝑥 - 7)(𝑥 + 2) ≠ 0
𝑥 ≠ 7 and 𝑥 ≠ -2
Hence, the domain is all real numbers except 7 and -2.

To find the solution of this question, use the formula of the exponential growth defined by 𝑦 = 𝑎(1 + 𝑟)^𝑥 in which 𝑎 is the initial value, 𝑟 is the growth rate, and 𝑥 is the number of time intervals that have passed.
Choice 𝐸 is correct – In this question, the initial value 𝑎 is 1, 427, 647, 786. The growth rate 𝑟 is 0.59% = 0.59 / 100 , while the time interval is 𝑥 = 2021 - 2018 = 3.
Hence, 𝑦 = 1, 427, 647, 786(1 + 0.59 / 100 )³ = 1, 453, 066, 534
The nearest value given is: 1, 453, 142, 111 which is choice 𝐸.

The area of a parallelogram is 𝐴 = 𝑏ℎ with 𝑏 is its base and ℎ is its height.
Choice 𝐶 is correct – The base of parallelogram 𝐴𝐵𝐶𝐷 is 4ℎ, and its height is ℎ.
As the area is 625 𝑐𝑚², then 4ℎ(ℎ) = 625
4ℎ² = 625
ℎ² = 625 / 4
ℎ = 25 / 2
𝐴𝐵 = 4ℎ = 4( 25 / 2 ) = 50 𝑐𝑚

Choice 𝐷 is correct – Using the converse of the Pythagorean theorem, if the triangle is obtuse, then 𝑐² > 𝑎² + 𝑏².
In option 𝐴, 13.6² > 9² + 10², then 184.96 > 181. It is an obtuse triangle.
In option 𝐵, 14.5² > 8² + 12², then 210.25 > 208. It is an obtuse triangle.
In option 𝐶, 10² > 6² + 7², then 100 > 85. It is an obtuse triangle.
In option 𝐷, 11² > 7² + 9², then 121 > 130 – Incorrect. It cannot be an obtuse triangle.

As 𝑥 gets infinitely large, then we need to find the limit when 𝑥 approaches infinity.
Choice 𝐶 is correct – Finding the limit:
limx → + ∞⁡ 2𝑥 + 1 / 𝑥 - 1 = limx → + ∞⁡ 2𝑥 + 1 - 𝑥 / 𝑥 = lim𝑥 → + ∞⁡ 𝑥 + 1 / 𝑥 ⁡ = ∞ / ∞ then it is indeterminate.
Using L’Hopital’s rule:
The derivative of 𝑥 + 1 is 1, and the derivative of 𝑥 is 1.
lim𝑥 → + ∞⁡ ⁡ 1 / 1 = 1
Or:
Choice 𝐶 is correct – Finding the limit:
lim𝑥 → + ∞⁡⁡ 2𝑥 + 1 / 𝑥 - 1 = lim𝑥 → + ∞⁡ 2𝑥 / 𝑥 - 1 = lim𝑥 → + ∞⁡⁡ 2 - 1 = 1

Remember that if 𝑓(-𝑥) = -𝑓(𝑥), then it is an odd function. If 𝑓(-𝑥) = 𝑓(𝑥), then it is an even function.
Choice 𝐵 is correct – Substituting 𝑥 by –𝑥 in 𝑓(𝑥):
𝑓(-𝑥) = 2(-𝑥)⁵ - 3(-𝑥)³ + (-𝑥)
𝑓(-𝑥) = -2𝑥⁵ + 3𝑥³ - 𝑥
𝑓(-𝑥) = -(2𝑥⁵ - 3𝑥³ + 𝑥) = -𝑓(𝑥).
It is an odd function.
(𝐼) is incorrect, and (𝐼𝐼) is correct.
A graph is symmetric about the 𝑥-axis if whenever (𝑎, 𝑏) is (𝑎, -𝑏) as well.
Choosing point of abscissa 𝑥 = 1, then 𝑓(1) can only be 0. The graph of this function cannot be symmetric about the 𝑥-axis otherwise it’s not a function.
(𝐼𝐼𝐼) is incorrect.

Choice 𝐸 is correct – If 𝑥 = 5, then the width of this rectangle is 𝑤 = 2(5) - 1 = 9.
The length of this rectangle is triple its width, then 𝐿 = 3(9) = 27.
The area of this rectangle is 𝐴 = 𝐿 ∙ 𝑤 = 27 ∙ 9 = 243 𝑐𝑚².

Choice 𝐵 is correct – The roots of the function are found by counting how many intersections between the graph of the function and the 𝑥-axis. There are 3 intersections, and then we have 3 roots.
Only choices 𝐵 and 𝐷 can be correct.
The shaded region has a form of a triangle. Its area is 𝐴 = 1 / 2 𝑏ℎ with 𝑏 its base and ℎ its height.
The base of this triangle is equal to the distance between the origin and point (0.366, 0). Then, 𝑏 = 0.366.
The height is equal to the distance between the origin and the point (0, 1). Then ℎ = 1.
𝐴 = 1 / 2 (0.366)(1) = 0.183 square units.
Choice 𝐷 is incorrect, and then choice 𝐵 is correct.

(𝑓 ∘ 𝑔)(𝑥) is a composition function which is an operation that takes two functions and produces another one such that (𝑓 ∘ 𝑔)(𝑥) = 𝑓[𝑔(𝑥)].
Choice 𝐷 is correct – In 𝑔(𝑥), 𝑥 = -2 is in the 2^𝑛𝑑 option such that -3 ≤ 𝑥 < 5.
Then 𝑔(-2) = 2(-2) + 3 = -1.
In 𝑓(𝑥), 𝑥 = -1 is in the 1^st option such that 𝑥 < 0.
Then 𝑓(-1) = -1 + 5 = 4.

𝐴 triangle inscribed in a circle such that one side is the diameter of the circle, then this triangle is a right triangle with this diameter being its hypotenuse.
Choice 𝐴 is correct – 𝐴𝐷𝐹 is an isosceles triangle at F inscribed in circle (C) and 𝐴𝐷^— is the diameter of (𝐶). Therefore, 𝐴𝐷𝐹 is a right isosceles triangle at 𝐹 with 𝐴𝐷^— being its hypotenuse.
Since 𝐴𝐷𝐹 is isosceles at 𝐹, then 𝐹𝐴 = 𝐷𝐹.
tan 𝐴 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 / 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = 𝐷𝐹 / 𝐹𝐴 = 1
1 - tan² 𝐴 = 1 - 1² = 1 - 1 = 0

Choice 𝐶 is correct – In function 𝑓(𝑥), we are adding (-1) to the parent function which is 𝑥 in our case as this is a linear function.
The graph is then translated 1 unit down.
Choices 𝐴 and 𝐵 are incorrect.
As 𝑥 is multiplied by 2, and 2 > 1, then it is stretched vertically.
Choice 𝐶 states that the function is translated 1 unit down, and stretched vertically.

To tackle this question, remember the following: an inverse function reverses another function, and two functions are parallel if their slopes are equal. If they are parallel, then they do not intersect.
Choice 𝐸 is correct – Both functions have slopes equal to 1, then they are parallel. Hence, (𝐼𝐼𝐼) is correct, and (𝐼𝐼) is incorrect.
Finding the inverse of 𝑓(𝑥) = 𝑥 - 2:
𝑦 = 𝑥 - 2
𝑥 = 𝑦 - 2
𝑥 + 2 = 𝑦
Then 𝑔(𝑥) = 𝑥 + 2 is the inverse of 𝑓(𝑥) = 𝑥 - 2. (𝐼) is correct.

An exterior angle of a triangle is the sum of the two opposite interior angles. Remember as well, that two angles in a straight line are supplementary.
Choice 𝐵 is correct – The exterior angle (3𝑥 + 15) is equal to the sum of (2𝑥 - 5) and (3𝑦):
3𝑥 + 15 = 2𝑥 - 5 + 3𝑦
3𝑥 - 2𝑥 - 3𝑦 = -5 - 15
𝑥 - 3𝑦 = -20
The two supplementary angles are (2𝑦 - 1) and (3𝑥 + 15):
2𝑦 - 1 + 3𝑥 + 15 = 180
3𝑥 + 2𝑦 = 166
Both results will form a system of two equations:

Solving this system will result: 𝑥 = 41.63 and 𝑦 = 20.54.
Or we can take sum of angles in a triangle that leads to 5𝑦 + 2𝑥 = 186

Choice 𝐴 is correct – Two lines are parallel if their slopes are equal.
The slope of line 𝑂𝐴, is 𝑚 = 𝑦₂ - 𝑦₁ / 𝑥₂ - 𝑥₁ = 3 - 0 / 1 - 0 = 3.
𝐵𝑥^→   is parallel to 𝑂𝐴^— then the slope of 𝐵𝑥^→   is 𝑚' = 3.
The equation of 𝐵𝑥^→   is 𝑦 = 𝑚'𝑥 + 𝑏:
𝑦 = 3𝑥 + 𝑏 (it is passing through 𝐵, then we can replace the abscissa and the ordinate of 𝐵 in the equation in order to find the value of 𝑏)
2 = 3(4) + 𝑏
2 = 12 + 𝑏
-10 = 𝑏
The equation of 𝐵𝑥^→ : 𝑦 = 3𝑥 - 10
𝑁 is the intersection of 𝐵𝑇^— with the 𝑥-axis. Its ordinate is 0.
Hence, 0 = 3𝑥 - 10
10 = 3𝑥
𝑥 = 10 / 3
Thus, the distance of 𝑂𝑁^— is 10 / 3 .
Point 𝑇 has the coordinates (3, -1) in order to have 𝑂𝐴𝐵𝑇 as a parallelogram.
The height drawn from 𝑇 to 𝑂𝑁^— (which is the 𝑥-axis also) is 1.
The area of the triangle 𝑂𝑁𝑇 is 𝐴 = 1 / 2 𝑏ℎ with 𝑏 its base and ℎ its height: 𝐴 = 1 / 2 ( 10 / 3 )(1) = 5 / 3 = 1.67

Choice 𝐷 – To solve 4 sin² 𝑥 - 1 = 0:
4 sin² ⁡𝑥 = 1
sin² 𝑥 = 1 / 4
sin⁡ 𝑥 = √ 1 / 4 = 1 / 2
𝑥 = sin^-1⁡ ( 1 / 2 ) = 30°

The area of a parallelogram is 𝐴 = 𝑏ℎ with 𝑏 its base and ℎ its height.
Half of this area is 𝐴' = 1 / 2 𝑏ℎ.
Choice 𝐴 is correct – The base of parallelogram 𝐹𝐺𝐻𝐼 is 𝑏 = (2𝑥 - 3)². The height is double the base, then ℎ = 2(2𝑥 - 3)²
𝐴' = 1 / 2 (2𝑥 - 3)² × 2(2𝑥 - 3)²
𝐴' = (2𝑥 - 3)⁴ = 16𝑥⁴ - 96𝑥³ + 216𝑥² - 216𝑥 + 81

Choice 𝐷 is correct – 𝐹𝐸𝑅𝐺 is a square. Its diagonal is equal to _𝑠√2 with 𝑠 is the side of the square.
Therefore 𝐹𝑅 = 5.6√2.
Segment 𝐹𝑅^— represents the diameter of the circle. The radius 𝑟 of the circle is half the diameter. Then 𝑟 = 𝐹𝑅 / 2 = 14√2 / 5.
The area of the circle is 𝐴 = π𝑟² = π( 14√2 / 5)² = 15.68π.
The area of the square is 𝐴' = 𝑠² = 5.6² = 31.36.
The area of the shaded region 𝐴'' is the subtraction of the area of the square from the area of the circle:
𝐴'' = 𝐴 - 𝐴' = 15.68π - 31.36 = 17.9

The circumference of a circle is 𝐶 = 2π𝑟, with 𝑟 is the radius of the circle.
Choice 𝐸 is correct – To find 𝑟, replace 𝑥 by 6, and 𝑦 by 3 (coordinates of point 𝐺), in the equation of the circle:
(6 - 3)² + (3 + 2)² = 𝑟²
3² + 5² = 𝑟²
𝑟² = 34
𝑟 = √34
The circumference of the circle: 𝐶 = 2π𝑟 = 2π(√34) = 36.63

A system of two linear equations can be represented in a matrix form using the coefficients to form a coefficient matrix, the variables to form a variable matric, and a constant matrix formed by the constants in the system.
Choice 𝐶 is correct – Fixing the arrangement of variables and constants in the system

we will have

The coefficients of 𝑥 are -2 and 3.
The coefficients of 𝑦 are 3 and -4.
The coefficient matrix is:

The variables are 𝑥 and 𝑦. The variable matrix is:

The constants are -1 and 1. The constant matrix is:

Then, choice 𝐶 is the correct one.

A parallelogram is a rectangle if the two consecutive sides are perpendicular (they form a right angle 90°). As the sides are considered as functions, then the product of their slopes is equal to -1.
Choice 𝐸 is correct – The slope of 𝑓(𝑥) = 𝑐𝑥 + 𝑏 is 𝑐.
The slope of 𝑔(𝑥) = -𝑑𝑥 + e is –𝑑.
The product of both slopes is 𝑐(-𝑑) = -𝑐𝑑.
It should be equivalent to -1. Then -𝑐𝑑 = -1
𝑐𝑑 = 1

The sum of the measures of the interior angles in a polygon is equal to (𝑛 - 2) × 180, with 𝑛 is the number of sides in the polygon.
Choice 𝐷 is correct – As the figure shows a regular heptagon, then all its angles are congruent. However, in a heptagon, there are 7 sides. Then the sum of the measures of the interior angles in it is:
(7 - 2) × 180 = 900°
Then 7( 1 / 7 𝑥 - 10) = 900
𝑥 - 70 = 900
𝑥 = 970
Choices 𝐵 and 𝐶 are incorrect.
∠𝑀𝐽𝐼 and ∠𝐾𝐽𝐼 are supplementary angles:
𝑚∠𝑀𝐽𝐼 + 1 / 7 (970) - 10 = 180
𝑚∠𝑀𝐽𝐼 + 970 / 7 = 190
𝑚∠𝑀𝐽𝐼 = 360 / 7
The sum of the measures of the interior angles in a triangle is 180°:
𝑚∠𝑀𝐽𝐼 + 𝑚∠𝐽𝑀𝐼 + 𝑚∠𝑀𝐼𝐽 = 180
360 / 7 + 90 + 3y + 4 = 180
3𝑦 = 242 / 7
𝑦 = 242 / 21 = 11.52