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+problem,answer,question_id
+"Solve the following equation for $n \in \mathbb{N}$:
+$n - 3 = \sqrt{3n + 1}$",8,Day 1 - Q1a
+"Write the following sentence as a single paragraph in terms of $t$:
+$\frac{4}{2t + 1} - \frac{7}{12t}$",$\frac{34t - 7}{(2t + 1)(12t)}$,Day 1 - Q1b
+"Solve the following parallel equations for $x, y, w \in \mathbb{Z}$:
+$\begin{cases} x + 2y = 143 \\ y + 3w = -74 \\ 4x + 5w = 4 \end{cases}$",51;46;-40,Day 1 - Q1c
+"In this question, $i^2 = -1$.
+Find both solutions to the equation in $z$ the following, where $z$ in number 
+Complex.Each answer should be in the form $a + bi$, where $a, b \in \mathbb{R}$.
+$z^2 + 12z + 261 = 0$",-6+15i;-6-15i,Day 1 - Q2a
+"In this question, $i^2 = -1$.
+He used a theory of Moivre to $(1 - \sqrt{3}i)^9$ written in the form $a + bi$, 
+where $a, b \in \mathbb{R}.$",-512,Day 1 - Q2b
+"Find the sum:
+$\int \cos6x\ dx$",\frac{1}{6}\sin(6x)+C,Day 1 - Q3a
+"The function is defined $f$ as follows for $x \in \mathbb{R}$:
+$f(x) = 2x^3 - 9x^2 + 5x - 11$
+Find the equation of the circle with a graph.$f$ at the point at which the$x = 2$.
+You don't need to simplify your answer.",y − (−21) = −7(x − 2),Day 1 - Q3bi
+"The function is defined $f$ as follows for $x \in \mathbb{R}$:
+$f(x) = 2x^3 - 9x^2 + 5x - 11$
+Find the coordinates $x$ the rebound point of $f$.",\frac{3}{2},Day 1 - Q3bii
+"The following function is distinguished from basic principles, in respect of $x$:
+$f(x) = x^2 - 7x - 10$",\frac{-238}{361},Day 1 - Q4a
+"The function is defined $g(x)$ for the$x \in \mathbb{R}$ in accordance with:
+$g(x) = \frac{6x + 1}{x^4 + 3}$
+Get the value $g'(-2)$, the following paragraph is added:$g(x)$ where $x = -2$.",-238/361,Day 1 - Q4b
+"It is a continuous operation.$h: \mathbb{R} \rightarrow \mathbb{R}$.
+The graph has a logarithmic minimum.$h(x)$ at point $(0, 5)$.
+Indicate whether the following statement is true or false:
+It must be$5$ is at least $h(x)$ for each real value of $x$. other
+Defend your answer.",False,Day 1 - Q4c
+"The first three terms of a concatenation sequence are as follows, where $p \in \mathbb{R}:
+\begin{cases} T_1 = 2p + 1 \\ T_2 = 5p - 3 \\ T_3 = 6p + 7 \end{cases}$
+Get the value $p$.",7,Day 1 - Q5a
+"They are $G_7 = 6$ and $G_11 = \frac{3}{8}$ the 7th and 11th term of a polynomial sequence, respectively.
+Find the two possible values of $r$, The Commission shall be assisted by the European Parliament.$r \in \mathbb{R}$.",\frac{1}{2};\frac{-1}{2},Day 1 - Q5b
+"A sequence of functions is defined.$F_0, F_1, F_2, \dots$ for $x \in \mathbb{R}, x \gt 0$:
+\The first one is the
+\The Commission shall:$F_0 = x^{2024}$
+\Item for $n \geq 1$, The function is $F_n$ the following paragraph is added:$F_{n-1}$ , $x$.
+\end{title}
+Write $F_1$ and $F_2$ in terms of $x$.",F1(x) = 2024 x^2023; F2(x) = 2024 × 2023 x^2022,Day 1 - Q5ci
+"A sequence of functions is defined.$F_0, F_1, F_2, \dots$ for $x \in \mathbb{R}, x \gt 0$:
+\The first one is the
+\The Commission shall:$F_0 = x^{2024}$
+\Item for $n \geq 1$, The function is $F_n$ the following paragraph is added:$F_{n-1}$ , $x$.
+\end{title}
+Find the first value of $n$ This leaves a$F_n=0$.",2025,Day 1 - Q5cii
+"$h(x) = x^2 + bx - 12$, where is$x \in \mathbb{R}$ and place it on a doorstep.$b$.
+Get the value $b$ This leaves a$x - 4$ in a factor of $h(x)$.",-1,Day 1 - Q6a
+"Two functions are defined, $f(x)$ and $g(x)$, for $x \in \mathbb{R}, x \gt 0$:
+\The first two terms of the equation are:
+Get the value $f(1.2)$. 
+Please answer in the form $a \times 10^n$, where $a \in \mathbb{R}, 1 \leq a \lt 10, n \in \mathbb{N}$, and which shall be$a$ right to one decimal place.",4.9\times10^4,Day 1 - Q6bi
+"Two functions are defined, $f(x)$ and $g(x)$, for $x \in \mathbb{R}, x \gt 0$:
+\The first two terms of the equation are:
+Get the value $x$ This leaves a$g(x) = 3.5$.
+Please answer in the form $e^p$, where $p \in \mathbb{R}$.",x=e^7,Day 1 - Q6bii
+"Two functions are defined, $f(x)$ and $g(x)$, for $x \in \mathbb{R}, x \gt 0$:
+\The first two terms of the equation are:
+Write the function $g(f(x))$ in terms of $x$, in the simplest form.",4.5x,Day 1 - Q6biii
+"Fiadh has a total annual salary of €54000.
+She pays income tax at a rate of 20% on the first €40000 of her salary and at a rate of 40% on the balance sheet.
+Work out his annual net salary, assuming no other deductions.",42175,Day 1 - Q7a
+"The first monthly repayment is made directly after the mortgage is taken out, and the second monthly repayment is made directly after the mortgage is taken out.
+Write down the immediate value of each of the first three monthly repayments they make, at the time they take out the mortgage.
+Let all values be in pieces. Do not overwhelm any powers.",\frac{1647.75}{1.00279};\frac{1647.75}{1.00279^2};\frac{1647.75}{1.00279^3},Day 1 - Q7bi
+"The first monthly repayment is made directly after the mortgage is taken out, and the second monthly repayment is made directly after the mortgage is taken out.
+Work out the amount of money that Wood and his partner borrowed for their mortgage.
+Correct your answer to the nearest euro.",334563,Day 1 - Q7bii
+"Fide puts money into a savings account, and she leaves it there for several years.
+This is the bottom line.$F(t)$, the amount of money in the account in euro after $t$ year, whereas$t \in \mathbb{R}, t \geq 0$:
+$F(t) = 5000 e^{0.04t}$
+Use a differential and find the rate at which the amount of money in the account increases after 3.5 years.",230,Day 1 - Q7ci
+"Fide puts money into a savings account, and she leaves it there for several years.
+This is the bottom line.$F(t)$, the amount of money in the account in euro after $t$ year, whereas$t \in \mathbb{R}, t \geq 0$:
+$F(t) = 5000 e^{0.04t}$
+Use an estimate and find the average amount of money in the account over the first 5 years.",5535,Day 1 - Q7cii
+"Fide puts money into a savings account, and she leaves it there for several years.
+This is the bottom line.$F(t)$, the amount of money in the account in euro after $t$ year, whereas$t \in \mathbb{R}, t \geq 0$:
+$F(t) = 5000 e^{0.04t}$
+Calculate the annual interest rate (AER) for this account.
+So let's say that you have a percentage increase in the amount of money in the account over the course of a year, and your answer is right up to 2 decimal places.",4.08%,Day 1 - Q7ciii
+"It is time.$R$ unit by sphere.
+The part of the sphere that intersects a smooth surface is called a cap, and its volume is:
+$C=\frac{\pi k^2}{3}(3R - k)$
+Here, it is.$C$ The volume of the pipe is $k$ The height of the pipe, where the$0 \lt k \leq R$.
+Get the value $C$, volume of the pipe, where:$R = 13$ and $k = 4$.
+# Please answer in terms of $\pi$.",\dfrac{560}{3} \pi,Day 1 - Q9a
+"It is time.$R$ unit by sphere.
+The part of the sphere that intersects a smooth surface is called a cap, and its volume is:
+$C=\frac{\pi k^2}{3}(3R - k)$
+Here, it is.$C$ The volume of the pipe is $k$ The height of the pipe, where the$0 \lt k \leq R$.
+A sphere has 8 units and a tube has $y$ Unit at altitude, where$0 \lt y \leq 8$.
+The volume of these pipes is ($36\pi y$) Unit$^3$.
+Used that, and out of the blue for $C$ above, and demonstrate that:
+$\frac{y}{3}(24 - y) = 36$",,Day 1 - Q9bi
+"It is time.$R$ unit by sphere.
+The part of the sphere that intersects a smooth surface is called a cap, and its volume is:
+$C=\frac{\pi k^2}{3}(3R - k)$
+Here, it is.$C$ The volume of the pipe is $k$ The height of the pipe, where the$0 \lt k \leq R$.
+A sphere has 8 units and a tube has $y$ Unit at altitude, where$0 \lt y \leq 8$.
+The volume of these pipes is ($36\pi y$) Unit$^3$.
+The equation has widened.$\frac{y}{3}(24 - y) = 36$ and set it up to the top of the ladder.
+I'll get this.",6,Day 1 - Q9bii
+"The diameter of the$x$ cm at the hemisphere.
+The following is added:$V(x)$, the volume of that hemisphere in cm$^3$, in accordance with:
+$V(x) = \frac{\pi}{12} x^3$
+Get the value $x$ when the volume of the hemisphere is more than 3 litres.
+Be sure your answer is correct to one decimal place.",22.5,Day 1 - Q9c
+"The diameter of the$x$ cm at the hemisphere.
+The following is added:$V(x)$, the volume of that hemisphere in cm$^3$, in accordance with:
+$V(x) = \frac{\pi}{12} x^3$
+The volume of the hemisphere is increasing at a constant rate of 450 cm$^3$ in the second.
+Find the rate at which a diameter ($x$) The radius of the hemisphere increases with time, when the$x = 20$ cm. Your answer should be in cm per second, to the right of one decimal place.",1.4,Day 1 - Q9d
+"It is time.$r$ cm at the corner and it is$h$ cm in height.
+The maximum surface area of the curve of the cone,$S$, be written as:
+$S = \pi r \sqrt{r^2 + h^2}$
+Re-allocate this to $h$ The Commission shall be assisted by the European Parliament.$S$, $r$, and $\pi$.
+Please answer in the form $\frac{\sqrt{S^2 - ar^n}}{br}$, where they were tendered$a$, $b$, and $n$.",\frac{\sqrt{S^2 - \pi^2 r^4}}{\pi r},Day 1 - Q9e
+"A plant body grows and sells.
+The function is defined $W(x)$ It can be used to simulate the height of a water spice plant, in mm, during the first 35 days after it starts growing.
+$W(x) = 0.667x + 1.5x^2 - 0.025x^3$
+Here, it is equal to $x$ and the number of days after the plant has started growing, where $0 \leq x \leq 35, x \in \mathbb{R}$.
+Use of$W(x)$ to assess the height of water spionage plant after 15 days.
+Please correct your answer to the nearest mm.",263,Day 1 - Q10ai
+"A plant body grows and sells.
+The function is defined $W(x)$ It can be used to simulate the height of a water spice plant, in mm, during the first 35 days after it starts growing.
+$W(x) = 0.667x + 1.5x^2 - 0.025x^3$
+Here, it is equal to $x$ and the number of days after the plant has started growing, where $0 \leq x \leq 35, x \in \mathbb{R}$.
+Write it down.$W'(x)$, the following paragraph is added:$W(x)$",0.667+3x-0.075x^2,Day 1 - Q10aii
+"A plant body grows and sells.
+The height of a plant can be simulated with the function $P(x)$, wherever it is.$x$ number of days after the plant starts growing.
+The derivative of this function is:
+$P'(x) = 1.1 + 2.73x - 0.078x^2$
+Find the range of values of $x$ This leaves a$P'(x) \gt 24$.
+In your answer, each value should be rounded to the nearest integer.",14 <= x <= 21,Day 1 - Q10b
+"A plant body grows and sells.
+In this part, they are proposals.$p$ and $r$, by $p, r \in \mathbb{R}$ and $0 \lt r \lt 0.9p$.
+The body sells plant food bags.
+The normal price per item is €$p$. 
+In the case of a retail outlet, the customer shall be able to choose between the following options:
+\The first one is the
+\Option 1: the normal price reduced by 10%, and a further reduction of €$r$ beyond that.
+\Optional item 2: the reduced normal price of €$r$, and that new price reduced by 10%.
+\end{title}
+Which option (1 or 2), if any, is cheaper?
+Write the price for each of the options (1 and 2) in terms of $p$ and $r$, to support your answer.",Rogha 1,Day 1 - Q10d
+"A group of 22 students were tested to find out how far, in metres, each of them could swim without stopping to take a break.$a$, $b$, $c$, and $d$ four entries have been replaced.
+\[\begin{array}{c|l}
+2 & b \quad 2 \quad 7 \\
+3 & a \quad 4 \quad 4 \quad 5 \quad 8 \\
+4 & 0 \quad 1 \quad d \quad 5 \quad 6 \quad 9 \\
+5 & 2 \quad 3 \quad 7 \quad 7 \quad 8 \\
+6 & 1 \quad 8 \quad c \\
+\end{array}
+\]
+Key: $2 \mid 7 = 27$ of a kind used in motor vehicles
+The data mode is 34 meters.$a$ write it down.",4,Day 2 - Q1ai
+"A group of 22 students were tested to find out how far, in metres, each of them could swim without stopping to take a break.$a$, $b$, $c$, and $d$ four entries have been replaced.
+\[\begin{array}{c|l}
+2 & b \quad 2 \quad 7 \\
+3 & a \quad 4 \quad 4 \quad 5 \quad 8 \\
+4 & 0 \quad 1 \quad d \quad 5 \quad 6 \quad 9 \\
+5 & 2 \quad 3 \quad 7 \quad 7 \quad 8 \\
+6 & 1 \quad 8 \quad c \\
+\end{array}
+\]
+Key: $2 \mid 7 = 27$ of a kind used in motor vehicles
+The range of the data is 49 meters.$b$ and value $c$ to receive.",b=0;c=9,Day 2 - Q1aii
+"A group of 22 students were tested to find out how far, in metres, each of them could swim without stopping to take a break.$a$, $b$, $c$, and $d$ four entries have been replaced.
+\[\begin{array}{c|l}
+2 & b \quad 2 \quad 7 \\
+3 & a \quad 4 \quad 4 \quad 5 \quad 8 \\
+4 & 0 \quad 1 \quad d \quad 5 \quad 6 \quad 9 \\
+5 & 2 \quad 3 \quad 7 \quad 7 \quad 8 \\
+6 & 1 \quad 8 \quad c \\
+\end{array}
+\]
+Key: $2 \mid 7 = 27$ of a kind used in motor vehicles
+The average of the data is 43.5 metres.$d$ to receive.",2,Day 2 - Q1aiii
+"The table below shows the prizes, in euros, a player can win in a game, as well as the probability of winning each prize.$x \in \mathbb{R}$.
+\I'm not sure I'm ready to go.
+\centering
+\The first is the ""Table of Contents"" section.
+\Other
+\textbf{Prize (€) } & Does not exist & 2 & \( x - 10 \) & \(x\) \\ \Other
+\The probability of the event is 30% and 40% and 28% and 2% .
+\The following table shows the
+\The following table shows the
+It costs €10 to play the game once.
+The game is fair game  i.e. the expected value of the money won is €0, and the 
+costs taken into account.
+Work out the value $x$.",40,Day 2 - Q2a
+"They are collective coincidences.$A$ and $B$.
+$P(A) = 0.1$ and $P(B) = 0.4$.
+Describe the value of each of the following: $P(A \cap B)$ and $P(A \cup B)$.",P(A \cap B)=0; P(A \cup B)=0.5,Day 2 - Q2b
+"They are two cases.$C$ and $D$, with a universal set $U$.
+$P(C)=0.5$ and $P(D)=0.7$.
+Get the most value.$P[(C \cup D)']$.
+Note: This is $(C \cup D)'$ completion of the inventory $C \cup D$ in the set $U$.",Max $P[(C \cup D)']=0.3$,Day 2 - Q2c
+"It is a parallel.$ABCD$.
+$\vert AB \vert = 10 \text{cm}$, $\vert BC \vert = 13 \text{cm}$, and $\vert \angle ABC \vert = 110^\circ$.
+Get away from me.$ABCD$, right to the$\text{cm}^2$ is close.",$122$,Day 2 - Q3a
+"It's an angle.$X$, by $0^\circ \leq X \leq 360^\circ$, and $\cos(2x) = \frac{\sqrt{3}}{2}$
+Work out all the possible values of $X$.","$X=15^\circ, 165^\circ, 195^\circ, 345^\circ$",Day 2 - Q3b
+"It's a triangle.$KLM$ where is$\vert MK \vert = 15\sqrt{3}$ cm, $\vert ML \vert = 45$ cm, and $\vert \angle KLM \vert = 25^\circ$.
+It is .$\theta$ the angle $\angle LKM$.
+Work out the two possible values of $\theta$, for the$0^\circ \lt \theta \lt 180^\circ$.
+Each answer should be correct to the nearest degree.","$\theta = 47^\circ, 133^\circ$",Day 2 - Q3c
+"The equator is the circle.$s$ than: $x^2 + y^2 + 4x - 6y + 5 = 0$.
+Write down a centre point and circle it.$s$.","Centre $= (-2, 3)$, $r = 2\sqrt{2}$",Day 2 - Q5ai
+"A circle has a midpoint on the perpendicular line through the point $(9, 0)$.
+The points are:$(7, 10)$ and $(12, 8)$ This is the first time that the Commission has proposed to the Council to adopt a directive on this matter.
+Find the equator of this circle.
+Note that your answer may contain non-integer values.","Centre $= (9, 5)$, $(x - 9)^2 + (y - \frac{31}{4})^2 = \frac{145}{16}$, or $x^2 + y^2 - 18x - \frac{31}{2}y + 132 = 0$",Day 2 - Q5b
+"It is a straight line.$[AB]$.
+The point is shared $C (6,11)$ the paragraph $[AB]$ internally in the ratio $1:3$.
+It is .$A$ point $(1, 13)$.
+Find the coordinates of a point $B$.","$(21, 5)$",Day 2 - Q6a
+"Find the vertical distance from a point $(5, −2)$ to the line: $y = \frac{4}{3}x - 11$.",$1.4$,Day 2 - Q6b
+"PK Hotels is a chain of hotels in Europe.
+The ages of those who stayed in PK hotels in
+The average life expectancy of a population is expected to be around 20 years, with a mean of 48.2 years and a standard deviation of 10.6 years.
+One person is chosen at random from those who stayed in a PK hotel in
+Find the probability that this person is less than 50 years old.",$56.75%$,Day 2 - Q7ai
+"PK Hotels is a chain of hotels in Europe.
+The ages of those who stayed in PK hotels in
+The average life expectancy of a population is expected to be around 20 years, with a mean of 48.2 years and a standard deviation of 10.6 years.
+Of those who stayed in PK hotels in 2023, just 10% are female.$A$ year 
+Find the value $A$, to the nearest integer.",$62$,Day 2 - Q7aii
+"PK Hotels is a chain of hotels in Europe.
+During their most recent visit, the$\frac{1}{5}$ of PK Hotel customers use the swimming pool.
+6 of the PK Hotels' customers are selected at random.
+Find the probability that 2 of them directly used the swimming pool.",$\frac{768}{3125}=0.24576$,Day 2 - Q7bi
+"PK Hotels is a chain of hotels in Europe.
+During their most recent visit, the$\frac{1}{5}$ of PK Hotel customers use the swimming pool.
+The following shall be chosen:$n$ of the customers of PK Austria randomly, where 
+$n \in \mathbb{N}$.
+It is .$0.0047$, right to 4 random centres, the probability that none of them
+The use of the swimming pool.$n$.",$24$,Day 2 - Q7bii
+"PK Hotels is a chain of hotels in Europe.
+PK Hotels is testing a new reservation system.
+The old booking system is shown to 45% of people who log on to the PK Hotel website; the new booking system is shown to the other 55%.
+It is randomly determined which booking systems (old or new) people will see.
+Of those who see the old system bookings, one third book a room.
+Of those who see the new booking system, two-fifths book a room.
+One person is randomly selected from those who booked a room via the PK Hotel website.
+Your answer should be in percentages, right down to the nearest percent.",59\%,Day 2 - Q7c
+"Tommy makes ornaments out of metal and glass.
+It makes an open metal cylinder that is 15 cm high and 5 cm thick.
+The circuit is a loop.
+Find the dimensions of this cube.
+Your answers should be in cm, to the right of one decimal place, as appropriate.","$15, 31.4$",Day 2 - Q8a
+"Tommy makes ornaments out of metal and glass.
+Tommy makes another roller coaster that is 22 cm high and 12 cm in diameter.
+The dimensions of this circuit are just right so that it can be placed inside a glass sphere.
+Find the volume of the sphere, in cm$^3$, You used the Pythagorean theorem in your solution.",$8240.2$,Day 2 - Q8b