Question
The elements of the universal set $\boldsymbol{U}$ are $\{1,2,3,4,5,6,7,8,9,10\}$.
Consider two subsets of $U$
Set A contains the multiples of 2 .
Set B contains the multiples of 3 .
Question
Determine the probability $\mathrm{P}\left(\mathrm{A} \mid \mathrm{B}^{\prime}\right)$.
▶️Answer/Explanation
$\frac{4}{7}$
Question
Two numbers are selected at random from $\boldsymbol{U}$. Calculate the probability that only one is an element of $A \cap B^{\prime}$.
▶️Answer/Explanation
1 multiply correct probabilities for first selected numbers without replacement
2 multiply correct probabilities for second selected numbers without replacement
3 correctly add their multiplied probabilities
Question
The table below shows an example of a completed addition grid.
Write down the missing values of $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$, in a simplified index form.
▶️Answer/Explanation
. 1 Correctly write a in a simplified index form
. 2 Correctly write $b$ in a simplified index form
. 3 Correctly write $\mathrm{c}$ in a simplified index form
$12 x^{-\frac{1}{2}} y^2$ or $\frac{2 y^2}{x^{\frac{1}{2}}}$ or $2 x^{-1 / 2} y^2$ seen DO NOT ACCEPT $y^2$ written as $y^{\wedge} 2$ and DO NOT ACCEPT $x^{-\frac{1}{2}}$ written as $\sqrt{x}$ or $\operatorname{sqrt}(x)$ or $x^{\wedge}-1 / 2$
$22 x y$ seen
$3 \frac{1}{2}$ or $1 / 2$ or 0.5 or $2^{-1}$ seen
Question
The table below shows an example of a completed addition grid.
Write down the values of $a, b$ and $c$, in a simplified exact form.
.
▶️Answer/Explanation
1 Correctly write a in a simplified exact form
. 2 Correctly write $b$ in a simplified exact form
. 3 Correctly write $\mathrm{c}$ in a simplified exact form.
$1 \log \left(\frac{1}{2}\right)$ or $\log (1 / 2)$ or $\log (0.5)$ or $-\log 2$ seen
$.2 \log 12$ seen DO NOT ACCEPT $\log (6 \times 2)$ as their answer
$.3 \log 32$ or $5 \log 2$ seen ACCEPT $\log 2^5$ DO NOT ACCEPT $\log (16 x 2)$ as their answer
A skateboard ramp set is built using functions provided in the diagram below:
The diagram is interactive. Hover over the intersection of each line.
Question
Determine the value of $a$.
▶️Answer/Explanation
1 Equate $f(x)$ and 2
. 2 Correct value of a
Question
Calculate the value of $b$.
▶️Answer/Explanation
AM1
.1 Equate $g(x)$ and 2
. 2 Correctly apply log rule
. 3 Correctly rearrange for their $x$ or their $-x$
. 4 The correct value of $x$
AM2
.1 Equate $g(x)$ and 2
. 2 Correctly apply laws of exponents
. 3 Correctly rearrange for their $x$
. 4 The correct value of $x$
Question
Hence, determine the length of the platform.
▶️Answer/Explanation
Correctly subtract their $\boldsymbol{a}$ from their $\boldsymbol{b}$
Below is a geometric sequence with first term $U_1=4$ and common ratio $r$
$$
4,2 \sqrt{2}, 2, \ldots
$$
Question
Write down the value of $r$.
▶️Answer/Explanation
Correctly write the value of $r$.
$\frac{1}{\sqrt{2}}$ OE DO NOT ACCEPT in words
ACCEPT $0.707(10.6 \ldots)$ or 0.71 or 0.7
DO NOT ACCEPT $\div \sqrt{2}$
Question
By continuing the pattern, determine the value of $n$ when $U_n=r$.
▶️Answer/Explanation
.1 correctly write at least two more terms & $.1(4,2 \sqrt{2}, 2,) \sqrt{2}, 1,\left(\frac{\sqrt{2}}{2}\right.$ OE $) \quad$ Equation with their $\frac{1}{\sqrt{2}}$ doesn’t get 1 \\
.2 correct value of $n$ & $.2(n=) 6$ & ACCEPT $U_6$
Question
Given that $U_{21}=2^k ; k \in Z$, find the value of $k$.
▶️Answer/Explanation
.1 correctly substitute 4 and 21 and their $r$ into the nth term of G.S formula
. 2 at least one correct intermediate step for their k using any method
.3 the correct value of $\mathrm{k}$ from their .1
$.1\left(U_{21}=\right) 4 \times$ their $\left(\frac{1}{\sqrt{2}}\right)^{21-1}$ OE ACCEPT their $0.0039(\ldots)$
1 DO NOT ACCEPT if their $r \geq 1$
2 Examples of correct intermediate steps :
Using powers of $2: \frac{2^2}{\text { their } 2^{10}}$ or $\frac{2^2}{\text { their } 2^{\left(\frac{1}{2}\right) 20}}$ or $2^2 \times$ their $2^{-10}$
Using logs : $\log _2\left(4 \times\right.$ their $\left.\left(\frac{1}{\sqrt{2}}\right)^{21-1}\right)=k$ OE ACCEPT not seeing $k$ Listing powers of 2 : see image
$$
\frac{\frac{\frac{\frac{2}{2}}{2}}{\frac{2}{2}}}{\frac{\frac{2}{2}}{2}}=0.00390625
$$
$.3(k=)$ their-8 ACCEPT $2^{\text {their- } 8}$
ACCEPT only if their $-8 \in \mathrm{Z}$
Question
Find the sum to infinity of $4+2 \sqrt{2}+2+\ldots$
Write your answer in the form $a+b \sqrt{2} ; a, b \in N$.
▶️Answer/Explanation
.1 substitute 4 and their $r$ into the sum to infinity formula
.2 correctly write their answer as one radical fraction
.3 correctly rationalize their denominator
.4 correct simplified sum to infinity
$$
1 \frac{4}{1-\text { their } \frac{1}{\sqrt{2}}} \mathrm{OE}
$$
2 their $\frac{4 \sqrt{2}}{\sqrt{2}-1}$ OE, DO NOT AWARD if their $r$ is $\sqrt{2}$
3 their $\frac{4 \sqrt{2}(\sqrt{2}+1)}{1}$
$48+4 \sqrt{2}$ ACCEPT only if their8 and their $4 \in \mathrm{N}$
The image below shows a cross-section of the snow cone.
Question
Show that $r=2.80 \mathrm{~cm}$, correct to three significant figures.AM1 (using sin or cos ratios).
▶️Answer/Explanation
1 correctly divide by two the 150 AND 5.4
.2 correctly substitute into trig ratio
. 3 correct value of $r$ before rounding
AG 2.80
AM2 (using sine rule)
.1 correctly substitute into sine rule
.2 correctly rearrange for $\mathrm{r}$ on one side
3 correct value of $r$ before rounding
AG 2.80
AM3 (using cos rule)
.1 correctly substitute into cosine rule
.2 correctly rearrange for $r^2$ on one side
. 3 correct value of $r$ before rounding
AG 2.80
AM4 (using tan ratio)
.1 correctly calculate the angle and correctly divide 5.4 by two
.2 correctly substitute $\tan 15$ or $\tan 75$ ratio into Pythagoras
. 3 correct value of $r$ before rounding
AG 2.80
Award any VALID method using same marking principles.
AM1 (using sin or cos ratios)
175 AND 2.7 seen. ACCEPT 15 AND 2.7 seen
$2 \sin 75=\frac{2.7}{r}$ OR $\cos 15=\frac{2.7}{r}$ OE ACCEPT $\frac{2.7}{\sin 75}$ OR $\frac{2.7}{\cos 15}$ seen
$3(\mathrm{r}=) 2.79(52 \ldots$.
. 3 ACCEPT their correct $r$ due to earlier rounding provided it rounds to 2.8
AM2 (using sine rule)
$1 \frac{5.4}{\sin 150}=\frac{r}{\sin 15}$ OE ACCEPT not seeing this step
$2(r=) \frac{5.4 \times \sin 15}{\sin 150}$ OE
$3(r=) 2.79(52 \ldots$.
. 3 ACCEPT their correct $r$ due to earlier rounding provided it rounds to 2.8
AM3 (using cos rule)
$15.4^2=2 r^2-2 r^2 \cos 150$ OE ACCEPT not seeing this step
$2\left(r^2=\right) \frac{5.4^2}{2-2 \cos 150}$ OE , or $7.81(33 .$.$) seen or 2 r^2=15.62(68 \ldots)$
$3(\mathrm{r}=) 2.79(52 \ldots$.
. 3 ACCEPT their correct $r$ due to earlier rounding provided it rounds to 2.8
AM4 (using tan ratio)
115 and 2.7 or 15 and 2.7 seen
$2 r^2=2.7^2+2.7^2 \tan ^2 15$ or $\left(r^2=\right) 2.7^2+\frac{2.7^2}{\tan ^2 75}$ OE or $7.81(33 .$.$) seen$
$3(\mathrm{r}=) 2.79(52 \ldots$.
. 3 ACCEPT their correct $r$ due to earlier rounding provided it rounds to 2.8
The whole sphere of ice melted in the cone, as shown in the diagram below.
Find the value of $h$.
▶️Answer/Explanation
.1 correct trig ratio using $R$ and $h$
.2 correctly write $\mathrm{R}$ in terms of $\mathrm{h}$ OR correctly write $\mathrm{h}$ in terms of $\mathrm{R}$
. 3 substitute 2.8 into volume of sphere formula OR substitute .2 into volume of cone formula
.4 evidence of equating their two volumes
.5 correctly rearrange their equated volumes to have $h$ or $\mathrm{h}^3$ on one side $\mathrm{OR}$ to have $\mathrm{R}^3$ of $R$ on one side
.6 correctly calculate their $\mathrm{h}$ after their rearrangement of their equated volumes
$.1 \tan 15=\frac{\pi}{h}$ or $\tan 75=\frac{\pi}{R} \quad$ or $\quad \frac{R}{\sin 15}=\frac{n}{\sin 75}$
. $2 \mathrm{R}=\mathrm{h} \tan 15$ or $\mathrm{R}=\frac{\mathrm{h}}{\tan 75}$ or $\mathrm{h}=\frac{\mathrm{R}}{\tan 15}$ or $\mathrm{h}=\mathrm{R} \tan 75$ or $\mathrm{R}=\frac{\mathrm{h} \sin 15}{\sin 75}$
or $h=\frac{R \sin 75}{\sin 15} \quad$ ACCEPT $h=3.73 R$ or $R=0.27 h$
2 implies .1
$.3(\mathrm{~V}=) \frac{4 \pi 2.8^3}{3}$ OR $\frac{\pi \text { their }(\mathrm{htan} 15)^2 \mathrm{~h}}{3}$ or $\frac{\pi \mathrm{R}^2 \frac{\text { theirR }}{\tan 15}}{3}$ or any from their . $2 \mathrm{OE}$
ACCEPT if $r=2.795$ for the sphere
ACCEPT $91.95(23 \ldots)$
$.4 \frac{4 \pi 2.8^3}{3}=\frac{\pi \text { their }(\mathrm{h} \tan 15)^2 \mathrm{~h}}{3}$ OE or $\frac{4 \pi 2.8^3}{3}=\frac{\pi \mathrm{theirR}^3}{3 \tan 15}$ or any from their $3 \mathrm{OE}$
$.5 \quad\left(h^3=\right) \frac{4 \pi 2.8^3}{\pi(\tan 15)^2}$ OE OR $\left(R^3=\right) 4(2.8)^3(\tan 15)$ OE $\quad .5$ implies .4
$.6(\mathrm{~h}=)$ 10.69(407 $\ldots)$
DO NOT AWARD the last mark if their $\mathrm{R}=2.8$ or their $\mathrm{R}=2.7$
Body temperature changes during the day. The graph below shows a cosine curve modelling the body temperature for Ingrid.
$\mathrm{B}$ is the temperature in degrees Celsius $\left({ }^{\circ} \mathrm{C}\right)$
$t$ is the time in hours after midnight.
This media is interactive
Ingrid knows it is best to sleep for 8 to 10 hours when her body temperature is $36.5^{\circ} \mathrm{C}$ or below.
Question
Suggest a sleeping schedule for Ingrid.
▶️Answer/Explanation
8 to 10 hours within the interval $6 \mathrm{pm}$ to 6 am.8 to 10 hours within the interval $6 \mathrm{pm}$ to 6 am
Ex: 8pm to 5 am ACCEPT correct 24-hour format ignoring am/pm
Question
Write down the time when Ingrid’s body temperature is at a maximum and a minimum.
▶️Answer/Explanation
AM1 (using the 12-hour clock) . 1 Maximum at $12: 00 \mathrm{pm}$ . 2 Minimum at $12: 00 \mathrm{am}$
AM2 (using the 24-hour clock) . 1 Maximum at 12:00 (am/pm) .2 Minimum at 24:00 (am/pm)
AM1 (using the 12-hour clock)
.2 ACCEPT 0:00 am
AM2 (using the 24-hour clock)
. 2 ACCEPT 0:00
During the day, Ingrid’s body temperature (B) can be modelled using the equation
$$
B=-0.5 \cos \frac{\pi}{12} t+36.5
$$
where $t$ is the time in hours after 12 am. Angles are in radians
Question
Write down the amplitude and period.
▶️Answer/Explanation
. 1 Amplitude $0.5 \mathrm{OE}$ . 2 Period 24
. 1 ACCEPT .5 DO NOT ACCEPT -0.5
Question
Determine the values of the maximum and minimum temperatures.
▶️Answer/Explanation
.1 Maximum 37
. 2 Minimum 36
Question
Calculate Ingrid’s body temperature at $7: 15 \mathrm{am}$, to the nearest one decimal place.
▶️Answer/Explanation
.1 evidence of substituting 7.25 into the formula
.2 the correct value of $B$
.3 correctly round their value of $B$ in .2 to $1 \mathrm{dp}$
$1(B=)-0.5 \cos \left(\frac{\pi}{12} \times 7.25\right)+36.5 \quad A C C E P T \quad(B=)-0.5 \cos (15 \times 7.25)+36.5$
2 36.66(071973…)
DO NOT ACCEPT the using degrees answer $(36.00027433)$
3 their 36.7
Ray’s body temperature is $0.25^{\circ} \mathrm{C}$ higher than Ingrid’s. The graph below shows two cosine curves modelling the body temperatures for Ingrid and Ray.
Question
Write down the equation modelling Ray’s body temperature.
▶️Answer/Explanation
.1 correctly write the equation modelling Ray’s temperature
$.1 R=-0.5 \cos \frac{\pi}{12} t+36.75 \quad$ using $R$ or any other letter ACCEPT $B=-0.5 \cos \frac{\pi}{12} t+36.75$
ACCEPT $\quad-0.5 \cos \frac{\pi}{12} \mathrm{t}+36.75$
Question
Hence, calculate the first time when Ray’s body temperature will reach $36.5^{\circ} \mathrm{C}$.
▶️Answer/Explanation
.1 evidence of correctly equating their expression in terms of $t$ with 36.5
.2 correctly rearrange for their $\cos \frac{\pi}{12} t$ on one side
. 3 correctly inverse their cosine in radians
.4 correct value of their first $t$ after correctly inverse their cosine
$.136 .5=$ their $-0.5 \cos \frac{\pi}{12} t+36.75$ or $36.5=-0.5 \cos \frac{\pi}{12} t+$ their 36.75 ACCEPT using $x$ instead of $t$
$$
.2 \cos \frac{\pi}{12} \mathrm{t}=\frac{\text { their }(-0.25)}{-0.5} \text { OE }
$$
. 2 ACCEPT correctly rearrange linear equation for $t$ but DO NOT AWARD .3 and .4
e.g ( $t=$ )their $\frac{36.5-36.75}{-0.5 \cos \left(\frac{\pi}{12}\right)}$.but do not award .3 and .4
.3 their $\frac{\pi}{12} \mathrm{t}=1.047(197551 \ldots)$ OE or $\frac{\pi}{12} \mathrm{t}=\frac{\pi}{3}$ ACCEPT not seeing this step
$.4(\mathrm{t}=)$ their4 $(\mathrm{am})$ or $04: 00 \mathrm{OE}$
ignore incorrect time of day after seeing their 4
These sprinters take a test that records their reaction time. The table below shows the results.
Question
Write down the mode and median reaction times.
▶️Answer/Explanation
.1 mode 0.78
2 median 0.77
Question
Show that the mean reaction time is $0.77 \mathrm{~s}$, for this group of sprinters.
▶️Answer/Explanation
1 add the product of grade and frequency
2 divide the sum of products by 20
0.77 AG
$$
.14 \times 0.75+3 \times 0.76+5 \times 0.77+6 \times 0.78+1 \times 0.79+1 \times 0.8 \mathrm{OE}
$$
1 ACCEPT 15.4 seen
.1 ACCEPT not seeing the whole operation from calculator screenshot provided shows at least 4 correct products. Ex:
Screenshot
$$
(4 \times 0.75+3 \times 0.76+5 \times 0.77+6 \times 0.78+1 \times 0 .
$$
Or
Screenshot
$$
3 \times 0.76+5 \times 0.77+6 \times 0.78+1 \times 0.79+1 \times 0.8^{\prime}
$$
$2 \frac{4 \times 0.75+3 \times 0.76+5 \times 0.77+6 \times 0.78+1 \times 0.79+1 \times 0.8}{4+3+5+6+1+1}$ ACCEPT $\frac{15.4}{20}$ seen
. 2 ACCEPT not seeing the whole operation from calculator screenshot Ex:
Screenshot
$$
(4 \times 0.75+3 \times 0.76+5 \times 0.77+6 \times 0.78+1 \times 0 .
$$
$$
\frac{\text { ans }}{20}=0.77
$$
Question
Draw a line of best fit.
▶️Answer/Explanation
.1 any two from
i. line within the zone
ii. fairly passing through points Ex: at least two points above and two points below the line
iii. line domain at least [5.5.10.5]
.2 the third from
i. line within the zone
ii. fairly passing through points. Ex: at least two points above and two points below the line
iii. line domain at least [5.5.10.5]
DO NOT award any marks for horizontal line
DO NOT award any marks if they have more than one line drawn
DO NOT award any marks if their line has positive gradient
Question
Using your line of best fit from (c), write down the value of $r$ for $h=4$ hours and $h=7.5$ hours.
$h=4$ hours $r=$
$h=7.5$ hours $r=$
Calculate the value of $w$ when $r=0.77 \mathrm{~s}$. Give your answer correct to two significant figures.
▶️Answer/Explanation
1 correct value of their $r$ for $h=4$ & .1 ACCEPT error $\pm 0.02$ DO NOT ACCEPT if $\mathrm{h}=4$ is not on their line \\
.2 correct value of their $r$ for $h=7.5$ & .2 ACCEPT error $\pm 0.02$ DO NOT ACCEPT if $\mathrm{h}=7.5$ is not on their line
\end{tabular}
Question
Explore the probability of winning a race for sprinters with different sleeping habits. In your answer you must:
– identify the two relevant factors affecting the probability of winning
– calculate the probability of winning for sprinters with different sleeping habits
– comment on the relationship between the probability of winning and sleeping habits
– justify the accuracy of your findings.
$$
w=24(100)^{-r}
$$
Where:
$w$ is the probability of winning a race.
$r$ is the mean reaction time in seconds.
▶️Answer/Explanation
one correct $w$ value from their $r$ without working
OR
At least two incorrect $w$ values from their $r$ with working seen
ACCEPT $w>1$
ACCEPT $w$ and its corresponding $r$ value seen in the table or in the response box
ACCEPT their rounding of $w$ provided it correctly rounds to 1 d.p
Ex: $w=0.6867$ and they write 0.68
DO NOT ACCEPT $w$ for $r=0.77$
Correct comment on the positive relationship between probability of winning and sleeping.
Ex: WTTE
When sleeping duration increases the probability of winning increases
ACCEPT:
-Good sleep increases probability of winning
-Bad sleep decreases probability of winning
-reaction time is better when sleeping well so probability of winning increases
-sleeping $10 \mathrm{~h}$ has probability 0.8 , sleeping $4 \mathrm{~h}$ has probability 0.2 and 0.8 is more than 0.2
-sleeping $10 \mathrm{~h}$ has $w=0.8$ while sleeping $4 \mathrm{~h}$ has $w=0.1$ only
DO NOT ACCEPT :
-comment involving only reaction time and sleeping.
-sleeping $10 \mathrm{~h}$ has probability 0.8 compared to sleeping 4 h has probability 0.1
Question
$$
w=24(100)^{-r}
$$
Where:
$w$ is the probability of winning a race.
$r$ is the mean reaction time in seconds.
Calculate the value of $w$ when $r=0.77 \mathrm{~s}$. Give your answer correct to two significant figures.
▶️Answer/Explanation
.1 correctly substitute 0.77 into the formula & $.1(w=) 24(100)^{-0.77}$ \\
.2 correct value of $w$ & $.20 .692(1675608 \ldots)$ ACCEPT not seeing this step \\
.3 correctly round their $w$ to $2 \mathrm{sf}$ & .3 their 0.69 OE
Question
Write down the missing values in the table.
▶️Answer/Explanation
correctly place 100 and 144
Question
Describe, in words, two patterns for $V$.
▶️Answer/Explanation
.1 correctly describe one pattern for $V$ in words with correct terminology
2 correctly describe a second pattern for $V$ in words with correct terminology
ACCEPT complete terminology only, for example (below are different descriptions):
DO NOT ACCEPT two from the same description
– The increase is increasing by a constant, the number you add increases constantly, the increase goes up by a constant, second difference is constant, the difference is in pattern $12,20,28 \ldots, V$ goes up by $12,20,28 \ldots$
– Quadratic
– Square numbers, square of even numbers
– Multiples of 4 , divisible by 4
DO NOT ACCEPT, for example:
Arithmetic, increasing, increasing by a constant
Even numbers, the square numbers, the multiples of 4
DO NOT ACCEPT The rule in words, for example:
2 times $n$ squared, $n$ multiplied by 2 squared, double of $n$ squared, twice stage number squared, the square of $n$ times 2 and product of $n$ with 2
Note:
More than two different patterns, all correct award (2 marks)
Ex: multiples of 4 , square numbers and it is 2 times $n$ squared
More than two different patterns, with any incorrect award (1 mark)
Ex: multiples of 4, second difference is constant and it is 3 times $n$
Question
Write down a general rule for $V$ in terms of $n$.
▶️Answer/Explanation
.1 the correct general rule
.2 the correct simplified general rule with correct notation for $V$ in terms of $n$
$.1(\mathrm{~V}=) 4 n^2$ or $(\mathrm{V}=) 4 n^{\wedge} 2$ or $(\mathrm{V}=) 4^{\star} n^{\star} n$ or $(V=)(2 \times n)^2$ or $V=4 \times n^2$
ACCEPT $V=4 x^2$
$.2 V=4 n^2$ or $V=(2 n)^2$
ACCEPT $V_n=4 n^2$ or $V(n)=4 n^2$ or use $v$ for $V$
DO NOT ACCEPT description in words
SC for 1 mark
if NR in 8c and correct general rule seen in $8 \mathrm{~b}$ condone incorrect notation award 1 mark
Question
Verify your general rule for $V$.
▶️Answer/Explanation
.1 correctly substitute $n \geq 5$ into their general rule (from $8 \mathrm{c}$ or $8 \mathrm{~b}$ ) . 2 correctly calculate their value of $V$ after substituting $n \geq 5$ .3 recognise that their correctly calculated value of $V$ is the same as their predicted value
.1 Ex: $4 \times 5^2$
2 Ex: 100 (for $n=5$ )
3 same as when candidate explains how the pattern continues
Ex: how 100 is obtained by adding 36 to 64
.3 ACCEPT seeing the value in the table in $8 a$ and seeing their matching calculated $V$ using $n \geq 5$
Ex: we find the candidate has 100 in the table for $n=5$
Question
Investigate the values in the table to find a relationship for the area $(A)$ of the rhombus in terms of $n$. In your answer, you should:
– predict more values and record these in the table
– describe in words one pattern for $A$
– determine a general rule for $A$ in terms of $n$
– test your general rule for $A$
– verify and justify your general rule for $A$
– ensure that you communicate all your working appropriately
▶️Answer/Explanation
1 correctly substitute $n \geq 5$ into heir general rule (from $8 c$ or $8 b$ ) 2 correctly calculate their value of $V$ after substituting $n \geq 5$ 3 recognise that their correctly zalculated value of $V$ is the same as their predicted value
.1 Ex: $4 \times 5^2$
2 Ex: 100 (for $n=5$ )
.3 same as when candidate explains how the pattern continues Ex: how 100 is obtained by adding 36 to 64
.3 ACCEPT seeing the value in the table in $8 a$ and seeing their matching calculated $V$ using $n \geq 5$
Ex: we find the candidate has 100 in the table for $n=5$
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