Learn Extracted exam questions A-Level Mathematics 9709 Mathematics November 2025 Question Paper 52
9709 Mathematics November 2025 Question Paper 52
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A coin is biased so that the probability of obtaining a head when it is thrown is 0.4. The coin is thrown repeatedly until the first head is obtained.
Find the probability that the first head is obtained on the 5th throw.
Find the probability that the first head is obtained after the 6th throw.
Kayla has a bag containing 3 red marbles, 1 blue marble and 2 green marbles. She selects one marble from the bag at random and does not replace it. She repeats this process until she obtains a green marble. The random variable $X$ is the number of marbles she needs to select until she obtains a green marble.
Draw up the probability distribution table for $X$.
Find $\mathrm{Var}(X)$.
The heights of the 124 Senior members of the Giraffes basketball club are normally distributed with mean 187.4 cm and standard deviation 6.4 cm. How many members of the club would you expect to have heights within 5 cm of the mean?
The heights of the Junior members of the Giraffes club are normally distributed with mean 172.7 cm and standard deviation $\sigma$ cm. 23% of these members have height less than 170.3 cm. Find the value of $\sigma$.
Gio has a pack of 18 cards and Ivy has a pack of $x$ cards. Each card shows a bus, a car or a train. Gio's pack: bus 6, car 10, train 2. Ivy's pack: bus $x-12$, car 9, train 3. One card is chosen at random from each pack. The probability that the two cards both show buses is equal to twice the probability that they both show cars.
Write down an equation in terms of $x$ and hence find the value of $x$.
Find the probability that the two cards have pictures of the same type of vehicle on them.
The times of 240 competitors taking part in an event are recorded correct to the nearest minute. Time (minutes) / Frequency: 1–10 / 12, 11–20 / 38, 21–25 / 68, 26–30 / 76, 31–50 / 46.
Draw a histogram to represent this information.
Calculate an estimate of the mean time taken by the 240 competitors.
For a randomly chosen person, their next birthday is equally likely to occur on any day of the week, independently of any other person's birthday.
Find the probability that, out of 10 randomly chosen people, none of them will have their next birthday on a Saturday or Sunday.
Find the probability that, out of 10 randomly chosen people, fewer than 3 will have their next birthday on a Wednesday.
Use a suitable approximation to find the probability that, out of 392 randomly chosen people, more than 65 will have their next birthday on a Friday.
Find the number of different arrangements of the 10 letters in the word ZOOLOGICAL in which the three Os are together and the two Ls are not next to each other.
Find the number of different arrangements of the 10 letters in the word ZOOLOGICAL in which there are exactly 5 letters between the two Ls.
Two letters are chosen at random from the 10 letters in the word ZOOLOGICAL. Find the probability that these two letters are different.