DP Mathematics HL Questionbank

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• 18M.3sp.hl.TZ0.2d: Determine the mean number of throws required to obtain a 1.
• 18M.3sp.hl.TZ0.2c: Find $G'\left( t \right)$.
• 18M.3sp.hl.TZ0.2b: Show that the probability generating function, $G\left( t \right)$, for X is given by...
• 18M.3sp.hl.TZ0.2a: State the distribution of X.
• 16M.3sp.hl.TZ0.5b: (i)     Show that $G(t)$, the probability generating function of $Y$, is given by...
• 16M.3sp.hl.TZ0.5a: Show that the probability distribution of $Y$ is given by...
• 16N.3sp.hl.TZ0.4b: By differentiating $J(t)$, prove that (i)    ...
• 16N.3sp.hl.TZ0.4a: Write down an expression for $J(t)$ in terms of $G(t)$ and $H(t)$.
• 17N.3sp.hl.TZ0.5c.ii: Identify the probability distribution given in part (c)(i) and state its parameters.
• 17N.3sp.hl.TZ0.5c.i: Show...
• 17N.3sp.hl.TZ0.5b: By considering the probability generating function, ${G_{X + Y}}(t)$, of $X + Y$, show that...
• 17N.3sp.hl.TZ0.5a.ii: Hence show that ${\text{Var}}(X) = \lambda$.
• 17N.3sp.hl.TZ0.5a.i: Find expressions for ${G’_X}(t)$ and ${G’’_X}(t)$.
• 17N.3sp.hl.TZ0.1b.ii: Given that $P(T < a) = 0.75$, find the value of $a$.
• 17N.3sp.hl.TZ0.1b.i: Sketch the graph of $F(t)$ for $0 \leqslant t \leqslant 2$, clearly indicating the...
• 17N.3sp.hl.TZ0.1a: Find the cumulative distribution function $F(t)$, for $0 \leqslant t \leqslant 2$.
• 12M.3sp.hl.TZ0.4d: (i)     Find the cumulative distribution function for X . (ii)     Hence, or otherwise, find the...
• SPNone.2.hl.TZ0.3a: Complete the grouped frequency table for these data.  
• SPNone.2.hl.TZ0.3b: Estimate the mean and standard deviation of the heights of these 80 boys.
• SPNone.2.hl.TZ0.3c: Explain briefly whether or not the normal distribution provides a suitable model for this...
• 13M.3sp.hl.TZ0.4a: (i)     Determine an expression for $F(x)$, valid for $1 \leqslant x \leqslant 2$, where F...
• 11N.3sp.hl.TZ0.3d: Find the median of X in terms of $\lambda$.
• 11N.3sp.hl.TZ0.3b: Find the cumulative distribution function, $F(x)$, of X.
• 11N.3sp.hl.TZ0.3c: Find the probability that the lifetime of a particular battery is more than twice the mean.
• 11N.3sp.hl.TZ0.3e: Find the probability that the lifetime of a particular battery lies between the median and the mean.
• 11M.2.hl.TZ1.1a: Estimate the (i)     median weight of the apples; (ii)     30th percentile of the weight of the...
• 11M.2.hl.TZ1.1b: Estimate the number of apples which weigh more than 110 grams.
• 15N.3sp.hl.TZ0.4a: Find $F(u)$, the cumulative distribution function of $U$, for...
• 15N.3sp.hl.TZ0.4b: Hence, or otherwise, find the value of $P(U > 20)$.
• 14N.3sp.hl.TZ0.1c: Find the interquartile range for $X$.
• 14N.3sp.hl.TZ0.1b: Find the cumulative distribution function for $X$.