You're viewing 3 free preview questions for Maths AI HL — subscribe to unlock 87 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Binomial Theorem · Paper 1 — Free Maths AI HL Practice Questions

1FoundationSAQ-SBinomial expansion and coefficients5 marksPaper 1~8 min

Consider the expansion of

(2x + 3)^5

(a)

Write down the general term of the expansion in terms of

r

, where

r = 0, 1, \ldots, 5

. [2 marks]

(b)

Hence find the coefficient of

x^2

in the expansion. [3 marks]

Solutions

2MasterySAQ-SBinomial expansion and coefficients5 marksPaper 1~8 min

Consider the expansion of

\left(2x + \dfrac{1}{x^2}\right)^n

, where

n \in \mathbb{Z}^+

and

n

is a multiple of 3.

(a)

Show that the coefficient of the term independent of

x

\dbinom{n}{\frac{n}{3}} 2^{\frac{2n}{3}}

. [3 marks]

(b)

Hence find the smallest value of

n

such that this coefficient exceeds 5000. [2 marks]

Solutions

3ChallengeSAQ-LApplications of binomial expansions8 marksPaper 1~12 min

A pharmaceutical company is testing a new drug. Clinical trials show that the probability of a patient experiencing a minor side effect is

0.08

. The drug is tested on

100

patients. Let

X

be the number of patients who experience the side effect.

(a)

Calculate the expected value and standard deviation of

X

. [2 marks]

(b)

Determine

P(X = 10)

, giving your answer correct to 4 significant figures. [2 marks]

(c)

Evaluate whether

P(8 \leq X \leq 12) > 0.5

. Justify your answer by calculating each relevant probability and summing them. [4 marks]

Solutions

Questions 4-90

Unlock these questions with Premium

That's every free question here — 3 of 90.

+87 more questions, plus Mock Papers & Worksheets, are waiting in Premium.