maths practice for alevels students, Exams of Mathematics

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Your Turn Questions:

‘in between’ Pure session

Bicen Maths

Bicen Question

a) Find the first three terms, in ascending powers of 𝑥, of the binomial expansion of

writing each term in simplest form.

A student uses this expansion with 𝑥 =

1 18

to find an approximation for 26

b) Using your answer to part (a), find the approximation correct to 3 decimal places

A different student uses this expansion with 𝑥 = −

23 2

c) Comment on the suitability of this student’s approach

d) Using your answer to part (a), find the coefficient of the 𝑥^5 term in the binomial

expansion of

−2𝑥 3 − 2 𝑥^2

Your Turn

IAL P3 June 25 Your Turn

IAL P3 Jan 21 Your Turn

Bicen Question

𝑓 𝑥 = 2 𝑥^3 − 25 𝑥^2 + 59𝑥 + 36

a) Use the factor theorem to show that (2𝑥 + 1 ) is a factor of 𝑓(𝑥) b) Express 𝑓(𝑥) in fully factorised form c) Hence solve the equation 2 × 27 𝑦^ − 25 × 9 𝑦^ + 59 × 3 𝑦^ + 36 = 0

Your Turn

IAL P2 June 2025 Your Turn

IAL P3 Jan 2023 (^) Your Turn

IAL P3 Jan 2025 (^) Your Turn

IAL P4 June 2025 (^) Your Turn

OCR Pure/Stats 2021 Your Turn

Bicen Question

A sequence of terms 𝑢 1 , 𝑢 2 , 𝑢 3 , … is defined by 𝑢 1 = 2 𝑢𝑛+ 1 = 𝑢𝑛 − 1 𝑢𝑛 a) i) Show that this sequence is periodic ii) State the order of this periodic sequence b) Find the value of ෍ 𝑛= 3

𝑢𝑛 Your Turn

IAL P2 Jan 2021 (^) Your Turn

IAL P2 June 2025 (^) Your Turn

Your Turn : Connected Rates of Change / Differential Equations

Connected rates of change:

e.g.

Differential equations, separate the variables

e.g.