IB Maths AA HL Topic 1: Number and algebra questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
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Question 1

Paper 1, no calculatorEasy5 marks

The concentration CC in mg L−1\text{mg L}^{-1} of a dye in a tank tt hours after treatment begins is modelled by

C(t)=32(14)t.C(t)=32\left(\frac14\right)^t.
(a)

Find the concentration after 32\frac32 hours.

[2]
(b)

Determine the time at which the concentration reaches 3 mg L−13\text{ mg L}^{-1} Use logarithms and give your answer exactly in terms of ln⁡\ln including units.

[3]

Question 2

Paper 1, no calculatorEasy6 marks

Let

R(x)=3x−2(x−4)(x+1).R(x)=\frac{3x-2}{(x-4)(x+1)}.
(a)

Express R(x)R(x) in partial fractions.

[3]
(b)

Hence determine the exact value of

∫01R(x) dx.\int_0^1 R(x)\,dx.
[3]

Question 3

Paper 1, no calculatorEasy6 marks

The rational function

R(x)=3x−1(x−3)(x+1)R(x)=\frac{3x-1}{(x-3)(x+1)}

is used as an integrand.

(a)

State the real values of xx for which R(x)R(x) is undefined.

[1]
(b)

Write R(x)R(x) in partial fractions.

[3]
(c)

Hence determine an antiderivative of R(x)R(x)

[2]

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