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IB Mathematics AA HL - Revision Ladder

Level 1

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Paper 1
Paper 2

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Question 1

no calculator

easy

[Maximum mark: 4]

Expand (2x+1)4(2x + 1)^4 in descending powers of xx and simplify your answer.

easy

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Question 2

no calculator

easy

[Maximum mark: 6]

A bag contains 77 blue and 55 red marbles. Two marbles are selected at random without replacement.

  1. Complete the tree diagram below. [3]

865fd050d3db84e24416b401670caec65ade51d0.svg

  1. Find the probability that exactly one of the selected marbles is blue. [3]

easy

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Question 3

calculator

easy

[Maximum mark: 6]

The following diagram shows part of a circle with centre O and radius 55 cm.

d3a02f29895c6ce0b991606f98b7b99a2c21d836.svg

Points A, B lie on the circle, chord AB has a length of 88 cm and AOˆB=θ\text{A\^{O}B} = \theta.

  1. Find the value of θ\theta, giving your answer in radians. [3]

  2. Find the area of the shaded region. [3]

easy

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Question 4

calculator

easy

[Maximum mark: 6]

A school basketball team of 55 students is selected from 88 boys and 44 girls.

  1. Determine how many possible teams can be chosen. [2]

  2. Determine how many teams can be formed consisting of 33 boys and 22 girls? [2]

  3. Determine how many teams can be formed consisting of at most 33 girls? [2]

easy

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Question 5

no calculator

easy

[Maximum mark: 6]

Let f(x)=px3qxf(x) = p x^3 - qx. At x=0x = 0, the gradient of the curve of ff is 22. Given that
f1(12)=2f^{-1} (12) = 2, find the value of pp and qq.

easy

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Question 6

no calculator

easy

[Maximum mark: 6]

The function ff is of the form f(x)=ax+b2x+cf(x) = \dfrac{ax+b}{2x+c}, for xc2x \neq -\dfrac{c}{2}, where a,b,cZa,b,c \in \mathbb{Z}. Given

that the graph of y=f(x)y = f(x) has asymptotes x=5x = -5 and y=2y = 2, and that the point

P(1,112)\left(1,-\dfrac{1}{12}\right) lies on the graph, find the values of a,ba, b and cc.

easy

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Question 7

calculator

easy

[Maximum mark: 6]

Given that logb3=10\log_b 3 = 10.

  1. Find the exact value of logb81\log_b 81. [2]

  2. Find the exact value of logb23\log_{b^2} 3. [2]

  3. Find the value of bb, giving your answer correct to 33 significant figures. [2]

easy

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Question 8

calculator

easy

[Maximum mark: 7]

In a geometric sequence, u2=6u_2 = 6, u5=20.25u_5 = 20.25.

  1. Find the common ratio, rr. [2]

  2. Find u1u_1. [2]

  3. Find the greatest value of nn such that un<200u_n < 200. [3]

easy

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Question 9

calculator

easy

[Maximum mark: 5]

Let f(x)=92ln(x2+4)f(x) = 9 - 2\ln(x^2 + 4), for xRx \in \mathbb{R}. The graph of ff passes through the point (p,3)(p,3), where p>0p > 0.

  1. Find the value of pp. [2]

The following diagram shows part of the graph of ff.

6016001b65155100f0dc6eb98ff244252ca74b02.svg

The region enclosed by the graph of ff, the xx-axis and the lines x=px = -p and x=px = p is rotated 360360^\circ about the xx-axis.

  1. Find the volume of the solid formed. [3]

easy

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Question 10

calculator

easy

[Maximum mark: 6]

A particle moves in a straight line with velocity v(t)=2t0.3t3+2v(t) = 2 t - 0.3 t^3 + 2, for t0t \geq 0, where vv is in ms1^{-1} and tt in seconds.

  1. Find the acceleration of the particle after 2.22.2 seconds. [3]

    1. Find the time when the acceleration is zero.

    2. Find the velocity when the acceleration is zero. [3]

easy

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