IB Mathematics AA HL  Revision Ladder
Level 1
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Question 1
[Maximum mark: 4]
Expand $(2x + 1)^4$ in descending powers of $x$ and simplify your answer.
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Question 2
[Maximum mark: 6]
A bag contains $7$ blue and $5$ red marbles. Two marbles are selected at random without replacement.

Complete the tree diagram below. [3]
 Find the probability that exactly one of the selected
marbles is blue. [3]
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Question 3
[Maximum mark: 6]
The following diagram shows part of a circle with centre O and radius $5$ cm.
Points A, B lie on the circle, chord AB has a length of $8$ cm and $\text{A\^{O}B} = \theta$.

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

Find the area of the shaded region. [3]
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Question 4
[Maximum mark: 6]
A school basketball team of $5$ students is selected from $8$ boys and $4$ girls.

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

Determine how many teams can be formed consisting of $3$ boys and $2$ girls? [2]

Determine how many teams can be formed consisting of at most $3$ girls? [2]
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Question 5
[Maximum mark: 6]
Let $f(x) = p x^3  qx$. At $x = 0$, the gradient of the curve of $f$ is
$2$. Given that
$f^{1} (12) = 2$, find the value of $p$ and $q$.
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Question 6
[Maximum mark: 6]
The function $f$ is of the form $f(x) = \dfrac{ax+b}{2x+c}$, for $x \neq \dfrac{c}{2}$, where $a,b,c \in \mathbb{Z}$. Given
that the graph of $y = f(x)$ has asymptotes $x = 5$ and $y = 2$, and that the point
P$\left(1,\dfrac{1}{12}\right)$ lies on the graph, find the values of $a, b$ and $c$.
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Question 7
[Maximum mark: 6]
Given that $\log_b 3 = 10$.

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

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

Find the value of $b$, giving your answer correct to $3$ significant figures. [2]
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Question 8
[Maximum mark: 7]
In a geometric sequence, $u_2 = 6$, $u_5 = 20.25$.

Find the common ratio, $r$. [2]

Find $u_1$. [2]

Find the greatest value of $n$ such that $u_n < 200$. [3]
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Question 9
[Maximum mark: 5]
Let $f(x) = 9  2\ln(x^2 + 4)$, for $x \in \mathbb{R}$. The graph of $f$ passes through the point $(p,3)$, where $p > 0$.
 Find the value of $p$. [2]
The following diagram shows part of the graph of $f$.
The region enclosed by the graph of $f$, the $x$axis and the lines $x = p$ and $x = p$ is rotated $360^\circ$ about the $x$axis.
 Find the volume of the solid formed. [3]
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Question 10
[Maximum mark: 6]
A particle moves in a straight line with velocity $v(t) = 2 t  0.3 t^3 + 2$, for $t \geq 0$, where $v$ is in ms$^{1}$ and $t$ in seconds.

Find the acceleration of the particle after $2.2$ seconds. [3]


Find the time when the acceleration is zero.

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

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