IB Maths AA SL/Question Bank/IB Mathematics: Analysis and Approaches

IB Maths AA SL IB Mathematics: Analysis and Approaches Question Bank

SL955 questions10 previewsSyllabus linked

[Maximum number: 4]

The following table shows the number of hours of play time, x, and sleep time, y, for a group of six children, over the period of one week.

The regression line of y on x for this data can be written in the form y=a x+b.

(a)

Find the value of a and the value of b.

[ 2 ]

(b)

Use the equation of the regression line to estimate the sleep time of a child whose weekly play time is 20 hours.

[ 2 ]

[Maximum number: 4]

The graph of a function f for $-3 \leq x \leq 3$ is shown in the following diagram.

The following graphs are transformations of the graph of y=f(x).

(A)

(B)

(C)

(D)

(E)

(F)

Consider the following table of transformations of y=f(x).
Next to each transformed function, write down the letter that corresponds to its graph.

[Maximum number: 4]

The scores achieved by 80 golfers in a competition are summarized in the following box and whisker diagram.

(a)

Find the interquartile range.

[ 2 ]

(b)

Find the number of golfers that scored between 70 and 74 .

[ 2 ]

[Maximum number: 5]

Consider the function $f(x)=\frac{(x-1)^{2}}{x}$ , where $x \in \mathbb{R}, x \neq 0$ .

(a)

Show that $\frac{(x-1)^{2}}{x}=x-2+\frac{1}{x}$ .

[ 2 ]

(b)

Hence, find $\int f(x) \mathrm{d} x$ .

[ 3 ]

[Maximum number: 5]

Write each of the following expressions in the form $\ln k$ , where $k \in \mathbb{Z}^{+}$ .

(a)

$\quad \ln 3+\ln 4$

[ 1 ]

(b)

$3 \ln 2$

[ 2 ]

(c)

$-\ln \frac{1}{2}$

[ 2 ]

[Maximum number: 5]

The following diagram shows a solid hemisphere with centre A(6,-1,-3).
Point B (4, -5, -9) lies on the curved surface.

(a)

Find AB , the radius of the hemisphere.

[ 2 ]

(b)

Hence, find the total surface area of the solid hemisphere.

[ 3 ]

[Maximum number: 6]

The discrete random variable X has the following probability distribution:

(a)

Find the value of k.

[ 2 ]

(b)

Find P(X>1.5).

[ 2 ]

(c)

Find E(X).

[ 2 ]

[Maximum number: 7]

Kiran and Logan collect the following data about the river Afon, where x is the distance in metres from the source and y is the depth in centimetres.

This data is represented in the following scatter diagram.

Kiran knows that the depth of the river is 0 cm at the source.
Kiran calculates $\bar{x}$ and $\bar{y}$ for the seven points given in the table on page 2 and draws a line on the scatter diagram through the mean point $(\bar{x}, \bar{y})$ and the point (0,0).

(a)

Find

[ 3 ]

(i)

the value of $\bar{x}$ and the value of $\bar{y}$ ;

(ii)

the equation of Kiran's line.

For the seven points given in the table Logan finds the regression line of y on x with equation y=a x+b, where $a, b \in \mathbb{R}$ .

[ 3 ]

(b)

Determine the value of a and the value of b.

[ 2 ]

(c)

By using the equation of Logan's regression line, estimate the depth of the river 350 m from its source.

[ 2 ]

[Maximum number: 4]

Consider the function $f(x)=x^{3}+5 x^{2}-8$ , where $x \in \mathbb{R}$ .

(a)

Find $f^{\prime}(1)$ .

[ 2 ]

(b)

Find the equation of the tangent to the graph of f at x=1.

[ 2 ]

[Maximum number: 7]

Consider the function f(x)=-2(x-1)(x+3), for $x \in \mathbb{R}$ . The following diagram shows part of the graph of f.

(a)

For the graph of f

[ 5 ]

(i)

find the x-coordinates of the x-intercepts;

(ii)

find the coordinates of the vertex.

The function f can be written in the form $f(x)=-2(x-h)^{2}+k$ .

[ 5 ]

(b)

Write down the value of h and the value of k.

[ 2 ]