Practice Paper 1 (DP IB Maths: AA SL)

The diameter of our moon is roughly 3.5 x 10³ km. Honzos is a spherical moon in a nearby galaxy and its diameter is eight times larger than our moon's.

State the radius of Honzos, giving your answer in standard form.

Approximately 75% of the surface of Honzos is available for cultivation.

The approximate surface area of Honzos that is available for cultivation can be expressed in the form , where  and .

State the values of  and .

Students are arranged for a graduation photograph in rows which follows an arithmetic sequence. There are 20 students in the fourth row and 44 in the 10th row.

Find the common difference, , of the arithmetic sequence.

Given there are 20 rows of students in the photograph, calculate how many students there are altogether.

The heights, in metres, of a flock of 20 flamingos are recorded and shown below:

An outlier is an observation that falls either more than 1.5 x (interquartile range) above the upper quartile or less than 1.5 X (interquartile range) below the lower quartile.

Find the values of and .

Using your answers to part (a), draw a box plot for the data.

Let , where , , and .

Find the equation of the tangent of  at .

Prove that 

Hence solve  where .

where  and . The line  meets the graph of  at exactly one point.

Show that .

can be written in the form , where 

Find the value of .

can also be written in the form  where

Find the values of  and .

By sketching the graph of , find the values of where the graph is both negative and decreasing.

Find the area enclosed by and the -axis.

Let where  is a constant.

Given that , find the value of .

Find

Show that the graph of  has exactly one minimum point and determine its -coordinate.

Given that the -coordinate of the minimum point is -4, find the value of .

Frank has a biased six-sided die.
The faces of the die are numbered 1 to 6.
Frank's score, , is the number which lands face up after his die is rolled.
The following table shows the probability distribution for .

	1	2	3	4	5	6

Frank plays the game twice and adds the scores together.

Find the probability Frank has a total score of 4, giving your answer as a fraction.

Jenny has a different biased six-sided die.
On Jenny's die, the faces are numbered as multiples of 3.
Jenny's score, , is the number which lands face up after her die is rolled.
The following table shows the probability distribution for .

	3	6	9	12	15	18

It is given that the range of possible values for  is .

Find the range of possible values for .

Hence, find the range of possible values for .

Frank and Jenny each roll their die once. The probability that Frank's score is at least as high as Jenny's is  .
Find the value of