Number & Algebra Toolkit (DP IB Analysis & Approaches (AA): HL): Exam Questions

Let , where ,  and .

Calculate the exact value of .

Give your answer from part (a) correct to

(i) two decimal places.

(ii) two significant figures.

Let , where   and 

Find the value of W. Give your answer as a fraction.

Give your answer from part (a) to

(i) three decimal places.

(ii) three significant figures.

A prism has a cross sectional area of and volume of .

Calculate the length of the prism.

The cross-sectional area of the prism is in the shape of a trapezium and its parallel sides measure 2 m and 2.4 m.

Calculate the height of the trapezium. Give your answer in cm.

Mary has found the exact answer for  is  .

Write down the exact answer of as a decimal.

Give your answer from part (a) correct to

(i) three decimal places

(ii) one significant figure.

It is given that  and , where  and  .

Find the size of the angles  and .

A circle has radius  equal to

Find the exact value of the area of the circle, giving your answer in terms of .

A medium rare steak should have an internal temperature of  to . Max decides to go to 10 different steak houses, he measures the internal temperature of a medium rare steak at each establishment and records the following:

51.0,   52.1,  62.9,  49.0,  59.8,  50.2,  54.3,  47.7,  48.6,   65.4

Find the mean internal temperature of Max’s recordings.

Max goes to 5 more steak houses and calculates the mean of all 15 restaurants to be 

Calculate the mean internal temperature from the 5 additional steak houses Max went to.

Max records one last steak that has an internal temperature of

Calculate the interval of  such that the mean internal temperature for all 16 steaks is within the temperature range for a medium rare steak.

The diameter of Earth is  m, correct to four significant figures.  The circumference of Mars is  m, correct to four significant figures. 

Modelling Earth and Mars as perfect spheres, find the difference between the volume of Earth and the volume of Mars, giving your answer in the form , where .

Solve the following systems of linear equations using technology.

(i)

(ii)

Write    as a sum of partial fractions.

Write as a sum of partial fractions.

Write as a sum of partial fractions.

The expression can be written as the sum of partial fractions in the form

where ⍺, A, B, C

Write down the value of ⍺.

Find the values of A, B, and C.

Consider the numbers a =

Giving your answer to 1 decimal place, calculate the value of

(i) a.

(ii) b.

(iii) c.

(iv) d.

Points P and Q have coordinates (a, b) and (c, d) respectively.

The formula for the distance, d, between two points with coordinates (x_1,y₁) and (x₂,y₂) is given in your formula booklet.

Using your answers from part (a), calculate the distance, d, between points P and Q. Give your answer correct to 1 decimal place.

Let and , where , , .

Find the exact value of .

Point A has coordinates (-1, 7) and point B has coordinates (11, 12).

The formula for the distance, d, between two points with coordinates and is given in your formula booklet.

Calculate the distance between points A and B.

The formula for the coordinates of the midpoint of a line segment with endpoints and is given in your formula booklet.

Calculate the midpoint of the line segment with endpoints A and B.

Let where a = 16, b = 7.5°, c = 3 and d = 5°.

Note:

Find the value of , giving your answer as a fraction.

Let

Find the value of , giving your answer as a fraction.

Calculate the value of , giving your answer as a fraction.

Consider the numbers and .

Giving your answers in the form , where , calculate

(i)

(ii)

(iii)

(iv) .

The formula for the distance, , between two points with coordinates and is given in your formula booklet.

Using your answers to part (a), estimate the distance between points and .

The mean height of the four tallest students in a classroom is 176 cm and the mean height of the six tallest students is 165 cm. The fifth tallest student is 4 cm taller than the sixth tallest student.

Find the heights of the fifth and sixth tallest students.

In this question give your answers in the form , where

The surface area of the Earth is approximately .

Given that the surface area of the Earth is approximately 13 times larger than the surface area of the moon, find an approximation for the surface area of the moon.

Given that the surface area of Jupiter is approximately , find how many times larger the surface area of Jupiter is than the surface area of the Earth.

Solve the following systems of linear equations using technology.

(i)

(ii)

Write in the form

where and are integers to be found.

The expression can be written as the sum of partial fractions in the form

Find the value of and .

The expression can be written as the sum of partial fractions in the form

, where

Write down the value of .

Find the value of and .