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International UAS Exam, advanced mathematical skills sample questions without images

In this section, you can choose how you want to view mathematical notation. In the screen reader version, mathematical notation is presented in Luetus format (a format that can be read by screen reader software). In the visual version, mathematical notation is presented in the same way as in the standard exam with images. You can use the checkbox below to switch between the two versions.

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Instructions for applicants

Read the questions carefully and select the answer that you think is correct. There is only one correct answer in each question.

Decimals are written with a decimal point, for example: 1.5. Numbers of five digits or more are written with a comma as a thousand separator, for example: 98,000.

You can try out the exam system’s built-in calculator, which you can open by clicking the 'Calculator' button (or by using the keyboard shortcut Shift + Alt + L or Cmd + Shift + L). Hide the calculator by clicking the 'X' icon (or by using the keyboard shortcut Shift + Alt + L or Cmd + Shift + L). Hiding the calculator does not erase the calculation displayed on the screen.

The exam system’s built-in calculator is not fully accessible with screen reader software. You may use, for example, the calculator integrated into your computer's operating system.

Symbols used in the questions:

% percent sign

^@ degree symbol

_ subscript sign

− minus

/ division sign

* multiplication sign

= equals to

~D Capital delta, Greek letter

Decimals are written with a decimal point, for example: 1.5

Numbers of five digits or more are written with a comma as a thousand separator, for example: 98,000

Sample question 1

The energy used in a 100 kilometres car trip is about 15 kWh. Assuming that the energy content of the fuel is 10 kWh/litre and the efficiency of the engine is 33%, how many litres of fuel are needed for a 100 kilometres car trip? Choose the best alternative.

Sample question 2

In radioactivity, half-life refers to the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay. If the half-life is 1000 years, which of the following alternatives is the best approximation of the time, when 7/8 of nuclei have decayed and 1/8 are remaining?

Sample question 3

The energy Q\mathit {Q} needed to cause a change of temperature ΔT\Delta\mathit{T} to an object with mass m\mathit {m} , is given by

Q=cmΔT\mathit{Q}=\mathit {c} \mathit {m} \Delta\mathit{T}

Here c\mathit {c} is the specific heat capacity of the object’s material. Assume that 20,000 J of energy is required to rise the object’s temperature by 2 degrees Celsius. Assume also that the mass of the object is 10 kg. What is the specific heat capacity of the material?

The energy Q needed to cause a change of temperature ~DT to an object with mass m, is given by

Q =c m ~DT

Here c is the specific heat capacity of the object’s material. Assume that 20,000 J of energy is required to rise the object’s temperature by 2 ^@C. Assume also that the mass of the object is 10 kg. What is the specific heat capacity of the material?

Sample question 4

What is the simplified form of the following expression?

z(z+2)−(z−2)z\mathit{z}(\mathit{z} +2)-(\mathit{z} -2) \mathit{z}

What is the simplified form of the following expression?

z (z +2) −(z −2) z

Sample question 5

Solve the equation for K1\mathit{K }_ {1} :

H=5bK2+K1 \mathit{H}=\dfrac{5\mathit{b}}{\mathit{K }_{2}+\mathit{K }_ {1}}

Solve the equation for K_1:

H =5 b /(K_2 +K_1)