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International UAS Exam, example questions of advanced mathematical skills

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.

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Example 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.

Example 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?

Example question 3

A box is lying in the back of an accelerating lorry. It is not attached, and it is only kept in place by friction. Which of the following pictures best describes the forces acting on the box? The lorry is accelerating towards the left.

Example question 4

Which of the following graphs illustrates the motion with constant acceleration?

In the graphs, symbol x\mathsf{\mathit {x}} signifies place, symbol v\mathsf{\mathit {v}} signifies velocity, symbol a\mathsf{\mathit {a}} signifies acceleration and symbol t\mathsf{\mathit {t}} signifies time.

Example question 5

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?

Example question 6

What is the simplified form of the following expression?

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

Example question 7

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

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

Example question 8

A robot’s arm (the red line segment in the picture) is fixed to point A according to the picture below. The length of the arm is adjustable. When length of the arm is 23 cm, it reaches point B in the picture. What is the length of the arm, when the other end reaches point C in the picture? Give your answer to the nearest centimetre.

Picture 8