IB DP Math MAI HL : IB Style Mock Exams – Set 5 Paper 1

Question

The shape of a vase is formed by rotating a curve about the y-axis.
The vase is 10 cm high. The internal radius of the vase is measured at 2 cm intervals along the height:

Use the trapezoidal rule to estimate the volume of water that the vase can hold

Answer/Explanation

Ans:

\(V=\pi \int_{0}^{10}y^2 dx\) OR \(\pi \int_{0}^{10}x^2 dy\)
h = 2
\(\approx \pi \times \frac{1}{2} \times 2 \times ((4^2+5^2)+ 2 \times (6^2+8^2+7^2+3^2))\)
= 1120 \(cm^3\) (1121.548…)

Question

 The ticket prices for a concert are shown in the following table.

  •  A total of 600 tickets were sold.
  • The total amount of money from ticket sales was $7816.
  • There were twice as many adult tickets sold as child tickets.

Let the number of adult tickets sold be x , the number of child tickets sold be y , and the
number of student tickets sold be z.

(a) Write down three equations that express the information given above.
(b) Find the number of each type of ticket sold.

Answer/Explanation

Ans:

(a) x + y + z = 600
15x + 10y + 12z = 7816
x = 2y

(b) x = 308, y = 154, z = 138

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