IB MATH AI SL, Paper 1, May, 2022, TZ1, Solved Past Paper

This question involves calculating the area of the roof of a doghouse that needs to be painted. The doghouse is described as having a front view composed of a square with an isosceles triangle on top. The total height of the doghouse is given as 1.35 meters, and the width is 0.9 meters. The base of the doghouse is a square, implying that the width of the square base is also 0.9 meters. The task is to determine the area of the two rectangular surfaces of the roof that are to be painted.

To solve this, you need to find the dimensions of the triangular part of the front view and use these to determine the slant height of the roof. The slant height will then be used to calculate the area of the rectangular surfaces of the roof. The problem requires understanding of basic geometry and trigonometry to find the necessary dimensions and calculate the area.

This question involves a vertical pole standing on horizontal ground. The bottom of the pole is designated as the origin, O, in a three-dimensional coordinate system. The top of the pole, labeled F, has coordinates (0,0,5.8), indicating that the pole is 5.8 meters tall. A rope is attached from the top of the pole, F, to a point on the ground, A, which has coordinates (3.2,4.5,0). The task is to find the length of the rope and the angle it makes with the ground.

This question involves a quadratic function that models the height of a baseball after it is hit by a bat. The function is given by:

$h(t)=-4.8t^2+21t+1.2$

where h(t) represents the height of the baseball in meters above the ground, and t is the time in seconds after the ball was hit. The function is quadratic, indicating that the path of the baseball is parabolic. The coefficients of the function provide information about the initial velocity and the acceleration due to gravity, which affects the ball's trajectory.

The question is divided into three parts, each focusing on different aspects of the function:

• Part (a): This part asks for the height of the ball at the instant it is hit by the bat, which corresponds to the initial condition of the function when t is zero.
• Part (b): This part requires finding the time t when the ball hits the ground, which involves solving the quadratic equation for when the height h(t) is zero.
• Part (c): This part asks for an appropriate domain for t in this model, which is the interval of time during which the ball is in the air.