AQR TSI Prep Skill Check

Front

What is the formula to find the number of rows of trees if there are 3x - 2 trees planted in each row and a total of 24x - 16 trees?

Back

The number of rows can be found using the formula: Number of rows = Total trees / Trees per row = (24x - 16) / (3x - 2).

Front

How do you calculate the probability of selecting a male from a group of males and females?

Back

Probability = (Number of males) / (Total number of people). For 4 males and 8 females, Probability = 4 / (4 + 8) = 4 / 12 = 1/3.

Front

What is the maximum height of a ball kicked from a height of 20 feet, modeled by the equation h(t) = 20 - 16t^2 + 32t?

Back

To find the maximum height, use the vertex formula for a quadratic equation. The maximum height occurs at t = -b/(2a) = -32/(2*-16) = 1. Plug t = 1 into h(t) to find h(1) = 20 - 16(1)^2 + 32(1) = 36 feet.

Front

What is the slope-intercept form of a line given two points, O(0,0) and C(6,9)?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (9 - 0) / (6 - 0) = 3/2. The equation of the line is y = (3/2)x.

Front

How do you set up an equation to find the number of sandwiches ordered if each person had either one soup or one sandwich?

Back

Let s = number of sandwiches and p = number of soups. The equations are: s + p = 18 (total people) and 7.75s + 4.50p = 113.50 (total cost).

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

How do you find the average of a set of numbers?

Back

Average = (Sum of all numbers) / (Total count of numbers).

Front

What is the definition of a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a ≠ 0.

Front

What is the formula for the probability of an event?

Back

Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes).

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, found using t = -b/(2a) for the function in the form f(t) = at^2 + bt + c.