DSAT Problem Solving Strategies 5

Question 1

A DSAT problem asks for the probability that a randomly selected student from a two-way table plays a sport AND is in 10th grade. What is the correct calculation?

Accepted Answer

(10th graders who play a sport) ÷ (total students)

Answer

For a joint probability (A AND B), divide the count satisfying both conditions by the total sample size.

Question 2

A student needs to compare the slopes of two lines given only their equations in standard form (Ax + By = C). What is the fastest method?

Accepted Answer

Rewrite each equation in slope-intercept form y = mx + b

Answer

Converting to y = mx + b isolates the slope m for direct comparison, which is more reliable than visual inspection or comparing raw coefficients.

Question 3

A DSAT problem states that a function is decreasing on an interval. What does this mean about the graph?

Accepted Answer

As x increases, y decreases on that interval

Answer

A decreasing function means that as you move left to right (x increases), the output values (y) fall.

Question 4

When should you use the discriminant (b² − 4ac) as a strategy on the DSAT?

Accepted Answer

To determine how many real solutions a quadratic equation has without fully solving it

Answer

The discriminant tells you the number of real solutions: positive → two real solutions, zero → one, negative → none, without needing to complete the full solution.

Question 5

A problem gives the equation of a circle (x − 3)² + (y + 2)² = 25 and asks for the radius. What is the quickest strategy?

Accepted Answer

Recognize the standard form and take the square root of 25

Answer

In standard circle form (x − h)² + (y − k)² = r², the radius is √25 = 5 by direct identification.

(DSAT) Digital SAT Practice Test

(DSAT) Digital SAT Practice Test

DSAT Problem Solving Strategies 5