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

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

Answer

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

Answer

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

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

Graph both lines and visually compare steepness

Answer

Compare the A coefficients directly

Answer

Find the x-intercepts of both lines

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

The graph has a negative y-intercept on that interval

Answer

The slope of the function equals zero on that interval

Answer

The function values are all negative on that interval

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

To find the vertex of a parabola

Answer

To factor a quadratic into two binomials

Answer

To find the axis of symmetry

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

Set both squared terms equal to zero and solve

Answer

Expand the equation and use the quadratic formula

Answer

Graph the circle and measure the diameter

Question 6

A student has 3 minutes left and 4 problems remaining. Which time management strategy is best?

Accepted Answer

Skip to the easiest-looking problems first, then guess on the rest

Answer

Attempt all four in order regardless of difficulty

Answer

Spend all 3 minutes on the first problem

Answer

Leave all four blank to avoid errors

Question 7

A question involves simplifying the expression (3x²y)(4xy³). Which property is key?

Accepted Answer

Product of powers property (add exponents when multiplying like bases)

Answer

Distributive property

Answer

Quotient of powers property

Answer

Power of a power property