DSAT Problem Solving Strategies 4

Question 1

A problem states: 'If f(x) = 2x² − 3x + 1, what is f(−2)?' What is the correct order of operations?

Accepted Answer

Substitute −2 for x, then compute following PEMDAS

Answer

Function evaluation always means substituting the given input value for x and then simplifying using the order of operations.

Question 2

On the DSAT Math section, a question shows a scatterplot and asks for the line of best fit. A student should look for:

Accepted Answer

A line that minimizes the overall distance from points to the line

Answer

A line of best fit balances the data points on both sides, minimizing total deviation, even though it may not touch any single point exactly.

Question 3

To solve 2x² − 8 = 0 most efficiently, which strategy avoids the quadratic formula?

Accepted Answer

Factor out 2 and isolate x²

Answer

Factor out 2 to get 2(x² − 4) = 0, then x² = 4, giving x = ±2 in two quick steps.

Question 4

A word problem involves consecutive integers whose sum is 78. Which equation correctly models this?

Accepted Answer

x + (x + 1) = 78

Answer

Consecutive integers differ by 1, so representing them as x and x + 1 and setting their sum equal to 78 is the correct model.

Question 5

A DSAT problem gives angle measures in a triangle as x°, 2x°, and (x + 30)°. What property allows you to write an equation?

Accepted Answer

The sum of all three interior angles of a triangle is 180°

Answer

The Triangle Angle Sum Theorem states all three interior angles add to 180°, giving x + 2x + (x + 30) = 180.

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