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

Set f(x) = 0 and solve for x first

Answer

Factor the expression before substituting

Answer

Find the vertex before computing f(−2)

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 passing through every data point

Answer

The line with the steepest possible slope

Answer

A horizontal line through the median y-value

Question 3

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

Accepted Answer

Factor out 2 and isolate x²

Answer

Complete the square

Answer

Use the discriminant

Answer

Graph the parabola and read x-intercepts

Question 4

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

Accepted Answer

x + (x + 1) = 78

Answer

x × (x + 1) = 78

Answer

x + x = 78

Answer

x + (x + 2) = 78

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 largest angle equals the sum of the other two

Answer

Vertical angles are equal

Answer

The exterior angle equals 90°

Question 6

When a problem has a long, complicated setup but a simple numerical answer choice list, which strategy can save time?

Accepted Answer

Work backward from each answer choice to see which satisfies the problem

Answer

Always solve algebraically from scratch

Answer

Identify the largest answer as most likely correct

Answer

Reread the problem three times before attempting

Question 7

A student must find the area of a shaded region created by subtracting a smaller shape from a larger one. What is the correct strategy?

Accepted Answer

Calculate the large shape's area minus the small shape's area

Answer

Find the area of the smaller shape only

Answer

Average the two areas

Answer

Multiply both areas together