Past SAT Math, GAT / Qudurat, and AP Calculus AB weekly challenges collected for focused review, solution analysis, and smarter practice.
Each archived challenge was previously published through the StudyGlitch Weekly Math Challenge system. Use the archive to revisit solution paths, compare trap answers, and connect the result to diagnostic-style SAT, GAT, and AP math practice.
2 past weekly challenges found. Open one card at a time for the full solution review.
Solve an SAT data analysis question by choosing the best linear model for a scatterplot.
Statistics and Data Analysis / Choosing an appropriate linear model from a scatterplotWhich of the following equations is the most appropriate linear model for the data shown?
A.
d = −48.1 + 2.02tUse a visible point on the trend line and test the model.
The graph shows a positive slope of about 2, so all choices have the same reasonable slope 2.02. To choose the model, test the intercept using a visible point. Around t = 230, the line is near d = 416.
For choice A:
d = −48.1 + 2.02(230)
d = −48.1 + 464.6 = 416.5
This matches the graph closely, so the appropriate model is d = −48.1 + 2.02t.
Because each answer choice has the same slope, the decision depends on the intercept. Choice A gives a predicted value near the line at the left side of the graph, while the other choices produce values much too high.
A common mistake is choosing the option with the largest intercept because the graph values are large. The variable t is also large, so the intercept must be interpreted through substitution.
The trap is reading the intercept as if t = 0 were visible on the same scale.
If this was difficult, it may show a weak spot in connecting graphs to equations.
This SAT statistics and data analysis question tests interpreting scatterplots and linear models.
For model-choice questions, plug in a visible coordinate from the graph.
Since all choices have slope 2.02, test only one visible point.
Practice an AP Calculus AB particle motion question about finding maximum speed from a velocity graph.
Applications of Differential Calculus / Interpreting speed as the absolute value of velocityThe object attains its maximum speed when t=
D.
3Speed is the absolute value of velocity.
The graph shows velocity, not speed. The speed is |v(t)|. The largest magnitude of velocity shown occurs at t=3, where v=-10. The speed there is 10, which is greater than the speed at the other listed times.
Although the velocity is negative at t=3, the speed is positive and equals the magnitude of velocity.
A common mistake is choosing where velocity is greatest rather than where speed is greatest.
The trap is ignoring negative velocity values when comparing speed.
If this was difficult, it may reveal weakness in particle motion vocabulary.
This AP Calculus AB applications question tests velocity and speed interpretation.
For particle motion, remember that speed is |v|.
Look for the point farthest from the t-axis.
