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.
41 past weekly challenges found. Open one card at a time for the full solution review.
Solve an SAT statistics question about how increasing sample size affects margin of error.
Statistics and Data Analysis / Understanding how sample size affects margin of errorA researcher is designing a study to investigate the average number of hours students at a high school spend reading per day. The researcher will report an estimated average number of hours students at the high school spend reading per day with an associated margin of error. The researcher is considering using a random sample of either 115 or 230 students from the high school. Which of the following would be the most likely effect of using the larger random sample compared to the smaller random sample?
A.
The reported margin of error would be lower.A larger random sample usually gives a more precise estimate.
Increasing the random sample size from 115 to 230 would most likely reduce sampling variability. A lower sampling variability means the associated margin of error would be lower.
The larger sample size affects the precision of the estimate, not the direction of the estimated average itself. The reported average could be higher or lower depending on the sample, but the margin of error is expected to decrease.
A common mistake is thinking a larger sample must change the reported average in a specific direction.
The trap is confusing margin of error with the sample mean.
If this was difficult, it may show a weak spot in sampling concepts.
This SAT statistics and data analysis question tests sampling and margin of error.
For margin-of-error questions, remember that larger sample size generally means smaller margin of error.
More data generally means a more precise estimate.
Practice an AP Calculus AB differentials question about the approximate change in area of a square.
Applications of Differential Calculus / Using differentials to approximate change in areaIf the side e of a square is increased by 1%, then the area is increased approximately
B.
0.02e2Use A=e2 and approximate the change with dA.
The area of the square is A=e2. A 1% increase in side length means de=0.01e. Since dA=2e,de,
dA=2e(0.01e)=0.02e2
The approximate change in area is found by multiplying the derivative of area with respect to side length by the small change in side length.
A common mistake is choosing 0.01e2, which treats the percent change in side length as the percent change in area.
The trap is forgetting that area changes approximately twice as fast percentage-wise as side length.
If this was difficult, it may reveal weakness in differential approximation.
This AP Calculus AB applications question tests linear approximation with differentials.
For small changes, use differentials: dA=A′(e)de.
A 1% change in e means de=0.01e.
Solve a medium GAT geometry question using the Pythagorean theorem and a 7-24-25 triangle.
Geometry / Using the Pythagorean theorem to find a missing sideA right triangle has hypotenuse 25 and one leg 7. What is the length of the other leg?
C.
24Use a2 + b2 = c2, where c is the hypotenuse.
Let the missing leg be x.
72 + x2 = 252
49 + x2 = 625
x2 = 576
x = 24
This is the classic 7-24-25 right triangle. Recognizing the triple makes the question very fast.
A common mistake is adding 7 and 25 or subtracting them directly. Side lengths in a right triangle are related through squares.
The trap is treating the hypotenuse like an ordinary side in addition/subtraction.
If this was slow, the improvement area is common right-triangle triples.
GAT right-triangle questions often become faster if you know common Pythagorean triples.
Recognize common triples like 3-4-5, 5-12-13, and 7-24-25.
If you recognize 7-24-25, solve instantly.
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.