Math I
Build connected understanding across quantities, equations, functions, coordinate geometry, congruence, and data.
- Problem types
- 659
- Practice variants
- 2,636
Page 19 of 19
Each problem type has four distinct practice variants. Open a preview to move among all four.
Determine whether a reported correlation coefficient is possible
Use technology to compute and interpret the correlation coefficient of a linear fit.
The correlation scale has fixed endpoints because standardized covariance cannot exceed perfect positive or negative linear alignment. Check every reported value against the closed interval from negative one to one; …
Preview problemClassify a statistical claim as correlational or causal
Distinguish correlation from causation.
Claim wording reveals the level of evidence being asserted. Phrases such as “tends to” or “is associated with” describe variables occurring together, while causal language says that changing one produces …
Preview problemDecide whether a study design supports causal conclusions
Distinguish correlation from causation.
Causal support comes from how groups are formed, not merely from a difference in their outcomes. When researchers randomly assign the treatment and otherwise handle groups alike, preexisting influences are …
Preview problemRewrite a cause-and-effect claim as an association claim
Distinguish correlation from causation.
Rewriting a causal claim requires preserving the variables and observed direction while lowering only the evidentiary force. Replace cause-and-effect verbs with tendency or association language, then state that the pattern …
Preview problemEvaluate whether evidence supports a causal claim
Distinguish correlation from causation.
Evaluate causal evidence by auditing the design before looking at which group scored higher. Assignment of the explanatory condition before the outcome, especially at random, reduces self-selection and confounding; an …
Preview problemInterpret a scatter plot association without overclaiming causation
Distinguish correlation from causation.
A scatter plot can describe direction, form, and strength without explaining why the pattern exists. Translate the axes into a contextual “tends to” statement, treating the cloud as an overall …
Preview problemSeparate reverse causation from confounding
Distinguish correlation from causation.
Reverse causation and confounding are different alternatives to a direct-effect story. Reverse causation flips the arrow between the two observed variables, while confounding introduces a third variable with separate arrows …
Preview problemSelect a common cause and map both arrows
Distinguish correlation from causation.
A credible common-cause explanation needs more than a vaguely related third variable. Draw two separate pathways from the candidate—one to each measured variable—and explain a plausible mechanism along both arrows; …
Preview problemUse time order to detect reverse causation
Distinguish correlation from causation.
Time order is a necessary test for causation: a proposed cause must occur before its effect. If the supposed outcome can precede and influence the supposed cause, the reverse direction …
Preview problemEvaluate direct, reverse, and common-cause models
Distinguish correlation from causation.
A two-variable association can be compatible with several causal diagrams. Test a direct pathway, a reverse-selection pathway, and a common cause separately, asking whether each could produce the same observed …
Preview problemChoose evidence that strengthens a causal claim
Distinguish correlation from causation.
To strengthen a causal claim, improve treatment assignment rather than merely enlarging an observational sample. Random assignment to treatment and control, a common prespecified outcome, and checks for adherence and …
Preview problem