Advanced Punctuation & Style
This punctuation mark can only follow a complete independent clause to introduce a list, explanation, or direct quote.
What is a colon?
For the quadratic equation ax² + bx + c = 0, this formula gives the x-coordinate of the parabola's vertex.
What is -b / (2a)?
In a scientific experiment, this is the variable that the researcher intentionally manipulates or changes.
What is the independent variable?
When solving an algebraic inequality, you must flip the inequality symbol whenever multiplying or dividing by this.
What is a negative number?
To prove an argument or hypothesis completely false using counter-evidence.
What is refute? (or: disprove)
Identify the error: "Either the students or the coach have forgotten the equipment."
What is subject-verb agreement? (or: 'have' should be 'has')
If a line has a slope of 3, this is the slope of any line perpendicular to it.
What is -1/3? (or: negative one third)
On standard scientific graphs, the independent variable is almost always plotted along this axis.
What is the x-axis? (or: the horizontal axis)
The test strategy of picking simple numbers like 2, 3, or 100 to replace abstract variables in complicated word problems.
What is plugging in numbers? (or: substitution)
Existing or present everywhere simultaneously; often used to describe modern technology or smartphones.
What is ubiquitous?
The term for a run-on sentence that improperly joins two independent clauses using only a comma without a conjunction.
What is a comma splice?
The value of x that makes the rational fraction (x - 4) / (2x - 10) undefined.
What is 5?
Estimating a data value that extends beyond the range of tested experimental points on a line graph is called this.
What is extrapolation?
Factoring x² - 49 into (x - 7)(x + 7) is an example of this high-frequency algebraic pattern.
What is difference of squares?
Acting purely out of selfless concern for the well-being of others, opposite of selfish.
What is altruistic?
Standardized writing tests prefer the concise phrase "Although it rained" over this wordy, passive phrase starting with "Despite the fact."
What is conciseness? (or: What is redundancy / wordiness?)
In a right triangle, if the side opposite angle θ is 6 and the hypotenuse is 10, this is the value of sin(θ).
What is 0.6? (or: 3/5)
In a drug trial, the group receiving a placebo rather than the active medicine is called this.
What is the control group?
If a question asks for (2x + 5), solving for x and selecting that value without calculating (2x + 5) is falling into this trap.
What is answering the wrong question? (or: not solving for the requested expression)
Dealing with matters sensibly and realistically, based on practical considerations rather than theoretical ideals.
What is pragmatic?
Identify the flaw: "Maya Angelou's poetry is more widely read than Emily Dickinson."
What is an illogical comparison? (or: comparing poetry to a person instead of poetry to poetry)
In trigonometry, the fundamental identity states that sin²(θ) + cos²(θ) always equals this constant number.
What is 1?
The ACT Science passage type where two or more researchers debate contradictory hypotheses explaining the same event.
What is Conflicting Viewpoints? (or: Scientist 1 vs. Scientist 2)
A mathematically derived answer that makes the original equation false or undefined when plugged back in.
What is an extraneous solution?
A statement that seems contradictory or impossible on the surface, but reveals a deeper truth upon examination.
What is a paradox?