Mathematics Practice Exam Review

A complete set of vocabulary flashcards covering the mathematical definitions, properties, and core problem structures across all 10 exam questions.

Maximum Integer Element

The largest integer value attainable by the greatest member of a set constrained by given properties, evaluated from options $19$, $20$, $21$, and $23$.

Combined Mean Score

The weighted average score calculated across all participants in multiple distinct cohorts (Group A and Group B), given as $81$, used to find the student count ratio between Group A and Group B.

Divisibility Remainder System

The remainder generated when a positive integer $n$ is divided by a modulus such as $30$, determined from known remainders of $4$ when divided by $6$ and $6$ when divided by $10$ (yielding $16$).

Determinant of Matrix Power ($\det(A^2)$)

The determinant of a squared matrix $A^2$, equal to $36$, where matrix $A$ contains a real parameter $k$, used to determine the sum of all possible values of $k$.

General Form of a Circle Equation

An equation in the standard $(x, y)$ coordinate plane formatted as $x^2 + y^2 + 8x - 6y = 0$, which defines a circle with an area equal to $25\pi$ square coordinate units.

Concentration Mixing Ratio

The proportion of two liquid solutions required to produce a mixture of target concentration (such as $30\%$ acid by mixing Vessel A containing $20\%$ acid and Vessel B).

Concentration Label Error

A problem condition where Vessel B is mistakenly read as $50\%$ acid rather than its actual $45\%$ acid concentration, leading to an incorrect mixing proportion and altered actual concentration.

Similar Triangle Area-to-Side Ratio

The geometric relationship where line segment $ST$ is parallel to side $QR$ of triangle $PQR$, dividing it into triangle $PST$ (area of $25\,\text{square inches}$) and trapezoid $STRQ$ (area of $56\,\text{square inches}$), establishing the side length ratio $\frac{PS}{PQ} = \frac{5}{9}$.

Exponential Quadratic Equation

An equation of the form $4^x - 17(2^x) + 16 = 0$, solved via the substitution $u = 2^x$ to find all real values of $x$ ($x = 4$ and $x = 0$), whose sum equals $4$.

Tangent Circle to Intersecting Lines

A first-quadrant circle simultaneously tangent to the $x$-axis and the line $y = x$, whose center is located at a distance of $10$ units from the origin.

Imaginary Unit ($i$)

The unit defined by $i^2 = -1$, which cycles through powers of $i$, $-1$, $-i$, and $1$.

Sum of Cyclic Powers of $i$

The summation $i^1 + i^2 + i^3 + \dots + i^{53}$, which sums to $i$ due to every $4$ consecutive integer powers summing to $0$, leaving the final term $i^{53} = i$.