GRE General Quantitative Reasoning Flashcards

24 sample cards from the Quantitative Reasoning deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the midpoint formula for the segment joining $(x_1,y_1)$ and $(x_2,y_2)$?

   $$\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right).$$

2. How are the slopes of parallel lines and of perpendicular lines related?

   Parallel lines have equal slopes ($m_1=m_2$). Perpendicular lines have slopes that are negative reciprocals: $m_1\cdot m_2=-1$.

3. What is the general shape and vertex form of a quadratic function's graph?

   The graph of $y=ax^{2}+bx+c$ is a parabola. In vertex form $y=a(x-h)^{2}+k$, the vertex is $(h,k)$; it opens upward if $a>0$ and downward if $a<0$.

4. How do you compute a composite function value $f(g(x))$?

   First evaluate the inner function $g(x)$, then substitute that result into $f$. For example, if $f(x)=x^{2}$ and $g(x)=x+1$, then $f(g(3))=f(4)=16$.

5. What are complementary and supplementary angles?

   Complementary angles sum to $90^{\circ}$; supplementary angles sum to $180^{\circ}$.

6. What is the relationship between vertical angles formed by two intersecting lines?

   Vertical (opposite) angles are congruent—they have equal measure.

7. When a transversal crosses two parallel lines, what is true of corresponding and alternate interior angles?

   Corresponding angles are equal, alternate interior angles are equal, and co-interior (same-side interior) angles are supplementary, summing to $180^{\circ}$.

8. What is the sum of the interior angles of any triangle, and of a quadrilateral?

   The interior angles of a triangle sum to $180^{\circ}$; those of a quadrilateral sum to $360^{\circ}$.

9. What is the sum of the interior angles of a polygon with $n$ sides?

   $$\text{sum}=(n-2)\times 180^{\circ}.$$

10. State the Pythagorean theorem and name a common Pythagorean triple.

    For a right triangle with legs $a,b$ and hypotenuse $c$: $a^{2}+b^{2}=c^{2}$. A common triple is $3\text{-}4\text{-}5$.

11. What is the circumference of a circle with radius $r$?

    $$C=2\pi r=\pi d,$$ where $d=2r$ is the diameter.

12. What is the area of a circle with radius $r$?

    $$A=\pi r^{2}.$$

13. How do you find the arc length and sector area for a central angle of $\theta$ degrees?

    Arc length $=\dfrac{\theta}{360^{\circ}}\cdot 2\pi r$ and sector area $=\dfrac{\theta}{360^{\circ}}\cdot \pi r^{2}$.

14. What is the inscribed angle theorem for a circle?

    An inscribed angle is half the central angle that subtends the same arc. Consequently, an angle inscribed in a semicircle is a right angle ($90^{\circ}$).

15. What is the area of a triangle, and the area of a parallelogram?

    Triangle: $A=\dfrac{1}{2}bh$. Parallelogram: $A=bh$, where $b$ is the base and $h$ is the perpendicular height.

16. What is the area of a trapezoid with parallel sides $b_1$ and $b_2$ and height $h$?

    $$A=\frac{1}{2}(b_1+b_2)h.$$

17. How do you compute the arithmetic mean (average) of a data set?

    $$\text{mean}=\frac{\text{sum of all values}}{\text{number of values}}=\frac{\sum x_i}{n}.$$

18. How do you find the median of a data set?

    Order the values; the median is the middle value if $n$ is odd, or the average of the two middle values if $n$ is even.

19. What are the mode and the range of a data set?

    The mode is the value that appears most frequently. The range is the difference between the largest and smallest values: $\text{range}=\max-\min$.

20. How is standard deviation interpreted, and what does a larger value indicate?

    Standard deviation measures how spread out data values are around the mean. A larger standard deviation indicates greater dispersion; a smaller one indicates values cluster near the mean.

21. What are the quartiles and the interquartile range (IQR)?

    Quartiles $Q_1$, $Q_2$ (median), and $Q_3$ divide ordered data into four equal parts. The interquartile range is $\text{IQR}=Q_3-Q_1$, the spread of the middle $50\%$ of the data.

22. What is the basic formula for the probability of an event $E$ with equally likely outcomes?

    $$P(E)=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}},\quad 0\leq P(E)\leq 1.$$

23. What is the addition rule for the probability of $A$ or $B$, and how does it simplify for mutually exclusive events?

    $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. If $A$ and $B$ are mutually exclusive, $P(A\cap B)=0$, so $P(A\cup B)=P(A)+P(B)$.

24. What is the multiplication rule for independent events, and the formula for the complement of an event?

    For independent events, $P(A\cap B)=P(A)\cdot P(B)$. The complement rule gives $P(\text{not }A)=1-P(A)$.

What this deck covers

Quantitative Reasoning flashcards FAQ