GED (General Educational Development) Mathematical Reasoning Flashcards

24 sample cards from the Mathematical Reasoning deck

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

1. Describe the substitution method for solving a system of equations.

   Solve one equation for one variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute.

2. Describe the elimination (addition) method for solving a system of equations.

   Multiply equations as needed so one variable's coefficients are opposites, add the equations to eliminate that variable, solve, then back-substitute.

3. How many solutions does a system have if the lines are parallel versus identical?

   Parallel lines: no solution. Identical (same) lines: infinitely many solutions.

4. In the coordinate plane, what does the ordered pair (x, y) represent?

   x is the horizontal distance from the origin (right positive, left negative); y is the vertical distance (up positive, down negative).

5. In which quadrant are both coordinates positive, and how are the quadrants numbered?

   Quadrant I has both positive (upper right); quadrants are numbered I–IV counterclockwise starting from the upper right.

6. What is the slope formula given two points (x₁, y₁) and (x₂, y₂)?

   slope m = (y₂ − y₁) / (x₂ − x₁), i.e., rise over run.

7. What is the slope-intercept form of a line, and what do its parts mean?

   y = mx + b, where m is the slope and b is the y-intercept (where the line crosses the y-axis).

8. What are the slopes of horizontal and vertical lines?

   A horizontal line has slope 0; a vertical line has an undefined slope.

9. How do the slopes of parallel lines compare to those of perpendicular lines?

   Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals (product = −1).

10. What is the definition of a function in terms of inputs and outputs?

    A function assigns exactly one output (y) to each input (x); no input value may have more than one output.

11. What is the vertical line test?

    If any vertical line crosses a graph more than once, the graph is not a function.

12. How can you compare the rate of change of two linear functions given as a table and an equation?

    Find each function's slope (change in y over change in x for the table; the coefficient of x for y = mx + b) and compare those values.

13. What is a key first step when solving a math word problem?

    Identify what is being asked and the relevant given information, translate words into a mathematical expression or equation, then solve and check units.

14. What are the formulas for the perimeter and area of a rectangle?

    Perimeter P = 2l + 2w; Area A = l × w.

15. What are the formulas for the circumference and area of a circle?

    Circumference C = 2πr (or πd); Area A = πr².

16. What is the formula for the area of a triangle?

    A = ½ × base × height.

17. What is the formula for the volume of a rectangular prism (box)?

    V = length × width × height (V = lwh).

18. What is the formula for the volume of a cylinder?

    V = πr²h (area of the circular base times the height).

19. What is the difference between volume and surface area of a solid?

    Volume measures the space inside (cubic units); surface area measures the total area of all outside faces (square units).

20. State the Pythagorean theorem and what its variables represent.

    a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse (the side opposite the right angle).

21. How do you convert between units, such as feet to inches, using a conversion factor?

    Multiply by a fraction equal to 1 that cancels the unwanted unit (e.g., 5 ft × 12 in/1 ft = 60 in).

22. How do you find the mean, median, and mode of a data set?

    Mean: sum of values ÷ number of values. Median: the middle value when ordered (average of two middle values if even count). Mode: the most frequently occurring value.

23. What does the range of a data set measure, and how is it calculated?

    Range measures spread; it equals the largest value minus the smallest value.

24. What is the basic probability formula for a single event?

    P(event) = (number of favorable outcomes) / (total number of possible outcomes), giving a value from 0 to 1.

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Mathematical Reasoning flashcards FAQ