ged math practice test

A a high school equivalency exam designed for individuals who did not graduate from high school but want to demonstrate they have the same knowledge and skills as a high school graduate

Which expression is undefined over the real numbers?
  • A. (-3)^0
  • B. 0/4
  • C. |-2|
  • D. (-7)^(1/2)
Correct Answer & Rationale
Correct Answer: D

The expression (-7)^(1/2) is undefined over the real numbers because it represents the square root of a negative number, which does not yield a real result. Option A, (-3)^0, equals 1, as any non-zero number raised to the power of 0 is defined. Option B, 0/4, simplifies to 0, which is a defined real number. Option C, |-2|, equals 2, as the absolute value of any number is always defined and non-negative. Thus, only (-7)^(1/2) fails to produce a real number, making it the only undefined expression in this context.

Other Related Questions

The equation and the graph represent two linear functions. Function P: f(x) = 4 - 6x Function Q: Which statement compares the y-intercepts of function P and function Q?
Question image
  • A. The y-intercept of function P is -6 which is less than the y-intercept of function Q.
  • B. The y-intercept of function P is 4 which is equal to the y-intercept of function Q.
  • C. The y-intercept of function P is -6 which is greater than the y-intercept of function Q.
  • D. The y-intercept of function P is 4 which is greater than the y-intercept of function Q.
Correct Answer & Rationale
Correct Answer: D

Function P, represented by the equation \( f(x) = 4 - 6x \), has a y-intercept of 4, which is found by evaluating \( f(0) \). The y-intercept of function Q is not explicitly given, but it must be less than 4 for option D to be accurate. Option A incorrectly states that the y-intercept of P is -6. Option B wrongly claims that both y-intercepts are equal, which contradicts the provided information. Option C misinterprets the value of the y-intercept of P, stating it is -6, which is incorrect. Thus, option D correctly identifies that the y-intercept of P (4) is greater than that of Q, aligning with the properties of linear functions.
Factor completely: b^2 + 3b - 4
  • A. (b + 4)(b - 1)
  • B. (b - 2)(b - 3)
  • C. (b + 1)(b + 2)
  • D. (b + 3)(b - 1)
Correct Answer & Rationale
Correct Answer: A

To factor the expression \( b^2 + 3b - 4 \), we need two numbers that multiply to \(-4\) (the constant term) and add to \(3\) (the coefficient of \(b\)). The numbers \(4\) and \(-1\) satisfy these conditions, leading to the factors \( (b + 4)(b - 1) \). Option B, \( (b - 2)(b - 3) \), yields \( b^2 - 5b + 6\), which does not match the original expression. Option C, \( (b + 1)(b + 2) \), results in \( b^2 + 3b + 2\), also incorrect due to the wrong sign on the constant term. Option D, \( (b + 3)(b - 1) \), gives \( b^2 + 2b - 3\), which again does not match. Thus, only option A correctly factors the expression.
Which graph represents a function?
  • A. Option A
  • B. Option B
  • C. Option C
Correct Answer & Rationale
Correct Answer: B

To determine which graph represents a function, we apply the Vertical Line Test. This test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function. Option A fails this test, as a vertical line can intersect the graph at multiple points, indicating it is not a function. Option C also does not satisfy the criteria, showing multiple intersections with vertical lines. In contrast, Option B passes the Vertical Line Test, as any vertical line drawn will intersect the graph at only one point, confirming it represents a function.
Two points (a,b) and (c,d) are shown on a graph. Which of the following equations correctly represents the slope of the line that passes through these points.
Question image
  • A. (b-d)/(a-c)
  • B. (d-b)/(c-a)
  • C. (b-d)/(c-a)
  • D. (d-b)/(a-c)
Correct Answer & Rationale
Correct Answer: B

To determine the slope of a line passing through two points, the formula used is \((y_2 - y_1) / (x_2 - x_1)\). In this case, for points \((a, b)\) and \((c, d)\), we can label \((x_1, y_1) = (a, b)\) and \((x_2, y_2) = (c, d)\). Option B, \((d - b) / (c - a)\), correctly applies this formula, with \(d\) as \(y_2\) and \(b\) as \(y_1\). Option A, \((b - d) / (a - c)\), incorrectly reverses the subtraction for both \(y\) and \(x\). Option C, \((b - d) / (c - a)\), misplaces the order of \(y\) values, leading to an incorrect slope sign. Option D, \((d - b) / (a - c)\), also incorrectly reverses the \(x\) values, yielding an incorrect result.