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 graph represents the solution of x + 5 ≤ 3?
  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D
Correct Answer & Rationale
Correct Answer: A

To solve the inequality x + 5 ≤ 3, we first isolate x by subtracting 5 from both sides, giving us x ≤ -2. Option A correctly represents this solution with a closed circle at -2, indicating that -2 is included in the solution set, and a shaded line extending to the left, showing all values less than -2. Options B, C, and D either depict open circles, which imply that the endpoint is not included, or incorrectly shade in the wrong direction or range, failing to accurately represent the solution x ≤ -2.

Other Related Questions

Which table shows a function?
  • A. Option A
  • B. Option B
  • C. Option C
  • D. Option D
Correct Answer & Rationale
Correct Answer: A

To determine which table represents a function, we look for a unique output for every input. Option A demonstrates this principle, as each input corresponds to a single output, confirming a functional relationship. In contrast, Option B features repeated inputs yielding different outputs, violating the definition of a function. Option C also presents multiple outputs for the same input, disqualifying it as a function. Lastly, Option D has inputs linked to multiple outputs as well, further indicating it does not represent a function. Thus, only Option A adheres to the criteria for a function.
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie. The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price. The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually. To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
Question image
  • A. $0.10
  • B. $4.38
  • C. $0.23
  • D. $4.28
Correct Answer & Rationale
Correct Answer: D

To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
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.
((5^3 * 2^4)^2)(5^(-2) * 2^5)
  • A. 5^3 * 2^11
  • B. 5^(-12) * 2^40
  • C. 5^4 * 2^13
  • D. (-5)^8 * 2^13
Correct Answer & Rationale
Correct Answer: C

To simplify the expression \(((5^3 * 2^4)^2)(5^{-2} * 2^5)\), first apply the power of a product rule. This gives \(5^{6} * 2^{8}\) from the first part. Next, combine this with the second part, \(5^{-2} * 2^{5}\). Adding the exponents for the base 5: \(6 + (-2) = 4\). For base 2: \(8 + 5 = 13\). Thus, the final expression simplifies to \(5^4 * 2^{13}\). Option A is incorrect as it miscalculates the exponents. Option B has incorrect exponents and signs. Option D introduces an unnecessary negative sign and does not match the simplified expression.