ASVAB Practice Test 1 Mathematics Knowledge

Mathematics Knowledge Practice Notes

• To find the value of ( y ) in the equation ( y = \left(\frac{x^2}{4}\right) - 2 ) with ( x = 8 ), calculate to find ( y = 14 ).

• The cube of a number is calculated by multiplying the number by itself three times; thus, ( 5^3 = 125 ).

• To calculate ( 2.5 \times 33 ), perform multiplication to get 67.5.

• The fourth root of 16 is the number that, when raised to the power of four, equals 16; therefore, it is 2.

• A line that passes through points (0, -1) and (2, 3) has the equation ( y = 2x - 1 ).

• To add 12 yards and 14 feet, convert yards to feet, compute ( \frac{(12 \times 3) + 14}{5} ), resulting in 10 feet.

• The multiplication of powers of the same base can be simplified; ( x^3 \times x^4 = x^{(3+4)} = x^7 ).

• The expression ( (x + 4)(x + 2) ) can be expanded to ( x^2 + 6x + 8 ).

• ( 1.5 \times 10^3 ) results in ( 1,500 ).

• A prime number is defined as a number greater than one that has no positive divisors other than 1 and itself; 11 is prime.

• The mode of a data set is the number that appears most frequently; in the series 4, 4, 8, 8, 8, 10, 10, 12, 12, the mode is 8.

• If ( a = 4 ), calculating ( \frac{a^3}{a} ) gives ( \frac{64}{4} = 16 ).

• Factorial notation ( 5! ) denotes multiplying all whole numbers from 5 down to 1, yielding 120.

• For the equation ( (900 \times 2) \div 6 ), compute directly to find the answer of 300.

• Evaluating ( x^x(x) ) with ( x = 2 ), results in ( 2^2(2) = 8 ).

• The equation ( (5 + 1)(6 \div 3)(8 - 5) = (3 + 3)x ) simplifies to find ( x = 6 ).

• The product of square roots ( \sqrt{49} \times \sqrt{64} = 7 \times 8 = 56 ).

• To compare fractions and determine the largest, the largest among ( \frac{2}{5}, \frac{3}{8}, \frac{7}{10}, \frac{13}{16} ) is ( \frac{13}{16} ).

• Solving the inequality ( 2 + x \geq 4 ) gives the result ( x \geq 2 ).

• The circumference of a circle can be calculated using the formula ( C = 2\pi r ); with a radius of 12 feet, it approximates to 75 feet.

• The volume of an aquarium measuring 16 inches long, 8 inches deep, and 18 inches high is calculated as ( V = length \times width \times height = 2,304 ) cubic inches.

• Triangle ABC is classified as an equilateral triangle, indicating all sides and angles are equal.

• The total measure of angles in a trapezoid is consistently 360 degrees.

• Angles classified as complementary add up to 90 degrees.

• Converting percentages to fractions: 24% translates to ( \frac{24}{100} = \frac{6}{25} ).

• A cube's volume relates to its side length cubed; given a volume of 64 cubic inches, the surface area is 96 square inches.

• The sum of all integers from 1 to 300 can be derived using the formula for the sum of an arithmetic series, yielding 45,150.

Test your Mathematics Knowledge for the ASVAB with this practice quiz. This set of flashcards covers a variety of mathematical concepts and problems, helping you prepare effectively. Each question is designed to challenge your understanding and improve your problem-solving skills.