Math Knowledge ASVAB Test 2024 With Complete Solutions

A: First, the distributive property must be used on the left side. This results in 3x + 6 = 14x -5. The addition property is then used to add 5 to both sides, and then to subtract 3x from both sides, resulting in 11 = 11x. Finally, the multiplication property is used to divide each side by 11. Therefore, x = 1 is the solution. - What is the solution? D: First, like terms are collected to obtain 12 - 5x = -5x + 12. Then, the addition principle is used to move the terms with the variable, so 5x is added to both sides and the mathematical statement 12 = 12 is obtained. This is always true; therefore, all real numbers satisfy the original equation. - What is the solution? E: The distributive property is used on both sides to obtain 4x + 20 + 6 = 4x + 6. Then, like terms are collected on the left, resulting in 4x + 26 = 4x + 6. Next, the addition principle is used to subtract 4x from both sides, and this results in the false statement 26 = 6. Therefore, there is no solution. - What is the solution? D: This is a one-step real-world application problem. The unknown quantity is the number of cases of cola to be purchased. Let be equal to this amount. Because each case costs $3.50, the total number of cases times $3.50 must equal $40. This translates to the mathematical equation 3.5x = 40 Divide both sides by 3.5 to obtain x = 11.4286, which has been rounded to four decimal places. Because cases are sold whole (the store does not sell portions of cases), and there is not enough money to purchase 12 cases, there is only enough money to purchase 11. - 4. How many cases of cola can Lexi purchase if each case is $3.50 and she has $40? a. 10b. 12 c. 11.4 d. 11 e. 12.5 A: First, the variables have to be defined. Let be the first integer; therefore, x = 1 is the second integer. This is a two-step problem. The sum of three times the first and two less than the second is translated into the following expression: 3x + (x + 1 -2). This expression is set equal to 411 to obtain 3x + (x + 1 -2) = 412. The left-hand side is simplified to obtain 4x -1 = 411. The addition and multiplication properties are used to solve for x. First, add 1 to both sides and then divide both sides by 4 to obtain x = 103. The next consecutive integer is 104. - 5. Two consecutive integers exist such that the sum of three times the first and two less than the second is equal to 411. What are those integers? a. 103 and 104 b. 104 and 105 c. 102 and 103 d. 100 and 101 e. 101 and 102 A: Let be the unknown, the number of hours Erin can work. We know Katie works , and the sum of all hours is less than 21. Therefore, x + 2x < 21, which simplifies into 3x < 21. Solving this results in the inequality x < 7 after dividing both sides by 3. Therefore, Erin can work lessthan 7 hours. - 6. Erin and Katie work at the same ice cream shop. Together, they always work less than 21 hours a week. In a week, if Katie worked two times as many hours as Erin, how many hours could Erin work? a. Less than 7 hours b. Less than or equal to 7 hours c. More than 7 hours d. Less than 8 hours e. More than 8 hours A: The chart is a bar chart showing how many men and women prefer each genre of movies. The dark gray bars represent the number of women, while the light gray bars represent the number of men. The light gray bars are higher and represent more men than women for the genres of Comedy and Action. - 7. From the chart below, which two types of movies are preferred by more men than women? a. Comedy and Action b. Drama and Comedy c. Action and Horror d. Action and Romance e. Romance and Comedy E: A line graph represents continuous change over time. The line on the graph is continuous and not broken, as on a scatter plot. Stacked bar graphs are used when comparing multiple variables at one time. They combine some elements of both pie charts and bar graphs, using the organization of bar graphs and the proportionality aspect of pie charts. A bar graph may show change but isn't necessarily continuous over time. A pie graph is better for representingpercentages of a whole. Histograms are best used in grouping sets of data in bins to show the frequency of a certain variable. - 8. Which type of graph best represents a continuous change over a period of time? a. Stacked bar graph b. Bar graph c. Pie graph d. Histogram e. Line graph C: The mean for the number of visitors during the first 4 hours is 14. The mean is found by calculating the average for the four hours. Adding up the total number of visitors during those hours gives 12 + 10 + 18 + 16 = 56. Then, 56 divide 4 = 14 - 9. Using the graph below, what is the mean number of visitors for the first 4 hours? C: The mode for a set of data is the value that occurs the most. The grade that appears the most is 95. It's the only value that repeats in the set. The mean is around 84.3. - 10. What is the mode for the grades shown in the chart below? B: The relationship between age and time for attention span is a positive correlation because the general trend for the data is up and to the right. As the age increases, so does attention span. - 11. What type of relationship is there between age and attention span as represented in the graph below?A: The area of the shaded region is calculated in a few steps. First, the area of the rectangle is found using the formula A =length x width = 6 x 2 = 12. Second, the area of the triangle is found using the formula: A = 1/2 x base x height = 1/2 x 3 x 2 = 3. The last step is to take the rectangle area and subtract the triangle area. The area of the shaded region is A = 12 -3 = 9m². - 12. What is the area of the shaded region? D: The volume for a cylinder is found by using the formula: V = (π x r²h = pi(2²) x 3.5 = 43.9in². - 13. What is the volume of the cylinder below? C: There are 0.006 kiloliters in 6 liters because 1 liter=0.001kiloliters. The conversion comes from the chart where the prefix kilo- is found three places to the left of the base unit. - 14. How many kiloliters are in 6 liters? E: The conversion between feet and centimeters requires a middle term. As there are 2.54 centimeters in 1 inch, the conversion between inches and feet must be found. As there are 12 inches in a foot, the fractions can be set up as follows: 3ft x 12in/1tft x 2.54cm/1in The feet and inches cancel out to leave only centimeters for the answer. The numbers are calculated across the top and bottom to yield: (3x12x2.5)/(1x1) =91.44 The number and units used together form the answer of 91.44 cm. - What is the solution? C: By switching from a radical expression to rational exponents,⁴√x⁶ = x^6/4 = x^3/2. Also, properties of exponents can be used to simplify x/x³ into x¹⁻² = x⁻² = 1/x².The other terms can be left alone, resulting in an equivalent expression x^3/2 - 1/x² + x - 2. - What is the solution? E: Using Descartes' Rule of Signs, count the number of sign changes in coefficients in the polynomial. This results in the number of possible positive zeros. The coefficients are 1, -3, 2, 1, and -3, so the sign changes from 1 to -3, -3 to 2, and 1 to -3, a total of 3 times. Therefore, there are at most 3 positive zeros. - What is the solution? A: 8 Exponent rule: a^b ×a^c = a ^ b+c The 16 and 16 combine and now were left with just adding the exponents. 1) 1/4+2/4= 3/4 2) 16^3/4 3) Factor 16 to 2^4 4) (2^4)^3/45) 4 x 3/4 = 3 6) 2^3 = 8 - What is the solution? B: 1) move 7 to the right side.