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Practice Question Answers

1. A In order to solve the problem use the following equation 56 x .43=$24.08. This question tests the candidate's ability to use the information presented in a word problem to answer a basic mathematical question. The solution requires a simple multiplication of the numbers provided. Answer B is incorrect because it yields the product of 56 x 43 if the candidate forgets to use the correct monetary unit. Answers C and D are incorrect. Neither provides the answer to the question. The only numbers given in the problem are 56 and 43, no combination of which will yield the results given in answer choices C and D.

2. B The question asks the candidate to demonstrate their knowledge of mathematical formulas to calculate areas and lengths. The formula that should be used is length+length+width+width, or 2 x length + 2 x width. This formula will yield the perimeter of a rectangle. Answer A is incorrect because it will give the area of a square or rectangle. The other two formula choices provided in answers C and D would not provide the perimeter of a rectangle. Answer choice C provides the circumference of a circle. Answer choice D does not provide a useable formula.

3. B In order to solve the problem candidates must use the following formulas 4 x 42.50=170; 170 x 10%=17; 170-17=$153. First, the candidate must calculate the total cost of the books which can be found by multiplying the number of books (4) by the cost of each book ($42.50). Once the total cost is found, candidates must find the amount of the discount. This is done by multiplying $170 x .10. This will yield a total discount of $17 which must be subtracted from the total cost of the books before the discount ($170).

4. C In order to answer this question, candidates must understand the way that elements are laid out on a coordinate plane. The vertices of a rectangle are linear and can be easily plotted on a grid. Candidates should use scratch paper to draw an XY axis with X-coordinates that span from -2 to 2 and Y-coordinates that span from 4 to -4. Because a rectangle is a linear shape, it is easy to determine the fourth vertex when the coordinates of the other three vertices are provided. This question tests a candidate's ability to plot points on a graph and to understand the linear structure of a rectangle.

5. D The problem must be solved using the following formulas 30 x 15=450 sq. ft.; ½ x 450=225 sq.ft. First, the candidate must calculate the entire area of the backyard by multiplying the length x width: 30x15=450. The student must know the formula for area and that area is measured in square feet. By multiplying ½ x 450 the candidate can calculate the exact amount of space that equals half of the entire yard's space. The result of 450 x ½ is 225. The deck must cover 225 square feet if Veronica and Sam want the deck to cover exactly half of the yard.

6. D In order to meet the criteria set up in question 5, the area of the deck must be 225 square feet. The area of a rectangle is calculated by multiplying the length of the deck by the width of the deck. Answers A, B, and C can be multiplied with the result of each pair being 225. The deck can measure 5x45, 9x25, or 22.5x10 and still take up the required 225 square feet of yard space. Answer D, when multiplied, results in a total area of 288 square feet. This is more than half of the yard space. The correct answer is D because it is the only set of dimensions that will not meet the requirements established in question 5.

7. B Candidates must be familiar with common statistical calculations such as mean, median, range, and mode. The mean is the total of all numbers divided by the quantity of numbers. Candidates may be given a set of numbers in a list form or in a more complicated form such as a chart or graph which they must interpret. Once the candidate is given a set of numerical data they must be able to employ the appropriate statistical formula. Given the numbers in this question, the formula is 10+12+8+5+2. This results in a total of 37 which must be divided by 5, which is the total of numbers in the list. 37/5=7.4 which is answer choice B.

8. C Candidates must be familiar with common statistical calculations such as mean, median, range, and mode. The mean is the total of all numbers divided by the quantity of numbers. Candidates may be given a set of numbers in a list form or in a more complicated form such as a chart or graph which they must interpret. Once the candidate is given a set of numerical data they must be able to employ the appropriate statistical formula. Given the numbers in the question, the range is found by locating the highest and lowest numbers in the list. Next, subtract the lowest number from the highest number. This will result in the range of the list of numbers.

9. A Candidates must use the chart pertaining to Mary's monthly budget. The chart shows the percentage of Mary's monthly income that is spent on specific items including utilities, gas, and rent. The most effective use of this chart requires that Mary's total monthly income be given. Question 9 states that Mary makes $2500 each month. Her monthly rent can be calculated by using the following equation 2500 x .25=$625. The candidate must be aware that the formula uses monetary units and percentages and they must take this into account when finding the answer.

10. C Candidates must use the chart pertaining to Mary's monthly budget. The chart shows the percentage of Mary's monthly income that is spent on specific items including utilities, gas, and rent. The most effective use of this chart requires that Mary's total monthly income be given. Question 10 states that Mary makes $2500 each month. The question also notes that there are 52 weeks in a year. First, find the amount spent on groceries each month by multiplying 2500 x 15%=$375. Next, find the amount spent on groceries each year by multiplying 375 x 12 because there are 12 months in a year. The result is $4500. Finally, divided $4500 by 52 weeks to determine the amount spent on groceries each week.

11. B Candidates must use the chart pertaining to Mary's monthly budget. The chart shows the percentage of Mary's monthly income that is spent on specific items including utilities, gas, and rent. The most effective use of this chart requires that Mary's total monthly income be given. Question 11 states that Mary makes $2500 each month. For each item on the chart, multiply $2500 by the percentage given. Add the results to find the total amount Mary uses each month. Now subtract that amount from $2500 to find the amount left over.

12. C Candidates must use the chart pertaining to Mary's monthly budget. The chart shows the percentage of Mary's monthly income that is spent on specific items including utilities, gas, and rent. The most effective use of this chart requires that Mary's total monthly income be given. Question 12 states that Mary makes $2500 each month. The candidate has already determined in question number 11 that Mary has $350 left over each month. If Mary has $350 leftover each month, 2/3 x 350=$233.33 which will be put into savings. Next, $350 - $233.33=$116.67 which is the amount left over.

13. A The basic formula for probability is P(E)=n(E)/n(S); E is the number of ways the event can occur, S is the total number of possible events. The formula reads the probability of the event equals the number of ways the event can occur divided by the total number of possible events. In this case, rolling a 5 on a dice that has 6 sides can occur only one way and the number of possible outcomes is equal to the number of sides on the die. So 1 divided by 6 is equal to 1/6.

14. D The basic formula for probability is P(E)=n(E)/n(S); E is the number of ways the event can occur, S is the total number of possible events. The formula reads the probability of the event equals the number of ways the event can occur divided by the total number of possible events. Two coins tossed could yield heads-tails, heads-heads, tails-heads, and tails-tails, so this means there are 4 possible outcomes. There are four possible outcomes and only one way to achieve two heads. Therefore, you have a one in four chance of getting two tails.

15. B Candidates must demonstrate knowledge of exponents. When multiplying exponential numbers, the exponents should be added together. When dividing exponential numbers, the exponents should be subtracted from each other. The exponents in question 15 are 9 and 3. Adding 9 and 3 results in 12. The correct answer is a¹². Answer C is the result of multiplying the exponents 9 and 3. Answer D is the result of dividing the exponents 9 and 3.

16. C This word problem provides information that the candidate must analyze and interpret. First find the number of calories left each day after Mike has consumed 3000 and used 1800. Use this formula 3000-1800=1200 net calories per day. Then multiply the number of calories left each day by the number of days. The formula is 1200 calories x 10 days= 12000 calories. Now divide 12000 by the number of calories in one pound. The question states that there are 3500 calories in a pound. 12000/3500=3.4 pounds. Mike will gain 3.4 pounds. In answer choice D, Mike would lose 3.4 pounds.

17. A This is a standard algebraic equation known as a linear equation. Each term is a constant or the product of a constant and one variable. It is possible for a linear equation to have multiple variables. The most common expression of a linear equation is y=ax+b. In this equation, x and y are the variables while a and b are the constants. This equation is considered linear because the solutions will form a straight line on a coordinate plane. The letter a represents the slope of the line and b is the point at which the line crosses the y-axis.

18. B This is a standard algebraic equation known as a quadratic equation. In a quadratic equation one or more of the terms is squared. The standard form of a quadratic equation is ax² + bx + c = 0. In this equation a, b, and c are constants. The letter x is the variable. This is called a quadratic equation because the root word quad means square and the highest exponent in the equation is a 2. A quadratic equation will produce a parabola on a graph.

19. D This is a standard algebraic equation known as an indirect variation. It may also be called an inverse variation. The equation is expressed as y=a/x. In this type of equation, y varies inversely with x. As x increases, y decreases or as x decreases, y increases. In other words, y will do the opposite of x. One is the dependent variable while the other is the independent variable. When graphing an indirect variation, the result is a hyperbola with a center at (0,0).

20. C This is a standard algebraic equation known as an exponential equation. In the equation y=a^x, x is the exponent and a is the constant. When graphing an exponential equation the result will always be positive and increasing, meaning it will be above the x-axis and increasing left to right. Candidates should know the basic equations of many algebraic equations. Candidates should also be able to identify the constants and variables within those equations as well as to describe the graph created by the equation.