Math Placement Test Practice Test Part 2

Tier 1 Answers and Explanations Whole Numbers and Fractions 1. ANSWER: a This problem uses the basic principle of multiplication. The shop offers 3 different activities for 2 days to choose from and offers 4 more different activities for the next 2 days. Since the question wants to know how many extreme sports are possible, and since there are 3 on one experience and 4 on the others, then 3 x 4 = 12. There are 12 possible extreme activities to choose from. 2. ANSWER: b This problem uses the formula for the area of a rectangle, A = l x w. In this case, the shape of the room is a square. So, the formula is modified, and the area of a square is A = s x s. To cover only half of the floor divide by 2. A = 11 x 11=121/2=60.5 sq. ft. 3. ANSWER: d Applying Least Common Multiple (LCM) will solve this problem. For example, at one Krispy Cremes, the sign will light up every 10, 20, 30, 40, 50, 60 minutes. At the next donut shop every 15, 30, 45, 60 minutes. Lastly, at the third shop every 20, 40, 60 minutes. So, when the signals “are ready” lights up at the same 9:00pm, it will be in every 60 minutes. The LCM for 10, 15, and 20 is 60. 4. ANSWER: a We can write figures 1 and 2 as fractions, 3/5 and 6/10. In order to add these two fractions, the denominators must be the same. You will need to find the Least Common Denominator (LCD) for fractions 3/5 and 6/10. Finding the multiples of 5, by counting by 5’s: 5, 10, 15, and so on. Finding the multiples of 10, by counting by 10’s: 10, 20, 30, and so on. Looking at the multiples of 5 and 10, 10 appears to be what both numbers have in common. Now we can use 10 to be the new denominator for each fraction. Since there is a new denominator, there should be a new numerator. The steps are as follows: 3 6 6 6 12 6      5 10 10 10 10 5 . Decimals 5. ANSWER: b Since each square is 1/100. Counting squares that are blue, there are 27. So, we can write this as a fraction, 27/100. 27/100 can be written as 27 hundredths. Then writing as an equivalent decimal, 0.27. Ratios, Rates and Proportions 6. ANSWER: c There are two ratios, 2 pints :4 liters and 6 pints (2 x 3, tripled the amount of sherbet): L liters. Using proportions, and setting the two ratios equal to each other, it follows, 2 6  4 L . By cross multiplying, 2 x L = 4 x 6. Multiplying both sides gives, 2L = 24. Solving for L, by dividing both sides by 2, gives, L = 12. So, it will take 12 liters of Ginger Ale for 6 pints of Lime Sherbet. 7. ANSWER: d To see if two ratios are in proportion, first make sure we are working with the same units, dollars to ounces. Then we set the two ratios equal to each other. Take the cross products of the numerator to denominator which must equal. This show proportions. The multiple-choice answers that are in proportion are a, b, and c. d is not in proportion because, 13 x 12 = 6 x 29 does not equal the same number. Therefore, the prices are not in proportion of each other. Percent 8. ANSWER: d By simply counting the unshaded blocks, there are 75 out of 100 blocks, unshaded. This represents 75% unshaded blocks. 9. ANSWER: b To find the discount price, you first multiply the discount rate x the original price. So, multiply, ($75.00 x .25 = $18.75, remember to change your percent to a decimal by dividing by 100. Therefore, by subtracting $18.75 from the original price of, $75.00, equals the discount price of $56.25. 10. ANSWER: a Note that since the discount is 40% of the original price, the price after the discount is 60% of the original price. The formula, Percent x Base = Amount can be used to find the original price, where Percent = 60% = 0.6, Base = original price, and Amount = $165. Substituting into the formula gives, 0.6 x original price = 165. Solving for the original price by dividing both sides of the equation by 0.6 gives $275. Measurements 11. ANSWER: c Start counting from the decimal point in the smaller unit, 87,000 mm and move 6 spaces to the left until you get to Km. Now move the decimal, in the number 87,000, 6 places to the left also. Since this is a whole number, the decimal is behind the last zero in 87.000 mm. The conversion is equal to 0.087Km. 12. ANSWER: c The two bottles must be in the same metric units. Convert 200ml to liters. Using Figure 5 above, this gives 0.2 L. Therefore, to find the difference, subtract, 0.2 from 3 and get, 2.8 L. 13. ANSWER: a Converting 56.8Kg to pounds, multiplying by 2.2, (1 kg = 2.2 pounds), therefore, Romiin weighs 124.96 pounds. Rounding to the nearest whole number, the answer is 125 lbs. Geometry 14. ANSWER: d The diameter of the tire is 2 times the radius, which is 34 inches. Using the formula above, C = 3.14 x 34 = 106.76. Rounding 106.76 to the nearest whole number gives 107. So, the circumference of the Lexus tire is 107 inches. 15. ANSWER: c 2  2 c 2 . Replace a and c in To find the missing side, b, use the Pythagorean theorem formula, a b the formula, with its respective values. Therefore, 2 2 2 a b  c 32 b2  52 9 b2 25 subtract 9 from both sides, 2 b  25  9 16 , take the square root of both sides, b 4 . 16. ANSWER: c Taking the square root of 169 13 . So, the positive root is +13. 17. ANSWER: c To find the perimeter of the polygon, add all sides around the shape. So, P = 4ft+8ft+4ft+4.5ft+14ft+5.6ft= 40.1 ft. Real Numbers 18. ANSWER: a Translated as a mathematical expression, denoted as, 8 32  6  4 8 9 6 4 Following PEMDAS, 8 3  4 24 4 , , 6 19. ANSWER: d Following PEMDAS, and look for representation of parentheses, working from left to right, take the square root of 36, take the absolute value of -50, left to right you add then subtract, 50 + 6 +35 56 + 35 91 50  6  70  3 , continuing PEMDAS, 20. ANSWER: b x Translated, we have, 4 9 Since x  4, 4 9 1 9 10 4 21. ANSWER: a By following orders of operations, and working from left to right, take the square of 4, by multiplying 4 times 4, and the same for 5 squared. Then subtract the two from each other, as follows: 16 – 25 = -9. 22. ANSWER: d Following orders of operations and working in parentheses first, subtracting the fractions gives, 6/6=1. Raising 8/9 to the zero power is 1. So 1 – 1 = 0. 23. ANSWER: c To write in expanded form, is, - 6 x 6 x 6 = - 216. The expanded notation is not (-6)(-6)(-6) = -216. Although the answer is the same, the number is a positive 6 and not a negative 6. Tier 2 Practice Test Questions Solving Equations and Inequalities 1. Solve the equation below for x, a. b. c. d. . x = -35 x = -17 x = 17 x = 35 2. Solve the equation below for y, a. b. c. d. x  9  26 41 y  90 . y = - 49 y = 131 y = 49 y = - 46 3. Solve, 7x + 11 = - 73. a. b. c. d. 12 13 -13 -12 4. Solve: a. b. c. d. 3 y 2  6 4 y = 7/8 y = 56 y = 8/7 y=8 5. Which equation gives a solution of all real numbers? a. b. c. d. x=1 x = -1 2x = 2x 2x = 3x 6. Which equation matches the following: Henry’s appetite is twice as big as Guy’s? Assume H represents Henry’s appetite and G represents Guy’s appetite. a. b. c. d. 2G = H GH = 2 2H = G 2+G=H 7. In the question above, if Guy can eat 2 full racks of baby back ribs, how many full racks of baby back ribs can Henry eat? a. b. c. d. 1 4 3 6 8. The diagram in Figure 9 below shows 4 graphs of inequalities. Which graph shows Figure 9 (Test continued on next page)  1 x 3 ? 9. An iguana has to keep its body temperature between 75 degrees and 95 degrees (Fahrenheit). Write this as an inequality, where x represents the iguana’s body temperature. a. b. c. d. x |x  75 and x | x 95  x | x 95   x | x 75  x |x  95  and x | x 75  h 28  2 10. When solving for h in and then graphing the solution, there will be [----blank----] on the number line. (Fill in the blank.) a. b. c. d. a closed circle an open circle an asterisk a small square Graphing 11. The coordinate plain allows us to plot points. These points are represented by ordered pairs, (x, y). x is called the domain and y is called the range. Given the following ordered pairs, (1,2), (4,6), (8, 10), (12, 14). What are the numbers in the domain? a. b. c. d. {2, 6, 10, 14} {1, 4, 8, 12} {1, 6, 8, 14} {2, 4, 6, 8} (Test continued on next page) 12. In Figure 10 below, Sponge Bob is drawn on the coordinate plane. In which quadrant is his red tie? a. b. c. d. I II III IV Figure 10 13. In a coordinate plane, in which quadrant will you find the ordered pair (-13,-5)? a. b. c. d. I II III IV (Test continued on next page) 14. Which of the graphs blow represents a linear equation? b. a. c. d. Figure 11 15. In Figure 11 below, what is the slope of the given line in simplest form? a. b. c. d. Slope is 2/4 Slope is ½ Slope is 4/2 Slope is 2/1 16. In the Figure 12 graph below, assuming lines n and o are parallel, which two lines are perpendicular? a. b. c. d. Lines m and o Lines n and o Lines l and m Lines m and A Figure 12 17. The formula, y = mx + b, can be used to identify the slope and y intercept of a line. Which variable in the formula represents the slope? a. y b. b c. x d. m 18. Determine the relationship between the lines, y = -2 and x = 5. a. b. c. d. The lines are diagonal The lines are supplementary The lines are parallel The lines are perpendicular Figure 13 19. In Figure 13 above, what is the slope of the blue line? a. The line doesn’t have a slope. b. m = 2 c. m = -2 d. m = 0 Exponents and Polynomials 20. Evaluate the expression a. b. c. d. 3x3  x 2 , where . 1/8 -3/8 -5/8 7/8 21. Given the polynomial expression a. b. c. d. 5 1 6 4 6 x4 5 x 1 , an example of a constant would be: 8x 7 5 x4 4 x 8 22. Add. 7  5  4  a. 3x 10 x 7 x 17 b. 11  x7 5 10  x 4 2 x  4 x 9 3x 7   10 x 5  7 x 17 5 3    c. 7 x 7 x 17 x 10  5  3   d. 7x 7 x 17 x 10 23. Consider a polygon whose side lengths are described by (x+3) , (x+7) , 2x, 8x, and (-6x-8). Find the perimeter of this polygon. a. b. c. d. 5x +1 3x - 8 2x + 6 6x + 2 (Test continued on next page) Concepts in Statistics 24.There are many types of graphical representations. Which graph records the number of observations in a set of data? a. A Frequency Table b. Bar Graphs c. Box and Whisker Plot d. Circle Graph 25. Find the mean of the following 5 NASCAR Motor Speedway tracks: Talladega 2.66 miles Pocono 2.5 miles, Atlanta, 1.54 miles, Bristol 0.533 mile, and Lowes (Charlotte) 1.5 miles. a. b. c. d. 1.074 miles 1.07445 miles 1.7466 miles 8.733 miles Figure 14 26. In Figure 14 above, the map shows several US hiking trails. What is the mode of the miles given for the trails? a. There is no mode. b. 751.43 miles c. 259 miles d. 2085 miles (Test continued on next page) 8 x 4 5 x2  4 x 7 Figure 15 27. In Figure 15 above, the square has the side length described by a polynomial expression. How many terms are this polynomial? a. 1 b. 2 c. 3 d. 4 (End of Tier 2 test)