SSAT <- Upper Level SSAT <- 2013 SSAT Mathematics Achievement Test (Quantitative 2) Practice Questions with Answers 2013 SSAT Mathematics Achievement Test (Quantitative 2) Practice Questions with Answers Share Quiz Get Embed Code Copy the code below to embed this quiz on your website: <iframe src="https://tutorone.ca/practice-test/?embed=true" width="100%" height="800" style="border: none; max-width: 100%;" data-source="tutorone" allowfullscreen></iframe> Copy Code 12345678910111213141516171819202122232425 2013 SSAT Mathematics Achievement Test (Quantitative 2) Practice Questions with Answers 1 / 25 Directions: Each question is followed by four suggested answers. Read cach question and then decide which one of the four suggested answers is best. Find the row of spaces on your answer document that has the same number as the question. In this row, mark the space having the same letter as the answer you have chosen. You may write in your test booklet. The polygon in Figure 1 has a perimeter of 35. If each side of the polygon has the same length, what is the length of one side? (Polygon in the figure is a trapezoid) 3 4 5 6 7 With a perimeter of 35 and 5. sides of equal length, the length of one side is \( frac{35}{5}\) = 7. 2 / 25 Mr. Suart sold peppermint candy to 18 customers and caramel candy to 33 customers. If 4 of these customers bought both types of candy, how many bought only caramel candy? 29 25 21 17 13 There were a total of 33 customers who bought caramel candy. Subtract from these from the 4 who bought both and you are left with the 29 who bought only caramel. 3 / 25 In a bag of 36 balloons, there is an equal number of balloons of each color. Which of the following CANNOT be the number of different colors in the bag? 2 3 4 5 6 Only factors of 36 (numbers that can be divided evenly into 36) can be the number of different colors in the bag. Since 5 is not a factor of 36, choice (D) is the correct answer. 4 / 25 Which of the following is a whole number less than 14 and also between 12 and 18? 11 12 12.5 13 14 The whole number must be less than 14 and also between 12 and 18. The only whole number that meets these criteria is 13 (choice D). 5 / 25 According to the graph in Figure 2, Susan spent about how many hours watching soap operas? 1 hour 2 hours 3 hours 4 hours 5 hours Soap operas take up 90 degrees out of a total of 360 degrees, which is one-fourth of the pie chart. Therefore, Susan spent about one-fourth of 12 hours, which is 3 hours, watching soap operas. 6 / 25 If \( R = 12 \), then what is \( \frac{1}{3} R \)? 27 20 16 12 8 To solve for \( R \), multiply both sides of the equation by 3, thus \( R = 36 \). Plugging 36 back into the expression \( frac{1}{3} R \) gives us: \( frac{1}{3} times 36 = 12 \). 7 / 25 Which of the following is closest to \( \frac{1}{4} \) of 49? 12 13 10 14 15 Calculating \( frac{1}{4} \) of 49 gives us approximately 12.25. Among the given options, the one that is closest is choice (A) which represents 13. 8 / 25 According to the graph in Figure 3, what was the average sales of Company M from 1993 to 1997? Figure 3 shows a line plot with sales for each year: (1993, $250,000), (1994, $260,000), (1995, $270,000), (1996, $260,000), (1997, $260,000). $250,000 $260,000 $265,000 $270,000 $275,000 To find the average, we sum the sales figures: $250,000 + $260,000 + $270,000 + $260,000 + $260,000 = $1,300,000. Dividing by 5 gives us an average of $260,000. 9 / 25 Which of the following is equal to \( 4 \oplus 5 \)? 3 4 3 1/5 3 4/5 20 This problem calls for substitution based on the operation defined as \( u oplus v = u - (1 - frac{1}{v}) \). For \( u = 4 \) and \( v = 5 \): \( 4 oplus 5 = 4 - (1 - frac{1}{5}) = 4 - (1 - 0.2) = 4 - 0.8 = 3.2. \) Therefore, the answer is choice (C) which can be represented as \( 3 frac{1}{5} \). 10 / 25 If \( a \oplus 3 = 2 \frac{1}{3} \), then what is \( a \)? 2/3 3 4 6 9 Substituting the values, we define \( u = a \) and \( C = 3 \), where \( a oplus 3 = 2 frac{1}{3} \). This can be expressed as \( a - (1 - 3) = 2 frac{1}{3} \). Thus, \( a - 3 = 2 frac{1}{3} \) leads to \( a = 3 + 2 frac{1}{3} = 3 + frac{7}{3} = 3 + 2.333... = 5.333... = 3 \). 11 / 25 In one and a half days, a point on the earth's surface rotates through an angle of approximately how many degrees? 90° 180° 360° 540° 720° A point on the earth's surface completes one full rotation (360°) each day. In one and a half days, the total angle rotated is \( 360° times 1.5 = 540° \). 12 / 25 Which of the following groups is arranged in order from smallest to largest? 3/7, 11/23, 15/32, 1/2, 9/16 3/7, 13/32, 11/23, 1/2, 9/16 11/23, 3/7, 15/32, 1/2, 9/16 15/32, 1/2, 3/7, 11/23, 9/16 1/2, 5/32, 3/7, 11/23, 9/16 To compare the sizes of the fractions, convert them to decimals or find a common denominator. The correct order from smallest to largest is \( frac{3}{7}, frac{13}{32}, frac{11}{23}, frac{1}{2}, frac{9}{16} \). 13 / 25 The rectangle below has a length three times as long as its width. If its width is \( x \), what is its perimeter? 6 2x^2 4x 6x 8x The length of the rectangle is \( 3x \). The perimeter \( P \) of a rectangle is given by the formula \( P = 2 times (length + width) = 2 times (3x + x) = 2 times 4x = 8x \). 14 / 25 This square has a side length of 1 inch. What is the diagonal distance from one corner to the opposite corner? 1 inch √2 inches √3 inches 2 inches 3 inches Using the Pythagorean theorem, the diagonal \( d \) of a square can be found using \( d = sqrt{(side^2 + side^2)} = sqrt{(1^2 + 1^2)} = sqrt{2} \) inches. 15 / 25 A plumber needs eight sections of pipe, each 3 feet 2 inches long. If pipe is sold only by the 10-foot section, how many sections must he buy? 1 2 3 4 5 Each section is 3 feet 2 inches long, which is equivalent to 38 inches. Therefore, 8 sections require \( 8 times 38 = 304 \) inches. Converting to feet, \( 304 \) inches is \( frac{304}{12} approx 25.33 \) feet. Since each section is 10 feet, the plumber needs to buy 3 sections. 16 / 25 The ratio of the area of the shaded part to the unshaded part is (image shows a square with side length X, shaded part covers a width of X/4 and length of X). What is the ratio? x:x/3 2:1 1:3 1:2 3:1 If the shaded area covers a width of \( frac{X}{4} \) and the length of the square is \( X \), then the area of the shaded part is \( frac{X}{4} times X = frac{X^2}{4} \). The unshaded part would be the remaining area of the square, which is \( X^2 - frac{X^2}{4} = frac{3X^2}{4} \). The ratio of shaded to unshaded is \( frac{frac{X^2}{4}}{frac{3X^2}{4}} = frac{1}{3} \). 17 / 25 An airplane on a transatlantic flight took 3 hours 40 minutes to get from New York to its destination, a distance of 2,000 miles. To avoid a storm, however, the pilot went off course, adding a distance of 400 miles to the flight. Approximately how fast did the plane travel? 655 mph 710 mph 738 mph 750 mph 772 mph Using the formula distance = rate × time, we can find the rate. The total distance traveled is \( 2,000 + 400 = 2,400 \) miles. The total time is 3 hours 40 minutes, which is \( 3 + frac{40}{60} = frac{11}{3} \) hours. Thus, rate \( = frac{2,400}{frac{11}{3}} approx 654.5 \) mph, which rounds to approximately 655 mph. 18 / 25 A photograph measuring 7" wide × 9" long must be reduced in size to fit a space that is 6 inches long in an advertising brochure. How wide must the space be so that the picture remains in proportion? 1 \( \frac{4}{7} \) inches 2 \( \frac{6}{7} \) inches 4 \( \frac{2}{3} \) inches 5 \( \frac{5}{7} \) inches 8 \( \frac{3}{4} \) inches This is a simple proportion problem. Let \( x \) be the unknown width. Setting up the proportion: \( frac{7}{9} = frac{x}{6} \). Cross-multiply: \( 9x = 42 \). Solving for \( x \) gives \( x = frac{42}{9} = 4frac{2}{3} \) inches. 19 / 25 The total area of the shaded part of the figure is (a figure shows a shaded square with a side length of 2 inches, containing an unshaded circle). \( \frac{2}{7} \) in² \( \frac{1}{2} \) in² \( \frac{6}{7} \) in² 1 \( \frac{3}{7} \) in² 2 \( \frac{1}{3} \) in² Subtract the area of the circle from the area of the square. The diameter of the circle equals the side length of the square. The area of the square is \( s^2 = 4 text{ in}^2 \). The area of the circle is \( pi r^2 = pi left(1right)^2 = pi text{ in}^2 \). So, the shaded area is: \( 4 - pi approx 0.86 text{ in}^2 \). 20 / 25 A certain population of microbes grows according to the formula \( P = A (2)^n \), where \( P \) is the final size of the population, \( A \) is the initial size of the population, and \( n \) is the number of times the population reproduces itself. If each microbe reproduces every 3 minutes, how large would a population of only one microbe become after 18 mins? 16 64 128 1,028 4,096 The population would reproduce 6 times in 18 mins - \( 2^6 = 64 \) 21 / 25 If \( z = y + 4 \), what does \( 4z + 3 \) equal? y + 7 4y + 15 4y + 17 4y + 19 Cannot be determined from the information given. Given \( z = y + 4 \), substitute to find \( 4z + 3 \). \( 4z + 3 = 4(y + 4) + 3 = 4y + 16 + 3 = 4y + 19 \). 22 / 25 If \( x \) is greater than 0 but less than 1, and \( y \) is greater than 2, which of the following is the least? \( \frac{y}{x} \) \( \frac{x}{y} \) \( xy \) \( \frac{1}{x-y} \) Cannot be determined from the information given. Choosing specific values for \( x \) and \( y \) can help solve this. Let \( x = frac{1}{2} \) and \( y = 3 \). For these values, we have: (A) \( frac{y}{x} = 6 \), (B) \( frac{x}{y} = frac{1}{6} \), (C) \( xy = frac{3}{2} \), and (D) \( frac{1}{x-y} = frac{1}{frac{1}{2} - 3} = frac{1}{-2.5} = -frac{2}{5} \). Since option D is negative, it is the smallest value. 23 / 25 In a restaurant, there are \( x \) tables that can each seat 4 people, and \( y \) tables that can each seat 8 people. What is the maximum number of people that may be seated? 4x + 8y 8x + 4y 12x + 12y 12xy 32xy If 4 people can sit at each of \( x \) tables and 8 people can sit at each of \( y \) tables, the maximum number of people that may be seated is \( 4x + 8y \). 24 / 25 Mrs. Smith bought 3 square pieces of fabric. A side of the largest piece is 2 times as long as a side of the middle one, and a side of the middle one is 3 times as long as a side of the smallest one. The area of the largest piece is how many times the area of the smallest piece? 112 81 36 9 3 Let the side length of the smallest piece be \( s \). Then the middle piece has a side of \( 3s \), and the largest piece has a side of \( 6s \). The area of the smallest piece is \( s^2 \), and the area of the largest piece is \( (6s)^2 = 36s^2 \). Therefore, the area of the largest piece is 36 times the area of the smallest piece. 25 / 25 Mr. Dali's car uses \( \frac{3}{2} \) gallons of gas each time he drives to work. If his gas tank holds exactly 9 gallons of gas, how many tanks of gas does he need to make 30 trips to work? 1 \( \frac{1}{2} \) 2 \( \frac{1}{2} \) 4 5 9 Determine the total amount of gas needed for 30 trips: \( frac{3}{2} times 30 = 45 \) gallons. Since his gas tank holds 9 gallons, Mr. Dali needs \( frac{45}{9} = 5 \) tanks of gas. Your score is Follow us on socials! 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