SSAT <- Upper Level SSAT <- Free SSAT Upper Level Math Practice Test 1 - 2011 - Math Achievement Free SSAT Upper Level Math Practice Test 1 - 2011 - Math Achievement 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 1234567891011121314151617181920 Free SSAT Upper Level Math Practice Test 1 - 2011 - Math Achievement 1 / 20 Bob is \(x\) years old, and Jerry is 5 years older. In terms of \(x\), what was the sum of their ages, in years, 4 years ago? \(2x + 3\) \(2x - 3\) \(x - 3\) \(x - 10\) Translate from English into math. Let Bob's current age be \(x\), and let Jerry's current age be \(x + 5\). To find their ages 4 years ago, subtract 4 years from each current age. 4 years ago, Bob was \(x - 4\) and Jerry was \(x + 5 - 4 = x + 1\). The sum of Bob's and Jerry's ages 4 years ago was: \((x - 4) + (x + 1) = 2x - 3\). 2 / 20 A game show contestant answered exactly 20 percent of the questions correctly. Of the first 15 questions, he answered 4 correctly. If he answered only one of the remaining questions correctly, which of the following may be true?I - There were a total of 20 questionsII - He answered 10% of the remaining questions correctlyIII - He didn't answer 9 of the remaining questions correctly I only I only I and II only II and III only I, II and III The contestant answered a total of 5 questions correctly. Using our percent formula, \( ext{Percent} imes ext{Whole} = ext{Part} \), we have: \( 20% imes ext{total number of questions} = 5 \). Multiply both sides of the equation by \( frac{100}{20} \), and the total number of questions equals 25. Thus, statement I is incorrect. For statement II, there were \( 25 - 15 = 10 \) questions remaining, and 1 of these 10 questions was answered correctly. So, he answered \( 10% \) of the remaining questions correctly, making statement II true. Finally, statement III is true because 1 of the remaining 10 was answered correctly, so 9 of these 10 were not answered correctly. Therefore, the correct answer is (D). 3 / 20 If \( C \) is the product of consecutive integers \( A \) and \( B \), then \( C \) must be greater than \( A + B \) a negative integer a positive integer an even integer an odd integer Let \( C = A imes B \). Pick two consecutive numbers for \( A \) and \( B \), such as 2 and 3. Their product is \( 6 \), which is positive. However, if we select 1 and 0, the product is 0, which is neither positive nor negative. Because the integers are consecutive, one of the integers must be even. Hence, the product of any two consecutive integers must be even. Therefore, the correct answer is (D). 4 / 20 A 40 percent discount is offered on all sweaters at Store S. If a cotton sweater is on sale for $54.00 and a wool sweater is on sale for $72.00, what was the difference in price of the sweaters before the discount? $16.00 $19.20 $20.00 $24.00 $30.00 The sweaters were sold for \( 100% - 40% \) of their original price. Using the percent formula, \( ext{Part} = ext{Percent} imes ext{Whole} \), we have \( 54 = 60% imes ext{old price} \). Converting \( 60]% \) to \( frac{60}{100} \) and solving gives an original price of \( $90 \) for the cotton sweater. Similarly, for the wool sweater, the original price was \( $120 \). Therefore, the difference in price before the discount is \( $120 - $90 = $30 \). 5 / 20 The maximum load that a railway car can carry is 18 tons of freight. If a train has 40 railway cars, and each of these carries \( \frac{5}{9} \) of a ton less than its maximum load, how many tons of freight is the train carrying? 604 697 7/9 640 5/9 648 660 Each car carries \( 18 - frac{5}{9} = frac{157}{9} \) tons of freight. Multiplying this by 40 cars gives the total freight: \( frac{157}{9} imes 40 = 697 frac{7}{9} \) tons. 6 / 20 In 2 hours, the minute hand of a clock rotates through an angle of 60° 90° 180° 360° 720° In one hour, the minute hand completes a full revolution of \( 360^circ \). In two hours, it revolves through two full circles, equating to \( 720^circ \). 7 / 20 Which of the following fractions is not more than one third? \(\frac{22}{63}\) \(\frac{4}{11}\) \(\frac{15}{46}\) \(\frac{33}{98}\) \(\frac{102}{303}\) A fraction is not more than \(frac{1}{3}\) if three times the numerator is not more than the denominator. Of the fractions listed, only \(frac{15}{46}\) has a numerator that is not more than \(frac{1}{3}\) of the denominator. 8 / 20 The length of each side of a square is \(\frac{2x+1}{3}\). The perimeter of the square is \(\frac{8x}{3} + 4\) \(\frac{8x+4}{3}\) \(\frac{2x}{3} + 4\) \(\frac{2x}{3} + 16\) \(\frac{4x}{3} + 2\) The figure is a square, so all four sides are equal in length. The perimeter is the sum of the lengths of the four sides. You could just multiply \(frac{2x+1}{3}\) by 4 to get the right answer. 9 / 20 The diagram shows a cube. The distance from A to X is 2 inches \(\sqrt{3} \) inches \(\sqrt{2} \) inches 1 inch \(\frac{1}{\sqrt{2}} \) inch The face of the cube is a square, 1 inch by 1 inch. Use the Pythagorean Theorem to find the length of the diagonal of the square: \(sqrt{2}\). 10 / 20 A motorist travels 180 miles to his destination at an average speed of 60 miles per hour and returns to the starting point at an average speed of 90 miles per hour. His average speed for the entire trip is 72 miles per hour 52 miles per hour 50 miles per hour 48 miles per hour 45 miles per hour The average speed for the entire trip is the total distance (360 miles) divided by the total time (5 hours), which yields 72 mph. 11 / 20 A snapshot measures 1 1/4 inches by 2 3/8 inches. It is to be enlarged so that the longer dimension will be 4 inches. The length of the enlarged shorter dimension will be \(2 \frac{1}{2} \) inches \(2 \frac{5}{8} \) inches 3 inches \(3 \frac{3}{8} \) inches \(7 \frac{3}{5} \) inches This is a proportion problem. Set up the proportion as follows: \(frac{1 frac{1}{4}}{2 frac{3}{8}} = frac{4}{x}\). Solving the proportion yields the enlarged shorter dimension as \(7.6 \) inches. 12 / 20 From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. Of the following, the ratio of the area of the circle to the area of the original square is closest in value to \(\frac{5}{8}\) \(\frac{2}{3}\) \(\frac{5}{7}\) \(\frac{7}{9}\) \(\frac{3}{4}\) To find the ratio of the circle to the area of the square, first find the area of each. The diameter of the circle equals the width of the square, which is 6 inches. The area of the circle is \(pi r^2\) and the area of the square is \(s^2\). The ratio is approximately \(frac{7}{9}\). 13 / 20 If the outer diameter of a metal pipe is 3.01 inches and the inner diameter is 2.21 inches, the thickness of the metal is 0.40 in 0.90 in 1.42 in 1.94 in 2.39 in The difference is 0.80 inches, but the outside diameter consists of two thicknesses of metal (one on each side). Therefore, the thickness of the metal is \(0.80 div 2 = 0.40\) inches. 14 / 20 A sports writer claims that her football predictions are accurate 40% of the time. During football season, a fan kept records and found that the writer was inaccurate for a total of 30 games, although she did maintain her 40% accuracy. For how many games was the sportswriter accurate? 5 15 20 40 60 If 40% of the games were predicted accurately, 60% of the games were predicted inaccurately. Let x = games played, then 0.60x = 30, giving x = 50 games played. Therefore, 50 - 30 = 20 games were won. Thus, the sportswriter was accurate for 20 games. 15 / 20 In a certain boys' camp, 40% of the boys are from New York State and 10% of these are from New York City. What percent of the boys in the camp are from New York City? 60% 50 % 33% 10% 4% Forty percent of the boys are from New York State, and 10% of them (0.10 of them) are from New York City. Therefore, 4% (0.40 x 0.10) of the boys in the camp are from New York City. 16 / 20 55 is to ____ as 110 is to 0.55. 0.275 0.900 4.50 9.00 22.5 This can be set up as a proportion where x is the unknown number: \(55:x = 110:0.55\). Note that 5 is one half of 110, therefore the denominators must also have the same relationship. One half of 0.55 is \(0.275\). 17 / 20 If \(n=\sqrt{30}\), then which of the following is true? 3 > n > 2 n = 4.5 5 < n < 6 n > 5 The square root of 30 is less than the square root of 36 (which is 6) and greater than the square root of 25 (which is 5). Therefore, \(n\) is between 5 and 6. 18 / 20 How would you move along the number line above to find the difference between two numbers? From E to B. From A to D. From B to D. From D to A. From B to E. To find the difference, you should move from the larger number to the smaller number. 19 / 20 How many sixths are there in \(\frac{3}{5}\)? \(2 \frac{3}{8}\) \(3 \frac{3}{5}\) \(4 \frac{1}{8}\) \(5 \frac{1}{5}\) 6 To find how many sixths are in \(frac{3}{5}\), divide \(frac{3}{5}\) by \(frac{1}{6}\). This is equivalent to multiplying by the reciprocal, resulting in \(frac{3}{5} times 6 = frac{18}{5}\) or \(3frac{3}{5}\). 20 / 20 Four games drew an average of 34,800 people per game. If the attendance at the first three games was 32,500, 35,000, and 38,000, how many people attended the fourth game? 33,700 37,000 39,000 40,500 43,000 Four games averaging 34,800 people per game total to 139,200 attendance. The total for the first three games was 105,500. Thus, the fourth game attracted \(139,200 - 105,500 = 33,700\) people. Your score is Follow us on socials! 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