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2004 PSAT Corrections - Math 4

2004 PSAT Corrections - Math 4. In the figure, which of the following line segments has a slope of 2? A. PA B. PB C. PC D. PD E. PE. 59%. This slopes UP 2 and over 1. B. C. D. E. PD goes up 5 and over 1. PB slopes down instead of up. A. P. PA slopes down instead of up.

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2004 PSAT Corrections - Math 4

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  1. 2004 PSAT Corrections - Math 4

  2. In the figure, which of the following line segments has a slope of 2? • A. PA • B. PB • C.PC • D. PD • E. PE 59% This slopes UP 2 and over 1. B C D E PD goes up 5 and over 1 PB slopes down instead of up. A P PA slopes down instead of up. PC is a vertical line

  3. When the 3 Adams children went to school one morning, they each took one of the other’s lunches. In how many ways could the 3 children have been paired with the lunches so that no one took his or her own? • A. One • B. Two • C.Three • D. Six • E. Eight 31% O X X O O X

  4. When the 3 Adams children went to school one morning, they each took one of the other’s lunches. In how many ways could the 3 children have been paired with the lunches so that no one took his or her own? • A. One • B. Two • C.Three • D. Six • E. Eight 31% X O O X X O

  5. 30% • If x and y are positive, which of the following represents x percent of y? • A. 0.01xy • B. 0.1xy • C. xy • D. 10xy • E. 100xy One way to think about this is as individual percents. 1% equals .01, so a certain percent (x) of y would be both of those variables times 1% or 0.01. The ? represents the equation we are looking for x i 100 ? y = Cross multiply xy = 100? xy 100 Divide both sides by 100 = ? Dividing by 100 is the same as multiplying by one hundredth. 0.01xy = ?

  6. 35% • In the xy-plane below, the circle has center O. Which of the following lines will divide the circle into two semicircles? • I. The line with equation y = x • II. The line with equation y = 4x • III. The line with equation y = 1 • A. I only • B. III only • C.I and II only • D. I and III only • E. I, II, and III ✔ ✔ y = 4x y = x (0, 3) O y = 1

  7. If (x4)5 = xa for all values of x, what is the value of a? 20 When you raise an exponent to another power, you just MULTIPLY them. 4(5) = 20

  8. In a straight line, the distance between Rockfield and Nearburg is 18 miles; between Nearburg and Carbonville the distance in a straight line is 13.4 miles. What is the least possible distance, in miles, from Rockfield to Carbonville? 4.6 Carbonville 13.4 miles Rockfield 18 miles Nearburg 18 - 13.4 = 4.6

  9. Let x△y be defined as x△y = xy - (x + y) for all positive integers x and y. What is the value of (4△2)△3? 987 Funky symbol problem! Order of operations stays the same 10 △ 3 x = 10 y = 3 x = 4 y = 2 42 - (4 + 2) 103 - (10 + 3) 16 - 6 = 10 1000 - 13 = 987

  10. The figure shows some circles, each measuring 2 inches in diameter, placed at one end of a 50-inch line segment. If there are 1-inch spaces between consecutive circles and the center of each circle is on the segment, what is the maximum number of circles that can be placed on the 50-inch line segment? 17 2 1 2 1 2

  11. 17 2 1 2 1 2 Each circle and space unit is 3 inches 50 ÷ 3 = 16⅔ Sixteen FULL units will fit on a 50 inch line 16 x 3 = 48 We will have 2 inches left over... … which is just enough room to fit one more circle!

  12. In the figure, each of the 16 small squares is to be colored red, blue, or green. • All squares in row 1 will be the same color. • All squares in column 1 will be red. • There will be an even number of blue squares. • There will be an even number of green squares. • No green square will share a common side or vertex with a red square. • What is the greatest possible number of squares that could be colored green? 2

  13. 2 • All squares in row 1 will be the same color. • All squares in column 1 will be red. • There will be an even number of blue squares. • There will be an even number of green squares. • No green square will share a common side or vertex with a red square. • 1 • 2 • 3 • 4 • 1 One of these has to be red since there is an even number of blue & green squares We need a couple of blues to separate the greens from the reds. • 2 • 3 • 4

  14. In the sequence above, each term after the first is equal to ⅓ the term immediately before it. What is the value of the first tem in the sequence that is less than 1/20? 1/45 27 5 1 5 3 15 9 5 3 5 1 5 1 15 = , , , ... , 3 15 1 15 ÷ = 3 ⅓ of this is ⅕. Rewrite this so it’s easy to divide by 3 This isn’t smaller than 1/20

  15. In the sequence above, each term after the first is equal to ⅓ the term immediately before it. What is the value of the first tem in the sequence that is less than 1/20? 1/45 27 5 1 15 3 45 9 5 3 5 1 5 1 15 = , , , ... , 1 45 3 45 ÷ = 3 Rewrite this so it’s easy to divide by 3

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