## 12/16/10

### 2010 PSAT - Wednesday - Section 2 (Math)

The following are TestTakers' suggestions for solving the problems on the October 13th, 2010 PSAT, Section 2 (a math section). Click "Read More" to view!

1. The easiest thing to do here is to solve for x and plug.
$2x + 4 = 8, 2x = 4, x = 2$
Plugging 2 into the equation gives you
$6(2) + 4 = 16$

2. "animals" is made up of mice, cats, and dogs in this problem. The total number of animals is 2 mice + 3 cats + 6 dogs = 11 animals. The ratio of cats to animals is just 3 cats / 11 animals. 3 to 11.

3. To find angle ACB, use the property of a straight line to determine that 110 + ACB must equal 180. ACB = 70.
Since a triangle has 180 degrees, x = 180 - 40 - 70 = 70

You could also backsolve. Starting with c), x = 50, which would make ACB = 90, (180 - 40 - 50 = 90). Since we need ACB to equal 70, that's too big. Move to a higher x value, which would give you a lower ACB value. d) x = 60, ACB = 80, still too big. e) x = 70, ACB = 70. Correct.

4. Of the 12 books, 3 are sold for \$5 (1 by Alex, 2 by Dana), 5 are sold for \$4.50 (2 by Alex, 3 by Dana), and 4 are sold for \$2.50 (4 by Alex, 0 by Dana). \$4.50 is the most frequently occurring sale price.

5. Convert both to the same unit, feet. 16 yards * 3 = 48 feet. 48 - 16 = 32.

6. Find the relationship between r and s. As s goes from 4 to 9 (increasing by 5), which answer also increases by 5?
$r^{2} / s = 1$
so which answer is directly proportional to s? $\inline r^{2}$

7. Plug in. As is the case with most percentage questions, plug in 100. Total customers = 100. If 20% chose black as their favorite car color, 20 out of the 100 chose black. 20 / 100 = 1 / 5

8. Vertical angles are always equal. Since RPQ = 40, TPU = 40. SPU = SPT + TPU. SPT = SPU - TPU. SPT = 70 - 40 = 30

9. f(x) = 2x. Take whatever is in the parentheses and multiply it by 2.

f(5t) = 2*5t = 10t

10. solve for expression!
ax + by = 14
+ ax - by = 4
= 2ax = 18, ax = 9

11. Equilateral triangle has equal sides. The perimeter is 18 so each side must equal 6. Because O is the center of the circle, each side of the triangle is also a radius of the circle. 2r = d. 2 * 6 = 12

12. Plug In! r = 2. 2(2) + 4 = 8 mph. At 8 mph, a car can travel 16 miles in 2 hours. e) 4r + 8 --> 4 * 2 + 8 = 16

13. Cut the figure into a rectangle and a triangle with the same base. The height of the rectangle is 4 and the base is 3. 3 * 4 = 12. The triangle has a base of 3 and a height of 6. (3 * 6) / 2 = 9. (12 + 9) = 21

14. Backsolve!
c) 10 < n =" 15." 6 =" 90" 60 =" 105">
d) n = 20. VV --> 20 * 6 = 120, GG --> 20 * 3 + 60 = 120. They're equal, but that doesn't count. GG is not cheaper.
e) n > 20. Say n = 21. VV --> 21 * 6 = 126, GG --> 21 * 3 + 60 = 123. Bingo!

15. Because triangles BCF and CDE are congruent, DE = CF = 3. CF + FE = CE --> 3 + 2 = 5. CE = BF = 5.
The area of the entire figure is the sum of the areas of the two triangles and the rectangle --> Area of triangle = 3 * 5 / 2 = 7.5. Area of rectangle = 2 * 5 = 10. 10 + 7.5 + 7.5 = 25

16. To get the largest value for one of the integers, the other 4 must be as small as possible.

Backsolve. Since this question is asking for the largest possible value, we start with e). 90 + 10 + 3 other distinct integers greater than 10, must equal 100. That is impossible since 90 + 10 is already 100, too big.
d) 10 + 84 = 94. too big
c) 10 + 64 = 74. The other 3 numbers must be 11, 12, and 13 (as small as possible while still being different and greater than 10). 74 + 11 = 85. 85 + 12 = 97. 97 + 13 = 110, too big.
b) 10 + 54 = 64. 64 + 11 + 12 + 13 = 100. Good.

OR

We know the smallest is 10. 10 + __ + __ + __ + __ = 100. Since each integer must be positive and different, the smallest combination of 4 of the 5 is:

10 + 11 + 12 + 13 + _x_ = 100. --> x = 100 - (10+11+12+13) = 54

17. Plug In! Start with x. If x = 6, y = 4, z = 3. x + y + z = 6 + 4 + 3 = 13
(x + y + z) / x = 13 / 6

18. Find the slope of the line first. m = (y1 - y0) / (x1 - x0) --> m = [(2) - (-5)] / [(3) - (/2)] = 7 / 5
To reflect each point about the line y = x means that the coordinates of each point would switch. Point A would become (-5, -2) and Point B would become (2, 3). The slope of that line would simply be the reciprocal of the original line. m = 5 / 7.

19. Plug In! Start with x. Choose a number that would make the equation easy to work with. In this case, it would be x =√5. This would make y = 1. 5(1) = (√5)(√5).

so (1)√5 / (5)√5 = 1/5

20. We need to isolate the # of popcorn containers sold. To do that, subtract the top line (popcorn + soda) from the bottom (just soda).

 a) 3 b) 4 c) 5 d) 6 e) 7 Change in popcorn & soda 325 – 275 = 50 350 – 325 = 25 375 – 350 = 25 325 – 375 = -50 375 – 325 = 50 Change in just soda 225 – 175 = 50 225 – 150 = -75 150 – 150 = 0 200 – 150 = 50 225 – 200 = 25 Change in popcorn 50 – 50 = 0 25 + -75 = 100 25 – 0 = 25 -50 – 50 = -100 50 – 25 = 25

B is the greatest.