SAT – Counting and Ordering

Q: Four people are to stand side by side for a photo. The shortest two people must stand at the ends, while the tallest two people must stand in the center. How many ways are there to arrange the people for the photo?
 
Answer: 4
Explanation: Use the Counting Principle.  Set up four blanks:
___  ___  ___  ___ to represent the four positions.
Decide on the number of possibilites for each position.
The first position has 2 possibilities (the 2 shortest people):
_2_  ___  ___  ___.  Whichever of the two shortest people isn’t in the first spot, will have to be in the fourth spot:
_2_  ___  ___  _1_.
Do the same for the middle two positions, using the two tallest people:
_2_  _2_  _1_  _1_.  Now, multiply these numbers together: 4.
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SAT – Volume

Q: A cylinder has a height of 20 cm and a diameter of 30 cm. To the nearest cubic centimeter, what is the volume of the cylinder?
 
Answer:  14,137
Explanation:  Use the formula for the volume of a cylinder, with r = 15 and h = 20.  Round to the nearest whole number.
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SAT – Percent change

Q: If the length of a rectangle is increased by 30%, while the width is decreased by 10%, by how much will the area increase? Give the answer as a percent.
 
Answer: 17%
Explanation:  Choose the length and width of the original rectangle to be 10.  Then, the length and width of the new rectangle are 13 and 9 (by increasing 30% and decreasing 10%).  The original area is 10 x 10 = 100.  The new area is 13 x 9 = 117.  The percent increase from 100 to 117 is (117-100)/100 = 17/100 = 17%.
Note that if this were an SAT problem with answer choices, you should immediately eliminate any ‘too easy’ answers, such as those related to the numbers 30 and 10 too directly.  Eliminate 20% and 40%.
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SAT / Algebra 1: Ratios

Q:  In my box of cereal, the ratio of flakes to raisins is 9:2. If there are a total of 220 flakes and raisins in the box, how many of these are flakes?
 
Answer:  180
Explanation:  Solve the equation: 9x + 2x = 220 to get x = 20.  ‘Flakes’ are the 9x part of the equation.  9(20) = 180.  Or, use my TI-84 Plus program ‘RATIO’.
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Geometry, SAT – angle relationships

Q: In the diagram below, what is the value of x?
 
 
198930_185618174816861_836602_n
 
 
Answer: 40
Explanation: The interior angle adjacent to 70 is 110. The other interior angle is 30 (from 180-150). Together, these two interior angles are 140. Subtract from 180.  The third angle of the triangle is 40.  x is a vertical angle to the 40, so it is also 40.
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SAT – systems of equations

Q: A phone call costs c cents for the first 10 minutes and n cents per minute for additional minutes. A 20-minute phone call costs 50 cents, and a 40-minute phone call costs 90 cents. What is the value of c?
 
Answer: 30
Explanation:  A 20-minute call costs c cents for the first 10 minutes and n cents per minute for each of the next 10 minutes.  So, c+10n=50.  A 40-minute call costs c cents for the first 10 minutes and n cents per minute for each of the next 30 minutes: c+30n=90.  Solve this system of equations.  Use my TI-84 Plus program CRAMER or an algebraic method such as substitution, elimination, Cramer’s Rule, etc.  c=30.
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SAT

Q: If seven squeeks equal one blip, and four blips equal one grrr, how many squeeks are equal to three grrrs?
 
Answer: 84
Explanation: One blip is 7 squeeks.  One blip is also 1/4 of a grrr.  So, 7 squeeks = 1/4 grrr.  Multiply both sides by 4 and you will get 28 squeeks = 1 grrr.  Multiply both sides by 3 and now 84 squeeks = 3 grrrs.
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Geometry – polygons

Q: What is the sum of the interior angles of a convex hexagon?
 
 Answer: 720
Use the formula (n-2)x180, with n=6 (because a hexagon has 6 sides).
(6 – 2) x 180
4 x 180
720
My TI-84 Plus program POLYGON will find this total for you.
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SAT – Remainders

Q: When the positive integer k is divided by 6, the remainder is 2. What is the remainder when k+2 is divided by 6?
 
Answer: 4
Explanation:  Choose a number for k that leaves a remainder of 2 when divided by 6.  For example, k = 8  (one group of 6, with 2 left, equals 8).  Now do k+2, or 10, divided by 6.  6 divides into 10 once, with 4 left.  The remainder is 4.  My TI-84 Plus program ‘REMAINDR’ will find this remainder for you.
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Geometry – Circles

Q: The radius of Circle M is twice as long as the radius of Circle N. What is the ratio of the area of Circle M to the area of Circle N?
 
Answer:  4:1 or 4/1. 
Explanation:  The ratio of the radii (2:1) is a length ratio. Square the length ratio to get the area ratio (4:1).  This works for all pairs of similar figures.
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