Tag Archives: SAT math

09.02.14
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SAT: Counting and Ordering

Q: How many ways are there to go from point A to point B on the rectangular prism below, by traveling only along exactly 3 edges of the prism?

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Answer: 6

Explanation: There are 3 ways to travel away from A, shown below in green. There are 2 ways to continue along each of these paths to B, shown in blue. That’s 3 x 2 = 6 paths to B along three edges of the prism. This is easier than making a mess of the diagram trying to draw all 6 paths (and making it hard to count them).

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09.02.14
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SAT – Counting and Ordering

Q:  When 5 people met for dinner, each person shook hands with each other person once.  How many handshakes happened?

Answer: 10

Explanation 1: Two people = a handshake.  This question is really ‘How many ways are there to choose 2 people from a total of 5, if the order is not important?’ It’s a combination question. Find the nCr function on your calculator. Type in 5 nCr 2. It’s 10. (There is a longer way to do it by hand, using the formula for nCr.)

Explanation 2: Person A shook hands with 4 people.  That’s  4 handshakes so far. Person B shook hands with 3 other people (his shake with A has already been counted). Person C shook hands with 2 other people.  Person D shook hands with 1 other person (E). Add: 4 + 3 + 2 + 1 = 10.

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09.01.14
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Algebra 1 – Find the equation of a line

Q:  Find the equation of the line that has the following intercepts:

x-intercept: 5,   y-intercept: -3

Answer:  y = 3/5 x – 3

Explanation:  The x-intercept is the point (5, 0).  The y-intercept is the point (0, -3).  Calculate the slope of the line passing through these points:

m= (0- -3)/(5 – 0) = 3/5

Using slope intercept form (y = mx + b), the equation is y = 3/5 x + b.  We just need to find b.  Or do we?  We could plug in an ordered pair and solve for b, but it’s not necessary.  We already have b, because in slope-intercept form, b always stands for the y-intercept.  So, b = -3.

The equation is: y = 3/5 x – 3

My TI-84 Plus program ‘LINES’ will find this equation for you, given the two intercepts.

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09.01.14
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SAT – Remainders

Q: When the positive integer b is divided by 5, the remainder is 1. When b is divided by 7, the remainder is also 1. If b is less than 100, what is the largest possible value for b?

Answer: 71

Explanation: b is an integer that is one more than a multiple of both 5 and 7.  The smallest such value is 35 +1 = 36.  But, we need the largest one less than 100.  The next common multiple of 5 and 7 is 70 (do 35 x 2), and the next one is 105 (35 x 3).  Use 70, and add 1.  71.

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09.01.14
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SAT – Number Properties

Q: A red light flashes every 10 minutes, and a blue light flashes every 6 minutes. If both lights flash together at 6:50 pm, when is the next time they will both flash together?
 
Answer:  7:20 pm
Explanation:  The least common mutiple of 10 and 6 is 30.  The light will both flash together again 30 minutes after 6:50, which is 7:20.
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09.01.14
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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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09.01.14
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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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09.01.14
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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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09.01.14
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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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08.27.14
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Geometry, SAT – angle relationships

Q: In the diagram below, what is the value of x?
 
 
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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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