Tag Archives: ACT math

08.11.14
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Algebra 1, 2 – systems of equations

Q: 100 people are to be seated at 22 tables. Some tables seat 4 people and some seat 6 people. If no seats are empty, how many tables seating 4 people are there?
 
Answer: 16
Explanation:  Solve the system: x + y = 22; 4x + 6y = 100.  My ‘CRAMER’ program will solve this for you! The number of 4-person tables is the x-value of the solution.
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08.09.14
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Algebra 1 – distance

Q: To the nearest tenth, what is the distance between the points (-6,2) and (6,5)?
 
Answer:  12.4 
(Use the distance formula, and round to the nearest tenth.)
My TI-84 Plus program DISTANCE will find this value.
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08.07.14
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SAT – Counting and Ordering

Q: Bob has ten different books, but must choose only three to bring along on his vacation. In how many ways can Bob choose three books?
 
Answer: 120
Explanation: This is a combination (not permutation) problem, because the order of the books in Bob’s bag does not matter.  Find the nCr function on your calculator and enter ’10 nCr 3′.  On the TI-84 Plus, nCr is in MATH, PRB, 3.  Or, do this by hand using the formula for nCr.
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08.05.14
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Geometry – Volume

 

Q: What is the maximum number of boxes with dimensions 4”x5”x8” that can be packed into one large box with dimensions 20”x20”x24”?
Answer:  60

Explanation: First, decide that a whole number of small boxes will entirely fill the large box.  To do this, look at the dimensions and match them.  4″ fits into 20″ five times.  5″ fits into 20″ four times.  8″ fits into 24″ three times.  That means, you’ll get five rows of small boxes, four boxes per row, and three layers deep.  So, the quickest way to get the answer is to multiply 5x4x3 = 60.

BUT if you don’t notice that, just do (large volume)/(small volume).

Large volume = 20x20x24 = 9600

Small volume = 4x5x8 = 160

(large volume)/(small volume) = 9600/160 = 60

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08.03.14
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Geometry – Volume

Q: Two rectangular prisms have the same volume. Prism 1 has dimensions 4 ft, 5 ft, and 7 ft. Prism 2 has dimensions 14 ft, 4 ft, and x ft. What is the value of x?
Answer:  2.5

Explanation:  Volume of a rectangular prism = (L)(W)(H)

Volume 1 = (4)(5)(7) = 140

Volume 2 = (14)(4)(x) = 56x

Since the volumes are equal, 56x = 140.  x = 2.5

 

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08.01.14
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SAT – remainders

If summer begins on a Tuesday and ends 100 days later, on which day of the week does summer end?

Answer: Thursday

Explanation:  A week has 7 days.  Dividing 100 by 7, you get 14 remainder 2.  That’s 14 weeks and 2 days.  Beginning on a Tuesday, 14 weeks later would land on a Tuesday too.  Two more days brings you to Thursday.

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07.31.14
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Geometry – circles

Q: The area of a 45 degree sector of circle M is 100 square units. What is the area of circle M?

Answer: 800 square units

Explanation:  The 45° sector is exactly 1/8 of the circle. (45/360 = 1/8)

100 = 1/8 of the area of the whole circle.

The area of the whole circle is 800.

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07.28.14
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Algebra 1, 2 – systems of equations

Two cubes and one pyramid weigh 9 lb. Seven cubes and two pyramids weigh 24 lb. All cubes weigh the same, and all pyramids weigh the same. What is the weight of one pyramid?

 
Answer: 5 lb

Explanation:  Let x be the weight of a cube.  Let y be the weight of a pyramid. 

The first sentence becomes: 2x + y = 9. 

The second sentence is: 7x + 2y = 24. 

Solve this as a system of equations by any method you choose… substitution, elimination, Cramer’s Rule, etc.  Or use my TI-84 Plus program ‘CRAMER’.

x = 2, y = 5

‘y’ is the weight of one pyramid, so the answer is 5.

 

 

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07.26.14
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Geometry – prism

 How many vertices does a rectangular prism have?


Answer:   8
rectangularprismvertices

If you have trouble drawing it or visualizing it, consider this instead:  A prism has two identical bases.  All of the vertices are along the edges of the two bases.  Since a rectangular prism has rectangles for bases, each base will have 4 vertices.  Two rectangular bases will have 8 vertices total.

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07.24.14
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SAT – counting and ordering

Q: You are 18th in line and your friend is 34th in line. How many people are in line between you and your friend?

Answer:  15

No, not 16! Do 34-18=16, but then subtract one. Why? The 16 includes either the person you started with (you) or the person you ended with (your friend), and you don’t want to include either person in the count.

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