# Geometry, SAT – angle relationships

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

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# SAT

Q: If seven squeeks equal one blip, and four blips equal one grrr, how many squeeks are equal to three grrrs?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Geometry – polygons

Q: What is the sum of the interior angles of a convex hexagon?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# Algebra 1 – distance

Q: To the nearest tenth, what is the distance between the points (-6,2) and (6,5)?

(Use the distance formula, and round to the nearest tenth.)
My TI-84 Plus program DISTANCE will find this value. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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?

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. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

# 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”?

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 