Arithmetic and Algebra

Question 1

What is the most common algebra trap?

Answer 1

DOING THE MATH!

See if there is an alternative method

Question 2

Transform algebra from unknowns with…

Answer 2

real numbers. Mentally easier

Question 3

What is the verbiage signal for testing cases?

Answer 3

“must be” or “Could be”

Design cases with the intent of disproving answers

Question 4

What are the signals for “smart numbers”?

Answer 4

1. When given unknown values
2. When given relative values
3. “find a variable expression”

Question 5

What is the appropriate smart number when given a percentage?

Answer 5

100

Question 6

What are the signals to “work backwards”?

Answer 6

1. The answer represents a single variable as an actual value. Can be plugged in

Question 7

What is the step in “working backwards” when you’re about to pick an answer choice to attempt?

Answer 7

Selecting either B or D! If B is too low, test D… if D was too high it must be C. If D is still low, than the answer is E

Question 8

Tips when testing cases…

Answer 8

1. Test enough valid cases to prove definitively an answer
2. Start with small integers such as 1 or 0
3. Test weird properties like negatives, primes and fractions

Question 9

What would be ideal in testing a case with…
1. Abs value
2. Exponents

Answer 9

1. negative
2. Fractions

Question 10

Rules with “smart numbers”

Answer 10

Different than testing cases

1. Stick to normal, easy values.
2. Avoid 0 or 1
3. Avoid numbers that appear in problem or repeats in general

Question 11

What is a good start number when given a fraction…

Answer 11

a lowest common denominator

Question 12

What is a good start number when given a ratio…

Answer 12

steal the ratio!

Question 13

What is a good start number when told to divide or do a Rate/work word problem with…

Answer 13

a multiple of the divisor value that will yield an integer

Question 14

What is a good start number when given a variable underneath a radical…

Answer 14

An even square

Question 15

If an unknown value is indirectly asked for or referred to in the question…

Answer 15

pick a smart number following the same rules.
exp. all employees are paid the same hourly wage

Question 16

If the question says pick the lowest value out of a pair, and you observe the pair in the answer choice…

Answer 16

Work backwards ONLY with the lowest value, since obviously the greater value would be rejected due to the Q stem criteria