Tip #41 to Get a Top SAT Math Score

On average, after memorizing and practicing Skills 41 and 42 for avoiding careless errors, most students gain 20 to 30 points! So learn these strategies.

Most Common SAT Math Careless Errors

1. Practice being focused, yet relaxed. You don't need to be tense and a wreck to excel on the SAT or in life. You can be intense and work quickly, yet be relaxed. Be fully present with each question: focused, relaxed, awake, and mindful. See "A Yoga Posture for the SAT," page 60.
2. (2x)² = 4x², not 2x². Square both the 2 and the x.
3. –2(3x – 3) = –6x + 6, not –6x = 6.

Remember to distribute the –2 to both the 3x and the –3.

4. , not x + 20

Remember that the 5 is under not only the 5x, but also the 20.

Let's look at this question:

Solution: Nice functions review! This is SAT function question type I. The f(2p) just means plug 2p in for x. So f(2p) = 3(2p)² = 3(4p²) = 12p². Careless error buster: Remember that the 2 gets squared. Also remember order of operations: multiply 3 by 4 after squaring 2.

Correct answer: D

Example Problems

Medium

1. If f(x) = –2x³, which of the following expresses f(–p) ?
   1. –2p
   2. 2p³
   3. –2p³
   4. 8p³
   5. –8p³
2. When m = –1, which of the following is equivalent to m(2x² – 2) ?
   1. –2x² – 2
   2. –2x² – 2
   3. 2x² – 2
   4. 2x² + 2
   5. x² + 2
3. If, find y when x = 3.
   1. a – 15
   2. 9a – 15
   3. 9a – 5
   4. a – 5
   5. a – 3

Hard

4. If m = 2p, then which of the following is equivalent to (m + 4)² ?
   1. 2p + 4
   2. 4p² + 4
   3. 2p² + 8p + 16
   4. 4p² + 8p + 16
   5. 4p² + 16p + 16
5. If f(x) = x(2x² – 2), find f(–2p).
   1. –16p³ + 4p
   2. –8p³ + 4p
   3. –8p³ – 4p
   4. 16p³ – 4p
   5. 8p³ + 4p

f(x) = x(x – 2)

g(x) = 3x

6. For functions f and g above, if g(m) = 27, find f(–2m).