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# Tip #41 to Get a Top SAT Math Score

By McGraw-Hill Professional
Updated on Sep 10, 2011

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

5. , not x + 20
6. 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.

### 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

1. 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
2. If f(x) = x(2x2 – 2), find f(–2p).
1. –16p3 + 4p
2. –8p3 + 4p
3. –8p3 – 4p
4. 16p3 – 4p
5. 8p3 + 4p
3. f(x) = x(x – 2)

g(x) = 3x

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

1. B Nice function review! f(–p) means plug –p in for x. So f(–p) =–2(–p)3 =–2(–p3) = 2p3. Careless error buster: Remember that the 2 is not inside the parentheses and does not get cubed with the p.
2. A Plug in m =–1 and simplify. m(2x2 – 2) = –1(2x2 – 2) =–2x2 + 2. Careless error buster: Remember to distribute the negative sign!
3. D Plug x = 3 into the equation to get not a – 15. Careless error buster: Remember to also divide the 15 by 3.
4. E Plug 2p in for m and then FOIL (2p + 4)2. You can use the algebra trick for FOILing a binomial if you know it, and if you don't, no sweat, just do it out: (2p + 4)2 = (2p + 4) (2p + 4) = 4p2 + 8p + 8p + 16 = 4p2 + 16p + 16. Skill 42 preview: When you FOIL, remember the middle term!
5. A Another function review, this is a good day. This question is similar to number 3 above, but more involved. Plug –2p in for x: f(–2p) = –2p (2(–2p)2 – 2) =–2p(2(4p2) – 2) = –2p(8p2 – 2) =–16p3 + 4p. Careless error buster: Remember to distribute the negative sign!
6. 360. Serious functions review! Plug m in for x and 27 in for the result: 27 = 3m, so m = 9. Next, plug –2m, which we now know equals –18, into the f function: –18(–18 – 2) = –18(–20) =+360. Skill 42 preview: Finish the question, don't stop with m = 9. Remember to ask, "Did I finish the question?"

Go to: Tip #42