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# Tip #44 to Get a Top ACT Math Score (page 3)

By McGraw-Hill Professional
Updated on Sep 7, 2011

On average, after memorizing and practicing Skills 44 and 45 for avoiding careless errors, most students gain 2 points on their ACT Math score! So learn these strategies.

### Most Common ACT Math Careless Errors

1. Practice being focused, yet relaxed. You don't need to be tense and a wreck to excel on the ACT or in life. You can be intense and work quickly, yet be relaxed. In fact, being intent and focused, yet calm and clear will help you avoid errors. Be fully present with each question: focused, relaxed, awake, and mindful. See "Yoga," page 66.
2. (2x)2 = 4x2, not 2x2.
3. Square both the 2 and the x.

4. –2(3x – 3) = –6x + 6, not –6x – 6.
5. Remember to distribute the –2 to both the 3x and the –3.

6. = x + 4, not x + 20.
7. Remember that the 5 is under not only the 5x, but also the 20.

Let's look at this question:

Solution: Nice functions review! Remember the key to functions on the ACT—whatever is in the parentheses gets plugged in for x. So, f(2p) just means plug in 2p for x. So f(2p) = 3(2p)2 = 3(4p2) = 12p2. Careless Error Busters: Remember that the 2 gets squared. Also remember order of operations, multiply 3 times 4 after squaring 2.

### Medium

1. (9x – 3) – (3x + 6) is equivalent to
1. 3(x + 3)
2. 3(2x + 3)
3. 3(2x – 3)
4. 3(3x – 1)
5. 3(x – 3)
2. If f(x) = –2x3, which of the following expresses f(–p)?
1. –2p
2. 2p3
3. –2p3
1. 8p3
2. –8p3
3. 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
4. If, , find y when x = 3.
1. a – 15
2. 9a – 15
3. 9a – 5
1. a – 5
2. a – 3
5. ### Hard

6. 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
7. If f(x) = x(2x2 – 2), find f(–2p).
1. –16p3 + 4p
2. –8p3 + 4p
3. –8p3 – 4p
1. 16p3 – 4p
2. 8p3 + 4p

1. C Careless Error Buster: Remember to distribute the negative sign!
2. (9x – 3) – (3x + 6) = 9x – 3 – 3x – 6 = 6x – 9 = 3(2x – 3)

3. G 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 in the parenthesis and does not get cubed with the p.
4. A Plug in m =–1 and simplify. m(2x2 – 2) = –1(2x2 – 2) =–2x2 + 2. Careless Error Buster: Remember to distribute the negative sign!
5. J Plug x = 3 into the equation to get not a – 15. Careless Error Buster: Remember to also divide the 15 by 3.
6. 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 45 Preview: When you FOIL, remember the middle term!
7. F Another function review, this is a good day. This question is similar to question #2 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!

Go to: Tip #45