Tip #44 to Get a Top ACT Math Score

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.

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. = x + 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! 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.

Correct answer: J

Example Problems

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)?
   6. –2p
   7. 2p³
   8. –2p³
   10. 8p³
   11. –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.
   6. a – 15
   7. 9a – 15
   8. 9a – 5
   10. a – 5
   11. a – 3

Hard

5. 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
6. If f(x) = x(2x² – 2), find f(–2p).
   6. –16p³ + 4p
   7. –8p³ + 4p
   8. –8p³ – 4p
   10. 16p³ – 4p
   11. 8p³ + 4p