Tip #29 to Get a Top ACT Math Score (page 2)
When approaching a question, students often say, "I have no idea where to start!" This book, and this strategy especially, tells you where to start.
- When you see x2 – y2, factor it to (x – y)(x + y).
- When you see (x – 3)(x + 2), FOIL it to get x2 – x – 6.
- When you see , reduce it to .
- When you see , simplify it to or just 7.07.
- When you see , use your calculator (top divided by the bottom) to convert it to 0.875.
Note: x2 – y2 = (x – y)(x + y) is the ACT's favorite kind of factoring, memorize it!
These steps tell you where to go with a question. I have seen this strategy dramatically help students, especially kids who get stuck and don't know what to do next—this strategy tells you what to do next.
Let's look at this question:
Solution: When you see x2 – y2, factor it.
- x2 – y2 = 84
- (x – y)(x + y) = 84 Factor x2 – y2 to (x – y)(x + y).
- 6(x + y) = 84 Substitute in 6 for the (x – y), since (x – y) = 6.
- (x + y) = 14
Correct answer: E
- If x – y = 4 and z = 6x – 5 – 6y, then z = ?
- For x2 ≠ 49, = ?
- The expression is equal to which of the following?
- When = 8, a2 – 64b2 = ?
- C Great springboard question. When you see a question like this, ask yourself, "Self, how do these equations relate?" There must be a quick easy way to do this, that's how they design the ACT. That's where springboard comes in. It tells you to factor whenever you can–if you can factor, that's what they want you to do, it's how to get the question correct. When you factor the second equation, you get
- F The ACT loves x2 – 49. When you see x2 – 49, factor it to (x – 7)(x + 7). Then the next step becomes clear–springboard helps you see what to do next. You don't even need to see it all in advance, just take it one springboard step at a time. So once you write (x – 7)(x + 7), you see that there is an (x – 7) on top too. Rewrite (x – 7)2 as (x – 7)(x – 7), and reduce/eliminate one of the (x – 7)'s:
- C Nine out of ten kids freak out, guess, and move on. But if you translate fractions to decimals, it's so easy! I love this strategy! So
- F Springboard, baby! Springboard helps you see what to do next. Follow all our springboard rules: When you have two equations like this, ask, "How are they connected; what's the back door?" Just asking the question usually helps you find the connection. Then you notice that means that a = 8b. (When you see a proportion, cross-multiply. It's how the ACT works! It's always the way to get the answer.) Next springboard rule: "When you see x2 – y2, factor it to (x – y)(x + y)." Guaranteed, if you see a2 – 64b2, that's what you need to do. So a2 – 64b2 = (a – 8b)(a + 8b). Lastly, plug 8b in for a to get (8b – 8b)(8b + 8b) = 0, since 8b – 8b = 0. Nice. Now that was fun.
z = 6(x – y) – 5. Since we know that
x – y = 4, we plug in 4 for the x – y to get
z = 6(4) – 5 = 19. Nice!
Moral of the question: Always ask, "How do the two equations relate?"
Then, just convert the answer choices and choose the best fit. Choice C is correct because
Go to: Tip #30
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