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Tip #45 to Get a Top ACT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 7, 2011

Medium

1. If f(x) = 3x2, which of the following expresses f(4p)?
1. 12p2
2. 32p2
3. 48p2
4. 64p2
5. 144p2
2. In a timed run, Maiko posted a time of 1 minute 45 seconds for a quarter-mile course. If she could maintain that pace, how many minutes would it take her to run 1 mile?
1. 8.2
2. 7.0
3. 6.4
1. 5.8
2. 2.9
3. Hard

4. If x = 3y, then which of the following is equivalent to (x – 2)2?
1. 3y – 2
2. 3y2 – 4
3. 3y2 + 6y – 4
4. 9y2 – 12y + 4
5. 9y2 + 18y + 4
5. For functions p and r such that p(x) = 2x(x – 2) and r(x) = , find r(p(–4)).
1. 0.5
2. 10
3. 12
1. 14
2. 16
6. Josh rode his bicycle from his house to his grandmother's house at a rate of 10 miles per hour. Later that day he rode home at a rate of 15 miles per hour. If the round trip took a total of 30 minutes, how many miles does Josh live from his grandmother?
1. 0.3
2. 3.0
3. 4.0
1. 4.5
2. 8

1. C f(4p) means plug 4p in for x. So f(4p) = 3(4p)2 = 3(16p2) = 48p2. Careless Error Buster: Remember that the 4 gets squared before you multiply by 3. Order of operations, my man.
2. G Since she ran a quarter (one-fourth) of a mile in 1 minute 45 seconds, to determine her time for a full mile, we multiply by 4. And 1 minute 45 seconds times 4 is not (1.45)(4) = 5.8, it is (1.75)(4) = 7, since 45 minutes is three-quarters (0.75) of an hour.
3. D Plug in 3y for x in the expression (x – 2)2 to get (3y – 2)2 = 9y2 – 12y + 4. Careless Error Buster: When you FOIL a binomial, remember the middle term.
4. K Plug –4 into the p function: p(–4) = 2(–4)(–4 – 2) = 48. Then plug 48 into the r function: r(48) = =16. Careless Error Buster: Follow the order of operations.
5. B Most kids have a tough time with this one. The key is that the distance is equal for both trips, so we set the (rate)(time) equal for the way there and the way back:
6. (Rate)(time) = (rate)(time)

Since the total trip was 0.5 hour, if we call one way t, then the return trip we can call (0.5 – t).

Notice that we should use hours, not minutes, since rate is in miles per hour.

10(t) = (15)(0. 5 – t)

10t = 7.5 – 15t

25t = 7.5

t = 0.3 hour

Now remember, the question asks for how far Josh lives, NOT the time, so D = RT and D = 10 mph (0.3 hour) = 3 miles. Careless Error Buster: Finish the question, don't stop with t = 0.3. Remember to ask, "Did I finish the question?"

Go to: Tip #46