Tip #49 to Get a Top SAT Math Score

Learning mantras is like learning martial arts. Practice until they become part of you, until you follow them naturally: when you see a proportion, you cross–multiply; when you see a linear pair, you fill in the angles. … This will fundamentally change you as a math student. In fact, after SAT prep, many students begin to like math; they realize that they "get" it, and it stops being intimidating, and becomes easy. I've even seen kids overcome serious math phobias with the Mantras. Your SAT score and probably even your math class grades will go way up.

Here are the rest of the SAT Math Mantras. Check the box next to each one when you have mastered it. Reread the Skill sections if you need to.

Skill 21. "Use the Diagram" to estimate an answer. Translate into decimals any answer choices that contain √ or π.
Skill 22. When a diagram is not drawn to scale, redraw it. And when a picture is described, but not shown, draw it!
Skill 23. When you see a right triangle, try a² + b² = c².
Skill 24. When you see a 30°, 45°, or 60° angle in a right triangle, try using the special right triangles.
Skill 25. Similar triangles have sides that are proportional.
Skill 26. Translate word problems from English to math.
Skill 27. When something can be factored, FOILed, reduced, or simplified, … do it.
Skill 28. Memorize the laws of exponents.
Skill 30. For the equation y = mx + b or y = ax + b, m or a is the slope and b is the y intercept.
Skill 31. When you see an arrangement question, draw a blank for each position, fill in the # of possibilities to fill each position, and multiply.
Skill 32. When an arrangement question mentions a "restriction," fill in the restricted positions first. When it mentions a "team of two," divide your result by 2.
Skill 33. When you see "probability," use the equation Probability = .
Skill 34. When you see "median" or "mode," rewrite the data as a list in order.
Skill 35. For the equation y = ax² + bx + c, the a tells whether the U–shaped graph opens up or down, and the c is the y intercept.
Skill 36. Logic questions are easy long as you stay focused and do NOT get intimidated.
Skill 37. Remainders are what's left over when you use long division.
Skill 38. When you see absolute value, look for the less obvious answer.
Skill 40. To solve a sequence question, write the next bunch of terms until you have as many as you need or until you see a repeating pattern.
Skill 41. "Careless errors are bad mmmkay," so underline all vocabulary words and remember to finish the question.
Skill 45. When you see a weird symbol question: (1) relax, (2) remember that no one has seen this symbol before, and (3) follow the directions given in the question.

Let's look at this question:

Solution: Draw a simple diagram. Anytime a picture or a situation is described, draw it (Skill 22). It helps you to see what to do next and to avoid careless errors. Without a diagram, many students answer 14 or 15, but the diagram shows that in height order, Ahmed is the 7th in both directions, so there are 6 students on each side of him. Thus, 6 students on his right plus 6 on the left plus Ahmed equals 13 students total.

Correct answer: 13

Example Problems

Name the skill(s) that you can use, and then solve each question.

Easy

If m < 0, which of the following is greatest?
1. m
2. 3m
3. 6m
4. 9m
5. It cannot be determined from the information given.
If p < –1, which of the following is greatest?
1. p
2. 1 + p
3. 1 – p
4. p³
If m(x) = 2(3x)², what is the value of m(n) ?
1. 18 n²
2. 36 n²
3. 56 n²
4. 72 n²
5. 144 n²

Medium

If the Yoga Club has 42 members and the Dungeons and Dragons Live Action Role Playing Club has 25 members and there are 18 students that belong to both clubs, how many people total will be at a joint meeting of both clubs, if all members attend?
1. 18
2. 31
3. 49
4. 58
5. 67
If 4 less than half a number is equal to thirty percent of the number, what is 3 times the number?
1. 2
2. 5
3. 12
4. 30
5. 60
For the numbers in the data set {3, 5, 1, 7, 7, 3, 2, p, 1, 3,}, the median is 3 and the only mode is 3. Each of the following could be the value of p EXCEPT
1. 3
2. 4
3. 5
4. 6
5. 7

Hard

Set M consists of m members, and set P consists of p members. And r represents the number of members that belong to both set M and set P. If set Z consists only of members who belong to either set M or set P, but not both, which of the following could represent the number of members of set Z ?
1. m + p – r
2. m + p – 2r
3. m – p – r
4. m – p + 2r
5. m + p
If each of the five finalists in the world SAT Math Olympics will face each of the others in head–to–head competition, how many of these one–on–one matches will be played?

The dartboard shown above has a small circle, with radius 3.5, inside a larger circle, with radius 5. When Matty randomly throws a dart at the board, which of the following is closest to the probability that it will land in the shaded region?

If |x – 3| = 4 and |y + 2| = 3, what is the greatest possible value for x – y ?
1. –8
2. –2
3. 0
4. 6
5. 12

Answers

Misbehaving Numbers (Skill 43), and Make It Real (Skill 16). A. Negative numbers with larger digits are smaller. Let's say m = –3. Then choice B equals 3m = 3(–3) = –9. And –3 is actually larger than –9.
Misbehaving Numbers (Skill 43), and Make It Real (Skill 16). C. Let's say p = –3. 1 – p is largest since 1 – p = 1 – (–3) = 4, while all other answers are negative.
Avoid Careless Errors (Skill 41) and Functions (Skill 14). A. Plug n in for x: m(n) = 2(3n)² = 2 (9n²) = 18n². Remember to square the 3 as well as the n, and then multiply by 2.
Logic (Skill 36). C. There are 42 yogis and 25 dungeon crawlers, so it would seem there are 67 total; but 18 are in both clubs, and have been counted twice. So at the joint meeting there are really 42 + 25 – 18 = 49.
Translation (Skill 26), and Finish the Question (Skill 42). E. Translate the words into math and solve:

0.5x – 4 = 0.3x add 4 to both sides

0.5x = 0.3x + 4 subtract 0.3x

0.2x = 4 divide by 0.2

x = 20 remember to finish the question

3x = 60

Median and Mode (Skill 34), and Use the Answers (Skill 1). E. When you see a median or mode question, rewrite the data as a list in order. Then try each answer choice. Choice E cannot be the value for p because it will make 7 tied with 3 as the mode.
B Logic (Skill 36) or Make It Real (Skill 16). B. There seem to be m + p total members of sets M and P combined. Usually, we then subtract the common members (r) to determine the total, but in the "hard" question we subtract 2r since set Z contains no members that are in both. We are not just avoiding double-counting, but eliminating the common members entirely. So, set Z has m + p – 2r members.
Arrangements (Skills 31 & 32). 10. Since we have one-on-one competition, we have two spots to fill, so draw two blanks. Five competitors can fill the first slot, and four can fill the second slot. Then multiply 5 × 4 = 20. Because Juan playing Ezra is the same as Ezra playing Juan, we divide by 2 and get 20/2 = 10.
Probability (Skill 33), Donut Area (Skill 18), or Use the Diagram (Skill 21). C. Probability = , so the probability of hitting the shaded region is You could also just "Use the Diagram" and realize that no other answers make sense and that the shaded region being half the area of the larger circle is the only feasible answer.
Absolute Value (Skill 38) and Misbehaving Numbers (Skill 43). E. When you see an absolute value question, remember to consider not only the obvious answer, but also the less obvious one. x can equal 7 or –1, and y can equal 1 or –5. So the greatest possible value for x – y = 7 – (–5) = 12.

Go to: Tip #50

« prev page
1
2
3
next page »

View Full Article