Tip #48 to Get a Top SAT Math Score

You've now learned the 47 skills that you need for the SAT. The Math Mantras remind you what to do when, what that girl who got an 800 does automatically. In Skills 48 and 49, let's make sure you've memorized the 47 SAT Math Mantras. Cut out the flash cards provided at the end of this book, and drill them until you are ready to teach them. Then do that. Once you're sure you've got 'em, check off the box next to each mantra.

Skill 1. When you see variables in the question and numbers in the answers, "Use the Answers."
Skill 2. "What is m in terms of p and q" is just a fancy way of saying "solve for m" or "use algebra to get m alone."
Skill 3. When you see the word "average" on the SAT, use sum = (average) × (# of items).
Skill 4. When you see vertical angles, a linear pair, or a triangle, calculate the measures of all angles.
Skill 5. When you see two parallel lines that are crossed by another line, eight angles are formed, and all the bigger–looking angles are equal, and all the smallerlooking angles are equal.
Skill 6. When you see a triangle with two equal sides, mark the two opposite angles as equal, and when all sides of a triangle are equal, mark all angles 60°.
Skill 7. An exterior angle equals the sum of the two far away interior angles.
Skills 8 and 9. Anytime you see a math vocab term, underline it.
Skill 10. Don't be intimidated by fancy vocabulary terms.
Skill 11. The slope of a line measures its steepness; the steeper the line, the biggerthe slope.
Skill 12. Parallel lines have equal slopes, like and . Perpendicular lines have negative reciprocal slopes, like and – . And lines reflected over the x axis or y axis have negative slopes, like and –.
Skill 13. The key to understanding tables and graphs is to read the headings and the legend if there is one.
Skill 14. f(3) means "plug 3 in for x."
Skill 15. f(m) = 9 means "What did we plug into the equation for x to get a result of 9?"
Skill 16. When you see variables in the question and variables in the answer choices, especially for word problems, use "Make It Real."
Skill 17. The SAT only expects you to use formulas provided in the question or in the info box at the beginning of the section.
Skill 18. The area of a donut equals the area of the big guy minus the area of the donut hole.
Skill 19. 4 boys to 5 girls could also be expressed 5 girls to 9 students. Also a ratio can be a reduced version of the real numbers.
Skill 20. When you see a proportion on the SAT, cross–multiply.

Let's look at this question:

Solution: The legend tells us that each ♥ represents 10 votes. Therefore, Superbad received 50 votes and Borat received 15, and 50 – 15 = 35. Remember that half a symbol represents 5 votes, not half a vote.

Correct answer: C

Example Problems

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

Easy

If , what is the value of a ?
1. 60
2. 40
3. 30
4. 20
5. 14
If the average (arithmetic mean) of the perimeters of two shapes is 14, what is the sum of the perimeters of the two shapes?
1. 0
2. 7
3. 14
4. 21
5. 28

Medium

If two sides of a triangle are equal, which of the following could be the measures of its angles?
1. 30, 30, 90
2. 35, 45, 100
3. 35, 35, 110
4. 30, 60, 90
5. 45, 45, 45
Five boys on an elevator have an average (arithmetic mean) weight of 120. A sixth boy wants to join them. If the elevator can hold 750 lb, what is the maximum the sixth boy can weigh in order for the group not to exceed the elevator's 750–pound weight limit?
If f(x) = 3x³, and f(b) = 24, then b =
1. –1
2. 0
3. 2
4. 8
5. 9
fruit cup contains apple, pear, and banana in the ratio 2 : 3 : 4. If a serving of fruit cup contains 9 pieces of pear, how many total pieces of fruit are in the cup?
The function M(u) = (2u)² – k expresses the number of songs Simon has memorized this year, where u represents months so far this year and M(u) represents songs memorized. If by the end of June he has memorized 9 songs, what is the value of k ?
1. 6
2. 9
3. 63
4. 135
5. 318

Hard

If a is a multiple of 3 and b is a multiple of 4, which of the following must be a multiple of 12 ?
1. ab
2. 3a + 4b
3. 4a + 3b
1. I only
2. III only
3. I and III
4. II and III
5. I, II, and III

In the diagram above, what is the value of a in terms of b and c ?
1. 90 + 4b + c
2. 180 – 3b – 2c
3. 180 + 2b + c
4. 360 – 4b – 2c
5. 360 + 3b – c
The average (arithmetic mean) of the bowling scores of a team of m students is 170, and the average of the scores of a class of n students is 182. When the scores of both teams are combined, the average score is 177.5. What is the value of m/n ?
1. 0.4
2. 0.6
3. 0.8
4. 1
5. 1.2

Answers

Proportions (Skill 20). D. When you see a proportion, cross-multiply. 3a = 60, so a = 20.
Average (Skill 3). E. The question asks for the sum, so use the sum formula: sum = (average) × (# of items). So sum = (14)(2) = 28.
Isosceles triangle (Skill 6) and triangle has 180° (Skill 4). C. If two sides of a triangle are equal, than two angles must also be equal, and since it is a triangle, the measures must add up to 180.
Average (Skill 3). 150. Since the average weight of the 5 boys is 120, their sum is (120)(5) = 600. When the sixth boy joins them, their weight cannot exceed 750 pounds, so the sixth boy can weigh up to 750 – 600 = 150.
Functions (Skill 15). C. f(b) = 24 means plug in bfor xand 24 as the solution:
Ratios (Skill 19) and proportion (Skill 20). 27. With the ratio of 2 : 3 : 4, there are 9 total pieces of fruit. So set up a proportion for pear to total: and cross-multiply to solve for x.81 = 3x,so x= 27.
Functions (Skill 14) D. Plug 9 in for M(u) and 6 (since June is the 6th month) in for u,and solve for k.

9 = ((2)(6))² – k

9 = 144 – k

–135 –k

135 = k

Make It Real (Skill 16) C. "Make It Real" turns this "hard" into an "easy." Choose numbers for the variables. Let's say a = 9 and b = 8. Then

I works since ab = (9)(8) = 72 which is a multiple of 12.

II flunks since 3a + 4b = (3)(9) + 4(8) = 59 which is not a multiple of 12.

III works since 4a + 3b = (4)(9) + (3)(8) = 60 which is a multiple of 12.

Since this is a late "medium," it's a good idea to test a second set of numbers to confirm that choices I and III both still work.

Geometry (Skill 4) and "What is ain terms of band c?" (Skill 2) D. The best way to solve this question is to realize that the angles marked with a, b's. and c's add up to 360, since they are the four angles of a four-sided shape. Then it's easy since a + 4b + 2c = 360, and we just solve for a.
Averages (Skill 3). B. Set up the sum formula for each team. The sum of the first team is 170m, and the sum for the second team is 182m.Now, set up the average formula to determine the average of the groups combined: add the two sums (170m + 182n) and divide by total bowlers (m + n) and set equal to the combined average 177.5.

Algebraically manipulate to get m/n. OK, I admit it, this question is tough. Without our strategies very few students can get it. But our strategies knock it down from nearly impossible to possible.

Go to: Tip #49

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