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Lesson 2 test taking strategies
- 1. LESSON 2 5 TEST-TAKING STRATEGIES For the PSAT and SAT
- 2. LEARN SPECIAL MATH STRATEGIES Strategy #1: Sub-in; substitute friendly numbers for the variables in the problem If ¾ of the citizens in New York cast their votes for Proposition A, and of the remaining citizens cast their votes for Proposition B, what fraction of the votes were cast for Proposition C? A. B. C. D. E.
- 3. LEARN SPECIAL MATH STRATEGIES Strategy #2: Backfill – fill in the answer choices that are given in the problem until you find one that works; one answer must be right! If the difference between one-third of a number and one-seventh of that same number is 8, then what is the number? A. 12 B. 21 C. 30 D. 42 E. 56
- 4. LEARN SPECIAL MATH STRATEGIES Strategy #3: Scan the answers – look for and eliminate answer choices that do not make sense (fractions, decimals, integers, percents, etc.) In the figure below, a small circle with the radius x is inside a larger square with side 6. What is the area, in terms of x, of the shaded region? A. 12 – 2 x B. 12 - x² x 6 C. 36 – 2 x D. x² - 36 E. 36 - x²
- 5. LEARN SPECIAL MATH STRATEGIES Strategy #4: Don’t waste time on complex arithmetic – if you find yourself bogged down, you have probably missed the point of the problem The sum of 5 consecutive integers is 1,000. What is the value of the greatest of these integers?
- 6. LEARN SPECIAL MATH STRATEGIES Strategy #5: Fill in what you know to help you find what is unknown– show measures on figures; on all drawn-to-scale figures, angles that look equal are equal In the figure below, what is the length of segment AB? B 8 C A. 10 5 B. 11 C. 12 A 20 D D. 13 E. Cannot be determined
Editor's Notes
- Use 100 as the sub-in value for the number of citizens in New York. ¾ of 100 is 75, so 75 citizens voted for Proposition A25 citizens remain and 4/5 of 25 is 20, so 20 citizens voted for Proposition B Only 5 of the 100 citizens remain, so 5/100 or 1/20 of the citizens voted for Proposition C
- (D) (1/3)*42 – (1/7)*42 = 8
- (E) To find the area of the shaded region, we must subtract the area of the circle from the area of the square. The area of the square is 36 (6 x 6), so we can eliminate (A), (B), and (D).We can also eliminate (C) because the circumference (instead of area) formula is used for the circle.These formulas are provided at the beginning of each Math Section.
- 202.Since there are 5 consecutive numbers summing to 1000, one of the numbers must be 200 since 1000/5 is 200. If we add 200 and the next 4 numbers, we will get a sum greater than 1000. So we can start at a number slightly before 200. In fact, if we start with 198, we find that 198+199+200+201+202=1000. So the greatest of the integers is 202.
- 13. The shape can be cut into a rectangle and a right triangle. The base of the right triangle is 12 (20 - 8). The height of the right triangle is 5 (the same as the height of the rectangle).Using the Pythagorean Theorem and substituting 5 and 12 for the two side lengths, yields 13 as the length of the hypotenuse, AB.