2.1 General Math Strategies Mr. Clavijo

Overview Strategies don’t depend of the format of the question. Strategies do not tell you specific steps to solve a problem. They are just approaches you can try

Strategy 1 Draw a Diagram Drawing a diagram can help you visualize a problem situation.

Example 1 Any goes shopping and spends one-third of their money on a new dress. She then goes to another store and spends one- half of the money she has left on shoes. If Any has $56 left after these two purchases, how much money did she have when she started shopping?

Strategy 2 Look at a Specific Case If a problem does not give specific numbers or the actual dimensions, make up a simple example using EASY numbers.

Example 2 The perimeter of a rectangle is 10 times as great as the width of the rectangle. The length of the rectangle is how many times as great as the width of the rectangle?

Strategy 3 Plug in Numbers to Find a Pattern Substitute a few test values for a variable until you discover a pattern

Example 3 When a positive integer k is divided by 5, the remainder is 3. What is the remainder when 3K is divided by 5?

Strategy 4 Choose a Convenient Starting Value when None Is Given If you need to figure out how a quantity changes without knowing its beginning value, choose any starting value that makes the arithmetic easy.

Example 4 The current value of a stock is 20% less than its value when it was purchased. By what percent must the current value of the stock rise in order for the stock to have its original value? (A)20% (B)25% (C)30% (D)33 1 / 3 % (E)50 %

Example 4.1 Fred gives 1/3 of his DVDs to Andy and then gives ¾ of the remaining DVDs to Jerry. Fred now has what fraction of the original number of DVDs? (A)1/12 (B)1/6 (C)1/3 (D)5/12 (E)1/2

Strategy 5 Make Organized Lists Some problems can be solved by making a list and then discovering a pattern.

Example 5 People enter a room at a time and are given a name tag in one of five possible colors. The colors are given out in this order: red, blue, white, green, and yellow. What is the color of the name tag that is given to the 93 rd person who enters the room? (A)Red (B)Blue (C)White (D)Green (E)Yellow

Example 5.1 What is the units digit of 3 35 ? (A)1 (B)3 (C)5 (D)7 (E)9

Strategy 6 Redraw Figures to Scale If a figure that accompanies a question is not a scale, then redrawing it a scale may reveal a fact.

Example 6 Note: Figure is not drawn to scale In the rectangle JKLM above, if JK = KL, what is the ratio of JH to KM? J K L M H

Strategy 7 Insert Units of Measurement When writing a proportion to solve a problem involving rates, include the units of measurement.

Example 7 The trip odometer of an automobile improperly displays only 3 miles for every 4 miles actually driven. If the trip odometer shows 42 miles, how many miles has the automobile actually been driven?

Example 7.1 A machine can stamp 72 envelopes in 45 seconds. How many envelopes can the same machine stamp in 2 minutes

Strategy 8 Work Backward When you only know the end result of a computation and want to find the beginning value.

Example 8 Sarah’s telephone service cost $21 per month plus $0.25 for each local call, and long-distance calls are extra. Last month, Sarah’s bill was $36.64, and included $6.14 in long-distance charges. How many local calls did she make?

Strategy 9 Use Reference Information as Needed Look back at the beginning of the test section and see if the formula you need is included in the reference.

Example 9 The diameter of the base of a right circular cylinder is 2, and the distance from the center of one base to a point on the circumference of the other base is 4. What is the volume of the cylinder in terms of π. (A)3π (B)5π (C)π√12 (D)π√15 (E)π√17

Strategy 10 Account for All Possible Cases Solving a problem may depend on braking it down so that all possibles cases are considered.

Example 10 In a certain homeroom class, 21 students are enrolled in math, 17 students are enrolled in biology, 9 are enrolled in both math and biology, and 3 students are not enrolled in either course. How many students are in the homeroom class? (A)22 (B)25 (C)28 (D)32 (E)50