3 Strategies to Tackling Multiple Choice questions 1

3 Strategies to Tackling Multiple Choice questions 1. Plug in a number 2. Back-solving 3. Guessing

Tackling Multiple Choice Questions 1. Plug in/Pick a number: – If there are variables in the answer choices, students should consider using the Pick a Number strategy. – Here's how it works: • Pick numbers for each of the variables. • Plug the numbers into the question and find the result. • Next, substitute the numbers for the variables in each answer choice. • Now simplify each answer choice and compare the results to the original value.

Plug in/Pick a number Using Pick a Number If s skirts cost d dollars, how much would s - 1 skirts cost? A. d - 1 B. d - s C. d / s - 1 D. d(s - 1) / s - What numbers did you select to represent the two variables? - Using these values, how much would s - 1 skirts cost? - Which answer choice matches this cost?

Plug in/Pick a number Tips for Picking a Number – Pick small numbers that are easy to work with. – When there are two variables, pick different numbers for each. – Avoid picking 0 or 1, as these often give several "possibly correct" answers. Plug carefully – When plugging values in for variables, make sure you are using the right number for each variable.

PRACTICE: Plug in/Pick a number

Explanation: Plug in/Pick a number

PRACTICE: Plug in/Pick a number

Explanation: Plug in/Pick a number

Tackling Multiple Choice Questions 2. Back-solving – Use when picking numbers and solving the problem isn’t possible – Work back-wards using answer choices

Back-solving • How to back-solve – Plug choices back into the question until you find the one that fits – Answer choices are arranged in order, either descending or ascending from (A) to (E) – Choose choice (C) first to plug into the equation to guide your next step • If it gives you too small an answer, then (A) and (B) or (D) and (E) can be eliminated depending on which values are smaller than (C)

Back-solving • When to back-solve – Question is a complex word problem & answer choices are numbers – The alternative is to set up multiple algebraic equations • When back-solving isn’t ideal – Answer choices include variables – Algebra quest. And word problems that have ugly answer choices (radicals, fractions)

Practice with Back-Solving

Practice with Back-Solving

Tackling Multiple Choice Questions 3. Guessing Avoid random guessing Make educated guesses Eliminate unreasonable answer choices Eliminate the obvious answers on hard questions – Eyeball lengths, angles, and areas on geometry questions – –

Guessing • Eliminate unreasonable answer choices – Which answers don’t make sense • Eliminate the obvious on hard questions – Obvious answers are usually wrong for hard questions – Don’t use this for easy questions, the obvious answer might be right

Guessing • Eyeballing lengths, angles, & areas – Use diagrams to help you eliminate wrong answer choices – Double check to see if the diagram is drawn to scale • If it’s not drawn to scale, you can’t use this strategy—figures are drawn to scale unless otherwise noted • If it is, estimate quantities or eyeball the diagram, angle, length, or area

Guessing • Eyeballing lengths, angles, & areas – eliminate answer choices that are too large or too small – With angles, compare them to 180°, 90°, or 45° angles • Use the corner of a piece of paper (right angle) to see if an angle is > or < 90° – With areas, compare an unknown area to an area that you do know

PRACTICE GUESSING

Grid-In Questions • No answer choices • 4 boxes and a column of ovals, or bubbles to write your answer • No penalty for wrong answers

Grid-In Questions • Some questions have only 1 correct answer, others have several • Digits, decimal points, fraction signs should be written in separate boxes • Bubble in underneath

Grid-In Questions • You can’t grid – Negative numbers – Answers with variables – Answers greater than 9, 999 – Answers with commas (1000 not 1, 000) – Mixed numbers (ex: 2 ½)

Grid-In Strategies • Write (. 7 not 0. 7) • Grid fractions in the correct column – Ex: 31/42 won’t fit & will need to be converted into a decimal • Place decimal points carefully – If decimal <1, enter the decimal point in the 1 st column (. 127) – Only grid in a 0 before the decimal if it is part of the answer (20. 5) – Never grid a decimal point in the last column

Grid-In Strategies • Long or repeating decimals – Grid the first 3 digits only and plug in the decimal point – Rounding to an even shorter answer may be incorrect – try not to round • If there is more than 1 right answer, choose 1 and enter it

Grid-In Strategies • If the answer has a range of possible answers, grid any value between that range – It’s easier to work with decimals – Ex: 1/3 < m < ½ • Don’t grid 1/3 or ½ -- that would be wrong • Grid. 4 or. 35 or. 45 • Check your work

Using Calculators • Help the most on Grid-ins • Use it only to save time • If you can’t think of a reason why using a calculator would make a problem easier or quicker to solve, don’t use it

Using Calculators 1. 2. 3. 4. Think first Decide on the best way to solve the problem Only then, use your calculator Check your answers • Be sure that calculations involving parenthesis are correct before pressing “enter” Don’t forget PEMDAS • – Parenthesis, exponent, multiply, divide, add, subtract

GRID IN PRACTICE 1 There are 12 men and 24 women in a chorus. What percent of the entire chorus is composed of women? (Disregard the percent sign when gridding your answer). 12+ 24= 36 24/36= 66. 6666 66. 6 OR 66. 7

GRID IN PRACTICE 2 Note: figure not drawn to scale If x and y are integers and x > 90, what is the minimum possible value of x ? One way to reason through this problem is as follows. The interior angles of a triangle add up to 180�. So x + y + 3 y = 180, or x + 4 y = 180. Try the smallest integer value of x greater than 90 in this formula, that is, x = 91. This gives , so. Thus if x = 91, . But y must be an integer, so x must be a larger number. Try the next greater integer value for x. If x = 92, then , so , which means that. Since y is an integer in this case, the minimum value of x is 92. 92

GRID IN PRACTICE 3 A gumball machine dispenses gumballs of different colors in the following pattern: green, blue, red, yellow, white, green, and green. Assuming the pattern repeats itself, if the machine dispenses 60 gumballs, how many of them will be green? This is a classic pattern question—with a twist. The key here is to count the number of elements in the given pattern. This pattern has 9 elements that repeat. Of these, three are green. So every time the machine goes through the pattern, 3 of the gumballs it dispenses are green. 60 is not a multiple of 9, but 54 is. When the machine is up to the 54 th gumball, it will have gone through this pattern of 9 exactly 6 times. So it will have dispensed green gumballs. For the remaining 6, just count into the pattern. Only one more green gumball will be dispensed 19