Tactics Quiz Review
Tactic 1: Draw A Diagram
- Useful when problems deal with several geometric figures (a square AND a rectangle, a cylinder AND a box, etc.)
- Useful when problems give you a lot of data – make a table to organize your info
Tactic 2: If a diagram is drawn to scale, trust it, then trust your eyes.
- Helpful to eliminate absurd choices
- Make a “ruler” to help you measure
- How do you know if a diagram is drawn to scale?
- Are all diagrams drawn to scale on the S.A.T. ?
Tactic 3: If a diagram is not drawn to scale, redraw it, then trust your eyes.
- Helpful to “see” properties of diagrams you wouldn’t have noticed otherwise
- Start by asking, “what’s wrong” with the existing picture
Tactic 4: Add a line to a diagram
- Useful for breaking irregular shapes into right triangles and rectangles to find total area
- Useful in circle problem to draw in a radius to an important point on the circle
Tactic 5: Test the answer choices starting with C.
- Why C? What is special about C?
Tactic 6: Replace Variables with Numbers
- Choose easy to substitute variables.
1. Substitute.2. Answer question.3. Check answer choices
Ex. 6 If w widgets cost c cents, how many widgets can you get for d dollars?
A) (100dw)/c
B) (dw)/(100c)
C) 100cdw
D) (dw)/c
E) cdw
Tactic 7: Choose an appropriate number.
- Choose the least common denominator (for fractions) or a multiple of 100 (for percents) as a starting population. Solve the problem by setting a proportion.
Ex. 7 In a class, 2/3 of the students wore green shirts on St. Patrick’s day. One-Fourth of the rest of the students wore blue shirts. All the rest wore red shirts. If 255 students wore red shirts, how many students are in the class?
Tactic 8: Eliminate the absurd choices, then guess.
- If you can eliminate at least one answer choice, you should guess.
- Look for absurd things like negative areas, answers that are grossly to big or small, etc.
Tactic 9: Subtract to find the shaded region.
- What you want = Everything – Parts you don’t want
- Be careful if the problem asks for area, perimeter, distance, etc.
Tactic 10: Don’t do more than you have to.
- Look for shortcuts!
Tactic 11: Pay attention to units.
- Any time a question refers to something with units, be sure to solve with those units.
- The wrong answer is nearly always a choice.
Ex. 11A diagram is 6inches by 12 inches.
How many square feet is the diagram?
Tactic 12: Use your calculator.
- Make an estimate!
Ex. 12What is the value of
Tactic 13: Don’t use your calculator.
- Look for shortcuts!
- Don’t be afraid to do a little algebra!
Ex. 13For what value of x is ?
Tactic 14: Make systematic lists.
- Find a pattern, use the pattern to predict your answer.
Ex. 14 Students are handed out red, blue, or white ribbons (in that order) as they enter the gym. What color of ribbon is given to the 352nd student as they walk into the gym?
A) red
B) white
C) blue
Tactic 15: Trust all grids, graphs, and charts.
- Same as tactic 2 – the information should be presented accurately.
- Use the info to try and eliminate absurd answers or make estimates.
Tactic 16: Handle strange symbols properly.
- If you see a strange symbol—follow the directions!
- These problems usually come down to substituting numbers into an algebraic expression and evaluating.
Ex. 16
For any numbers a and b, . What is the value of ?
Tactic 17: Add equations.
- Any time you have two or more equations, try adding them together and see if that “helps”.
- If addition doesn’t work, try subtraction.
- There are NO problems on the SAT that require the substitution/elimination techniques from Algebra.
Ex. 17 If 12a + 3b = 1 and 7b – 2a = 9, what is the average of a andb?
General Notes:
- Sometimes considering your answer choices is just as important as attempting to solve the problem. Tactics 5, 6, 8, and 12 all take answer choices into account.
Example:
Jason earned a 25% raise in pay from week 1 to week 2.
During his 2nd week of work, Jason earned $110. How much did he earn in week 1?
A) $82.50
B) $85.00
C) $88.00
D) $137.50
E) $146.67
Avon S.A.T. Prep Math 1