Geometry 1
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———————————————————————————-REVIEW INSTRUCTIONS——————————————————————————————
Thorough review is critical to the learning process and for most people should take a significant amount of time (and effort!) potentially equally or surpassing the amount of time taken to do the question set.
- Redo questions that you got wrong or struggled on without looking at the answers or explanations. Think. Rethink. Push yourself. Put pen to paper. Don’t review with only your eyes!
- Once you’ve solved or if you aren’t able to solve in about 10 minutes carefully review the explanation (if provided). Again, put pen to paper and redo the question along with the explanation.
- If we haven’t provided an explanation or if our explanation didn’t clear up your doubts google the first few words of the question and confirm the solution on the GMAT forums.
- Except for CR and RC, take a screenshot and add it to your dropbox review folder so you can easily revisit the question when assigned review in your HW schedule.
- Bring questions that you still find difficult to QA or to our sessions. For sessions add the screenshots to the “review in session” folder in your dropbox.
Here’s a video outlining the review process: https://www.youtube.com/edit?o=U&video_id=X6k3niNoGuA
This is a crucial part of the preparation so let’s make sure we get it right. If you have any questions contact andrew@atlanticgmat.com or luciano@atlanticgmat.com.
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- Question 1 of 12
1. Question
CorrectIncorrectHint
[Latex Page]
For the square with unknown side length start by defining everything in terms of S.
SQUARE
Area = $Side^{2}$
Perimeter = 4*Side
Diagonal = $Side*\sqrt{2}$For a circle with unknown radius start off by defining everything in terms of Radius R.
CIRCLE
Area = $Pi*Radius^{2}$
Circumference = 2Pi*Radius
Diameter = 2*RadiusWith shapes that overlap try to define everything with one variable. In this case in terms of R or in terms of S.
In terms of data sufficiency strategy this is a counting equations question. A quick memorization: With a square inscribed in a circle or a circle inscribed in a square you can define everything about the square and the circle by knowing Side, Radius, Area, Perimeter, Circumference… of either shape.
- Question 2 of 12
2. Question
CorrectIncorrect - Question 3 of 12
3. Question
CorrectIncorrectHint
\(\)
With a cube of unknown edge length always define the dimensions as follows:Volume = $S^{3}$
Surface Area = $6*S^{2}$
Greatest Distance Inside/Interior diagonal that goes through the middle of the Cube from the top vertice to the bottom one on the opposite side = $S*sqrt{3}$ - Question 4 of 12
4. Question
CorrectIncorrectHint
Triangle
Area = (Base*Heigh)t/2
A height and a base must meet at a 90 degree angle. If the triangle isn’t a right triangle (one with a right angle) then the height is NOT one of the sides. It must be drawn.
In a right triangle
with C being the side opposite the 90 degree angle. C is also the longest side.
Within a triangle angles that are equal have sides opposite them that are also equal.
- Question 5 of 12
5. Question
CorrectIncorrectHint
Rectangle
Area = Length*Width
Perimeter = 2(Length + Width)
Diagonal =
The formula for the diagonal is derived from the pyth. theorem:
- Question 6 of 12
6. Question
CorrectIncorrectHint
Bisects = cuts in half.
- Question 7 of 12
7. Question
CorrectIncorrect - Question 8 of 12
8. Question
CorrectIncorrectHint
Triangle
Area = (Base*Height)/2
In a right triangle
with C being the side opposite the 90 degree angle. C is also the longest side.
- Question 9 of 12
9. Question
CorrectIncorrectHint
For the square with unknown side length start by defining everything in terms of S.
SQUARE
Area =
Perimeter = 4*Side
Diagonal =
- Question 10 of 12
10. Question
CorrectIncorrectHint
In the coordinate plane try to draw squares, rectangles, or lines that form 90 degree angles in order to calculate area (or anything else).
Triangle
Area = (Base*Heigh)t/2
A height and a base must meet at a 90 degree angle. If the triangle isn’t a right triangle (one with a right angle) then the height is NOT one of the sides. It must be drawn.
In a right triangle
with C being the side opposite the 90 degree angle. C is also the longest side.
- Question 11 of 12
11. Question
CorrectIncorrectHint
Try plugging in some numbers. Try different types of numbers. Different types of numbers to try: Integers, Decimals, 0, 1, Odd, Even, Negative, Positive. This list also works well for number picking in Data Sufficiency.
- Question 12 of 12
12. Question
CorrectIncorrectHint
Pick numbers and increase each one by 20%. Multiply them and do the percent change. The shortcut is to take the 20% or .2 and add it to one and square it. So (1.2)(1.2) = 1.44. So if each side is increased by 20% the area is increased by 44%.
Percent Change = (New/Old – 1)100. To increase something (let’s use 50 for this example) by a certain percent (let’s use 10%): 50*10% + 50 = 55. Or in one step (10% + 100%)50 which really equates to 1 + .1 or 1.1. So 1.1*50. Same answer, 55.