2019 AMC 8 Problems Problem 1
心理学专业排名
Ike and Mike go into a sandwich shop with a total of to spend. Sandwiches cost each and soft drinks cost each. Ike and Mike
plan to buy as many sandwiches as they can and u the remaining money to buy soft drinks. Counting both soft drinks and sandwiches, how many items will they buy?
沪江英语听力网
Solution 1
We maximize the number of sandwiches Mike and Ike can buy by finding the lowest multiple of that is less than This number is
Therefore, they can buy sandwiches for They spend the remaining money on soft drinks, so they buy soft drinks. Combining the items, Mike and Ike buy soft drinks.
The answer is
Problem 2
cet 6Three identical rectangles are put together to form rectangle , as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of
rectangle ?
Solution 1
We know that the length of the shorter side of the 3 identical rectangles are all 5 so we can u that by eing that the longer side of the right rectangle is the same as 2 of the shorter sides of the other 2 left rectangles. This means
that which is the longer side of the right rectangle, and becau all the rectangles are congruent, we e that each of the rectangles have a longer side of 10 and a shorter side of 5. Now the bigger rectangle has a shorter length of 10(becau the shorter side of the bigger rectangle is the bigger side of the shorter rectangle, which is 10) and so the bigger side of the bigger rectangle is the bigger side of the smaller rectangle + the smaller side of the smaller rectangle, which is . Thus, the area is for
choice ~~Saksham27
Solution 2
Using the diagram we find that the larger side of the small rectangle is 2 times the length of the smaller side. Therefore the longer side is . So the area of the identical rectangles is . We have 3 identical rectangles that form the large rectangle. Therefore the area of the large rectangle
is . ~~fath2012
Solution 3
We e that if the short sides are 5, the long side has to
be becau the long side is equal to the 2 short sides and becau the rectangles are congruent. If that is to be, then the long side of the BIG rectangle(rectangle ) is becau long side +
aoyshort side of the small rectangle is . The short side of
rectangle is becau it is the long side of the short rectangle. Multiplying and together gets us which is .
~~mathboy282
Problem 3
Which of the following is the correct order of the
fractions and from least to greatest?
Solution 1
Consider subtracting 1 from each of the fractions. Our new fractions would then be and . Since , it follows that the answer
is
-will3145
Solution 2
We take a common
denominator:
Since it follows that the answer
is .
-xMidnightFirex
~ dolphin7 - I took your idea and made it an explanation.
Solution 3
When and , . Hence, the answer
is . ~ ryjs
This is also similar to Problem 20 on the AMC 2012.
festival是什么意思Problem 4
Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of
rhombus ?迈克尔杰克逊英文
考试心理
dervesSolution 1
A rhombus has sides of equal length. Becau the perimeter of the rhombus
is , each side is . In a rhombus, diagonals are perpendicular and bict each other, which means = = .
Consider one of the right triangles:
whenever的用法
= , and = . Using Pythagorean theorem, we find
that = .
酬谢是什么意思Thus the values of the two diagonals are = and = . The area of a rhombus is = = =
~phoenixfire
Solution 2 (Heron's)
