8th Grade Test Corrections

This problem is not terribly difficult if you know what to do.

All you need to do is find the scale factor.  The scale factor is the number being multiplied by the original shape to make the scale shape.  In this case, the original shape is Triangle ABC.  So you create the following equations: 10 * x = 4 and 7.5 * x = 3  Then solve.  10 * x /10 = 4/10, so x = 0.4  Do the same for 7.5 * x /7.5 = 3/7.5

Dividing 3 by 7.5 is the same as 30/75.  Simplification leads to 6/15 then 2/5.


Look at the next one:

First you should have seen that a semicircle was half a circle.  Glass is on the inside of the shape, so you need area, NOT circumference.  Area of a circle is pi * radius squared and 15^2 is 225.  So 225 * 3.14 = 706.5 but DON'T STOP THERE.  That's Area of a whole circle.  Half of 706.5 is 353.25.

This one is also multi-step.

The words that tell you what to do are at the end of the paragraph.  Price per square foot is a ratio.  The word same means that the booths are proportional.  So the steps are to find the area of each booth and then find the price of the second.  10-foot by 12-foot is a rectangle unless otherwise stated in the problem, so the first booth is 10 * 20 = 120 square feet.  The second booth is 12 * 14 = 168.00  So your proportion should be:

Then your cross products are 12096 = 120 x   Then divide.  Remember you're dividing by a multiple of ten so you can simplify the division.  And you get 100.8

This one is multi-step, too (seeing a pattern? Most of the STAAR is also multi-step), but easy.  I'll show you why.

So in this chart there is one complete ratio of width to length, which are the dimensions.  Everyone look in the problem to see that the dimensions should be proportional, which means set up a proportion. You should use 4 width and 6 length first.  I recommend using 1 after that because it will make things easy.

Working it out you should get 6 = 4x.  Then you divide 6 by 4 and get 1.5 = x.  You can then use the ratio of 1 to 1.5 much easier on the last two numbers, 8 to 12 and 10 to 15.  All that's left is that pesky 2.  x over 2 = 1 over 1.5 results in 1 1/3 = x.

This one is not so pretty.  It's doable, but you should use fractions.