**SAT Geometry Problem with Solution**

Let’s solve the Geometry problem I posted on Tuesday. Here is the problem one more time, followed by a solution.

**Level 4 Geometry**

An ice cube with a side of length 2 centimeters has a density of approximately 0.92 grams per cubic centimeter. Given that density is defined as mass per unit volume, what is the mass of the ice cube, to the nearest gram?

**Solution: **The volume of the ice cube is *V* = 2^{3} = 8. The problem tells us that *D* = *M*/*V*, where *D* stands for density and *M* stands for mass. So, *M* = *DV* = 0.92 ⋅ 8 = 7.36 grams. To the nearest gram, this is **7**.

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**SAT Geometry Problem with Solution**

Let’s solve the Geometry problem I posted on Tuesday. Here is the problem one more time, followed by a solution.

**Level 4 Geometry**

An ice cube with a side of length 2 centimeters has a density of approximately 0.92 grams per cubic centimeter. Given that density is defined as mass per unit volume, what is the mass of the ice cube, to the nearest gram?

**Solution: **The volume of the ice cube is *V* = 2^{3} = 8. The problem tells us that *D* = *M*/*V*, where *D* stands for density and *M* stands for mass. So, *M* = *DV* = 0.92 ⋅ 8 = 7.36 grams. To the nearest gram, this is **7**.

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If you’re preparing for the SAT, you may want to check out the *Get 800* collection of SAT math books.

**SAT Geometry Problem**

Here is an SAT geometry problem for you to try. A solution will be posted tomorrow. You can post your own solutions in the comments.

**Level 4 Geometry**

An ice cube with a side of length 2 centimeters has a density of approximately 0.92 grams per cubic centimeter. Given that density is defined as mass per unit volume, what is the mass of the ice cube, to the nearest gram?

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If you’re preparing for the SAT, you may want to check out the *Get 800* collection of SAT math books.

**Difficult Passport to Advanced Math Problem**

with Solution

with Solution

Today I would like to provide a solution for the SAT math problem I posted on Friday.

**Level 5 Passport to Advanced Math**

*y* = *x*^{2} + 5*x* + 6

7*x* + 4 – *y* = 0

How many solutions are there to the system of equations above of the form (*x*,*y*), with *x* a real number?

(A) 0

(B) 1

(C) 2

(D) More than 2

*** ****Solution by substitution: **We solve the second equation for *y* by adding *y* to each side of the equation:

7*x* + 4 = *y*

We now replace *y* by 7*x* + 4 in the first equation to get

7*x* + 4 = *x*^{2} + 5*x* + 6

We now add –7*x* – 4 to each side of the equation to get

0 = *x*^{2} – 2*x* + 2

The equation *x*^{2} – 2*x* + 2 = 0 has discriminant

*b*^{2} – 4*ac *= (–2)^{2} – 4* *⋅ 1 ⋅ 2 = 4 – 8 = –4

Since the discriminant is negative, there are no real values of *x* that satisfy the equation. So, the answer is choice **A**.

**Notes: **(1) To learn more about the discriminant of a quadratic equation, see the following post: The Discriminant of a Quadratic Equation

(2) For one method of solving quadratic equations, see the following post: The Quadratic Formula

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28 ACT Math Lessons – Beginner Course

Now Half Price

~~Today I would like to announce the release of~~* 28 ACT Math Lessons to Improve Your Score in One Month – Beginner Course*.

~~The paperback is now on sale on Amazon for 50% off. Click the following link to get to the book’s Amazon page: 28 ACT Math Lessons – Beginner~~

The sale has ended. Thank you to all who participated.

Check out my other ACT math books here: Get 800 ACT Math Books

**A Trick For Free Two Day Shipping**

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

**This next part is very important!** After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

Thank you all for your continued support!

**Difficult Passport to Advanced Math Problem**

Here is a nice SAT problem for you to try. I will post my own solution within the next few days. Meanwhile, feel free to post your own solutions in the comments.

**Level 5 Passport to Advanced Math**

*y* = *x*^{2} + 5*x* + 6

7*x* + 4 – *y* = 0

How many solutions are there to the system of equations above of the form (*x*,*y*), with *x* a real number?

(A) 0

(B) 1

(C) 2

(D) More than 2

Share this problem with your Facebook friends that are preparing for the SAT

If you’re preparing for the SAT, you may want to check out the *Get 800* collection of SAT math books.

28 ACT Math Lessons – Intermediate Course

Now Half Price

Today I would like to announce the release of* 28 ACT Math Lessons to Improve Your Score in One Month – Intermediate Course*.

The paperback is now on sale on Amazon for 50% off. Click the following link to get to the book’s Amazon page: 28 ACT Math Lessons – Intermediate

Visit my website to see all of my other books: Get 800 Books

**A Trick For Free Two Day Shipping**

I would like to finish this post with a little trick you can use to get free 2 day shipping on any of the books you decide to purchase without making any additional purchases. If you have never used Amazon Prime you can sign up for a free month using the following link.

Sign Up For Amazon Prime For Free

If you have already had a free trial of Amazon Prime you can simply open up a new Amazon account to get a new free trial. It just takes a few minutes! You will need to use a different email address than the one you usually use.

**This next part is very important!** After you finish your transaction, go to your Account, select “Manage my prime membership,” and turn off the recurring billing. This way in a month’s time Amazon will not start charging you for the service.

After shutting off the recurring billing you will still continue to receive the benefit of free 2 day shipping for one month. This means that as long as you use this new Amazon account for your purchases you can do all of your shopping on Amazon for the next month without having to worry about placing minimum orders to get free shipping.

Just be aware that certain products from outside sellers do not always qualify for free shipping, so please always check over your bill carefully before you check out.

Well I hope you decide to take advantage of this very special offer, or at the very least I hope you will benefit from my Amazon “free 2 day shipping trick.” Here is the link one more time:

Sign Up For Amazon Prime For Free

Thank you all for your continued support!