What level of maths is this?

[Laura Corin]

I really have no idea what people mean by 'pre-algebra', 'Algebra I', etc. These are some sample questions:

 

1) Multiply out these brackets: (i) (y + x)(y - x) (ii) (6 - x) squared

 

2) Solve these equations: (i) 2x squared minus 8x equals zero (ii) x squared minus 10x plus 25 equals zero.

 

3) A plane flew 100km on a bearing of 125 degrees. How far west must it then fly to be due south of its starting point?

 

4) Find the value of tan 48 degrees.

 

5)Solve this pair of simultaneous equations:

3c plus m equals 127

2c plus 3m equals 136

 

6) Find the surface area of a cylinder of radius 5cm and height 10cm.

 

Any ideas?

 

Thanks

 

Laura

[Jann in TX]

There is some overlap--as some of these concepts may be introduced in Pre-Algebra--but the factoring one--number 2--is definitely Algebra 1.

[Crimson Wife]

I've got young kids so it's been a while since I've seen pre-algebra. But from what I remember in 7th grade, it was solving simple equations involving variables. Things like x + 10 = 27 or y-squared = 81.

[Laura Corin]

What about questions 3, 4 and 6?

 

Laura

[AndyJoy]

With the exception of problem 2, all of those concepts were in the Glencoe Pre-Algebra book I taught from last year.

[SkateLeft]

My oldest daughter used the Dolciani books for pre-algebra, so I'll see what I can remember and take a shot at these. I believe #1 and #2 were pre-algebra.

 

#3 and #4 most definitely were not. In fact, neither of those are covered in any of the algebra 1 materials I have here, and as I recall from my own schooling, using trigonometric functions were something we did in analytic geometry and trigonometry. (Edited to add that I just found the pre-algebra books, and there *is* some use of trigonometric functions, which I guess I missed, but there isn't any repeated use of such functions to solve problems.)

 

#5 is solving a system of equations, which would be algebra 1 more than pre-algebra. (I see it covered in the Saxon Algebra 1 text I have here, but I don't remember if it was covered in my dd's pre-algebra course.)

 

#6 is something that we covered in pre-algebra.

Edited October 20, 2008 by sailmom

[In The Great White North]

I do think it varies by publisher.

 

I would have put 4 in trig and 6 in geometry, although the last chapter in the geometry book did have trig functions in it.

 

#1 and #2 were definitely in the Algebra I book. We didn't do pre-alg so I don't know if they were there or not.

 

#3 looks more like geometry, or even vectors, to me.

 

#5 was algebra.

 

(However, back in the day, "pre-algebra" wasn't something most people took. It was a watered down algebra to ease the students who weren't quite ready into high school math. It makes sense that there would be quite a bit of overlap between pre-algebra and algebra I. My personal theory is that by pushing algebra back to 8th grade for most students (who aren't quite ready for it), they created a need for pre-algebra across the board.)

[EKS]

Algebra I except 4 and 6 which are geometry.

[Laura Corin]

Is that there is more custom than logic to learning schedules in different countries. All the questions came from Maths Prep 3, which is used by the brightest pupils in private schools in the UK during the year they turn thirteen.

 

I don't think that this necessarily means that they are ahead of similar children in the US, rather that, because the UK does mixed maths all the way through (instead of a procession of Algebra, Geometry, Algebra, Trig) some topics come up earlier in the UK, whilst some, I'm sure, are delayed compared to the US.

 

Thanks to all

 

Laura

[Myrtle]

I nominate the following as the definition of "pre-algebra" to urbandictionary.com

 

Pre-algebra: Learning algebra before you learn algebra.

 

Algebra is distinguished from grade school arithmetic based on the fact that letters are used instead of numbers. In other words, the properties of the real numbers are applied to letters. After the student gains facility with dealing with an unknown he will learn to apply to substitute a single letter with an expression. For example: instead of dividing something by x he divides something by x + 3.

 

Ideally, the student would be able to state the properties of the real numbers, formal definition of division, subtraction, inequality, etc and state how they are used in solving equalities and inequalities.

 

 

 

See also: pre-algebra, algebra 1, algebra 2, algebra 1/2, algebra 2 3/4, modern algebra, post modern algebra, abstract algebra.