Now substitute u for every x^2, the equation is transformed into u^2-13u+36=0. There is a standard strategy to achieve this through substitution.įirst, let u = x^2. Here, it would be a lot easier when factoring x^2 - 13x + 36 = 0. If, by the way, you’re interested in similar practice sheets for more elementary math, I have a page with links to several others.Solve for x in x^4 - 13x^2 + 36 = 0.įirst start by converting this trinomial into a form that is more common. Every time you reload, you’ll get a new set of problems. I think you’re best off with your own local copy of the page, but you can also just point your browser to the copy on my server. ![]() If you can’t get it to fit on one page, adjust the top and bottom header margins in Line 19 and/or the height of the cells in Line 30. I think I could get it to print on a single page in Firefox, but I don’t know (and really don’t want to know) how to suppress headers and footers there. You’ll have to turn off the printing of headers and footers, and you’ll probably have to set the margins to Minimal in Chrome to keep it from bleeding over onto another page. This will print on a single sheet of paper if you open it in Safari or Chrome on a Mac. I did it this way because it makes the equations look more like those you see in books and on tests, but you can change to whatever you like by fiddling with the array. By choosing the coefficients randomly from the array, I’m keeping the leading A A coefficient small, with one being the most common value. The a 1 a_1 and a 2 a_2 coefficients are generated on Lines 43-45.As I said earlier, there’s a Boolean flag that determines whether the output is a set of expressions or a set of equations.A couple of things you may want to change: The rest of the code is concerned with making the problems look the way a teacher or textbook would present them: with real minus signs instead of hyphens, suppressing the coefficient when it’s one, eliminating a term entirely if its coefficient is zero. That’s all pretty much handled in Lines 41–62. I start by using a random number generator to set the constants in the expression ( a 1 x + c 1 ) ( a 2 x + c 2 ) (a_1 x + c_1)(a_2 x + c_2)Īnd then multiply the two binomials to get the quadratic expression A x 2 + B x + C A x^2 + B x + C Small numbers, usually 1.Ĥ4: var a1 = coeffs Ĥ5: var a2 = coeffs Ĥ8: var c1 = Math.floor(Math.random()*9 + 1) Ĥ9: var c2 = Math.floor(Math.random()*9 + 1) ĥ1: // Change the signs of the constants at random.ġ01: for (j=0 j' + single_problem() + '') There’s a Boolean flag you can set if you just want quadratic expressions, not equations.ģ8: // Set to true for equations, false for expressions.Ĥ1: // Construct the parts of the binomial (a1*x + c1)(a2*x + c2)Ĥ2: // Coefficients. ![]() This same sheet can be used to practice factoring, completing the square, and using the quadratic formula. I use a pretty big font and provide plenty of space below each problem to work out the solution. I print some out, have him do one or two, and go over them with him. So, as with elementary math, I made up an HTML/JavaScript page that generates a new set of problems every time it’s (re)loaded. ![]() There are only so many problems in his book and making up new ones that have simple integer answers is harder and more time-consuming than you’d think. ![]() My younger son could use some algebra practice. Next post Previous post Quadratic practice sheet
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