Grade 10 Math exercises?

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In summary, when using the quadratic formula, the sign of the x values needs to be switched in order to obtain the correct factored form of the equation. This is because of the way the quadratic formula is derived and the concept of solving a quadratic equation.
  • #1
yawie
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Hi
Does anyone know any good sites that offer Grade ten math exercises? It's for my sister. Canadian grade ten math, she's doing stuff like quadratic equations, factoring, linear equations.
Also can someone explain to me why when you factor an equation with the quadratic equation the answers signs are reversed from when you do it manually? Like when I do it manually I'll get x= -5, 4 but when I do it with the quadratic equation it becomes x= 5, -4
Thanks! I don't know how to explain it to my sis!

Yawie
 
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  • #2
Yawie,
Browse through this page and u should find a lot of sites that might be helpful,
http://directory.google.com/Top/Kids_and_Teens/School_Time/Math/ [Broken]

As for the quadratic equations,
i really don't understand what's the problem. Can u clarify with an example?

-- AI
 
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  • #3
Thanks! I'll go check that out!

About the quadratic thing. I think the right word was quadratic formula...sorry. =P
for instance:
lets say for x^2 + 5x + 4
if i do it by trial and error the answer would be (x+4)(x+1)
however, if i do it with the quadratic formula...the complicated one. I don't know how to write it... the answer would be (x-4)(x-1) which doesn't work when u multiply them out.
btw how do u write out those complicated equations?

Thanks alot!
Yawie
 
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  • #4
edit: oops sorry, misread the question.
 
  • #5
i think i know the answer to your quadratic equation question.
its because the formula for factored form is y=a(x-s)(x-t), so since its -s and -t, you need to change the sign in front of each x value (or zero) before you put it in the equation manually.
for example if the quadratic equation gave you the roots x=5 and x=-3, you would need to switch them to -5 and 3 before putting them in the equation like so :
y=a(x-5)(x+3)
hope it helped! :D
- Bradie
 
  • #6
yawie said:
Thanks! I'll go check that out!

About the quadratic thing. I think the right word was quadratic formula...sorry. =P
for instance:
lets say for x^2 + 5x + 4
if i do it by trial and error the answer would be (x+4)(x+1)
however, if i do it with the quadratic formula...the complicated one. I don't know how to write it... the answer would be (x-4)(x-1) which doesn't work when u multiply them out.
btw how do u write out those complicated equations?

Thanks alot!
Yawie

Think about how the factorised form comes about, and what it means to "solve" a quadratic.

By using the quadratic formula, you are essentially solving the following equation:

x^2 + 5x + 4 = 0

Which, as you obtained, has the two solutions x=-4 and x=-1.

Now when a quadratic equation is in the form:

(x-a)(x-b) = 0,

We know that EITHER x-a=0 or x-b=0 (or maybe both), since the product of two numbers can only be zero if one or both numbers are zero. Solving these two equations yields the solutions x=a and x=b. Can you now see why the sign reverses?

So in the example you gave, solving for its zeros gives the two solutions x=-4 or x=-1, therefore any factored form should have the same two zeros. If you use the one without changing the signs:

(x-4)(x-1),

and try plugging either x=-1 or x=-4 into it, you will see that it doesn't equal zero, so it cannot be the same quadratic.
 

1. What is the purpose of Grade 10 Math exercises?

The purpose of Grade 10 Math exercises is to help students develop a strong foundation in mathematical concepts and skills. These exercises cover a range of topics, including algebra, geometry, and trigonometry, and are designed to build upon the knowledge gained in previous grades and prepare students for more advanced math courses.

2. How often should Grade 10 Math exercises be completed?

The frequency of completing Grade 10 Math exercises may vary depending on the individual student's needs and pace. However, it is generally recommended to do math exercises on a regular basis, at least a few times a week, to reinforce learning and improve understanding of concepts.

3. Are there any specific strategies for solving Grade 10 Math exercises?

There are several strategies that can be helpful when solving Grade 10 Math exercises. These include breaking down the problem into smaller, more manageable parts, using diagrams or visual aids, and checking your work for errors. It is also important to follow the order of operations and show all steps in your solution.

4. How can I track my progress with Grade 10 Math exercises?

Many textbooks and online resources provide answer keys or solutions to Grade 10 Math exercises, which can be used to check your work and track your progress. Additionally, teachers often assign grades or provide feedback on completed exercises, which can also serve as a measure of progress.

5. Are there any additional resources available for Grade 10 Math exercises?

There are many additional resources available for Grade 10 Math exercises, including online tutorials, practice quizzes, and study guides. It is also helpful to consult with teachers or tutors for extra support and clarification on any challenging concepts.

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