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JSS3: MATHEMATICS - 1ST TERM

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  1. Binary Number System I | Week 1
    5Topics
    |
    1 Quiz
  2. Binary Number System II | Week 2
    6Topics
    |
    1 Quiz
  3. Word Problems I | Week 3
    4Topics
    |
    1 Quiz
  4. Word Problems with Fractions II | Week 4
    1Topic
    |
    1 Quiz
  5. Factorisation I | Week 5
    4Topics
    |
    1 Quiz
  6. Factorisation II | Week 6
    3Topics
    |
    1 Quiz
  7. Factorisation III | Week 7
    3Topics
    |
    1 Quiz
  8. Substitution & Change of Subject of Formulae | Week 8
    2Topics
    |
    1 Quiz
  9. Simple Equations Involving Fractions | Week 9
    3Topics
    |
    1 Quiz
  10. Word Problems | Week 10
    1Topic
    |
    1 Quiz
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To make a quadratic expression a perfect square, add half the coefficient of x (or whatever letters are used) and square the result.

 i. x2 + 5x 

Step 1: half the coefficient of  x

\( \frac{5}{2} \)

Step 2:  square the result

\(\scriptsize x^2 + \normalsize {\left(\frac{5}{2}\right)}^2 \\ = \left ( \scriptsize x + \normalsize \frac{5}{2} \right)^2 \) \({\left(\frac{5}{2}\right)}^2 = \frac{25}{4}\)

\( \frac{25}{4} \) must be added to make it a perfect square

ii. y2 + 9y

= \(\scriptsize y^2 + \normalsize {\left(\frac{9}{2}\right)}^2 \\ = \left ( \scriptsize y + \normalsize \frac{9}{2} \right)^2 \)

\( \frac{81}{4} \) must be added to make it a perfect square

iii.  h2 – 3h 

= \(\scriptsize h^2 \: – \: \normalsize {\left(\frac{3}{2}\right)}^2 \\ = \left ( \scriptsize h \: – \: \normalsize \frac{3}{2} \right)^2 \)

\( \frac{9}{4} \) must be added to make it a perfect square

iv. x2 + 7x 

= \(\scriptsize x^2 + \normalsize {\left(\frac{7}{2}\right)}^2 \\ = \left ( \scriptsize x + \normalsize \frac{7}{2} \right)^2 \)

\( \frac{49}{4} \) must be added to make it a perfect square

v. x2 – 10x 

= \(\scriptsize x^2 + \normalsize {\left(\frac{10}{2}\right)}^2 \\ = \left ( \scriptsize x + \normalsize \frac{10}{2} \right)^2 \)

\( \frac{100}{4} \: \scriptsize = 25 \) must be added to make it a perfect square

vi. \( \scriptsize y^2 \: – \: \normalsize \frac{2y}{3} \)

= \( \scriptsize y^2 \: – \: \left (\normalsize \frac{\frac{2y}{3}}{2} \right) \)

= \( \scriptsize y^2 \: – \: \left (\normalsize \frac{2}{3} \: \times \: \frac{1}{2} \right) \)

= \(\scriptsize y^2 \: – \: \normalsize {\left(\frac{2}{6}\right)}^2 \\ = \scriptsize y^2 \: – \: \normalsize {\left(\frac{1}{3}\right)}^2 \\ \left (\scriptsize y \: – \: \normalsize \frac{1}{3}\right)^2 \)

\( \frac{1}{9} \) must be added to make it a perfect square

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