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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
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    1 Quiz
  6. Factorisation II | Week 6
    3Topics
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    1 Quiz
  7. Factorisation III | Week 7
    3Topics
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    1 Quiz
  8. Substitution & Change of Subject of Formulae | Week 8
    2Topics
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    1 Quiz
  9. Simple Equations Involving Fractions | Week 9
    3Topics
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    1 Quiz
  10. Word Problems | Week 10
    1Topic
    |
    1 Quiz
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One of the major uses of Algebra is to express mathematical relationships in form of formulae.

A formulae is an equation that describes the relationship between two or more quantities.

Letters are used to represent unknown values in a formulae.

For example the frequency f in cycles per unit time i.e.

F = \(\frac {\omega}{2\pi} \)

This formulae shows the relationship between frequency (f) and circular velocity (\( \scriptsize \omega \))

F is called the subject of the formulae or equation.

i. If, F = ma, find F when  m = 10 and  a = 6

F = ma

F = 10 x 6

F = 60N

ii. If y = m + c,  find y when m = 5, = -2,   c  = -3.

             y = mx   +  c

            y = 5 x -2 + -3

             y = -10 – 3

              y  = -13

iii. If, V = mgh  find v when  m = 10, g = 9.8  and  h = 5

              V  = mgh

              V = 10 x 9.8 x 5   =  490

iv. If y =  16x2  – 9z2,  find y when x = 7, and  z  =  5

y =  16 (7)2 – 9 (5)2

y = 16 x 49 – 9 x 25

y = 784 – 225

y = 559

v. The sum of terms in a geometric progression is given as

s = \( \frac{a( 1 \; – \; r^n)}{1 \; – \; r} \)

Calculate s when  n = 4, a = 3 and r = 3

s = \( \frac{a( 1 \; – \; 3^4)}{1 \; – \; 3} \)

s = \( \frac{( 3(-80)}{-2} \)

s = \( \frac{(-240)}{-2} \)

s = 120

vi. Here’s a formulae for finding the area of a triangle;

A = \( \scriptsize \sqrt{s(s \; – \; a)(s \; – \; b)(s \; – \; c)} \)

Where s = \( \frac{a + b + c}{2} \)  and a, b and c are the three sides

Find the area of a triangle when a = 5cm, b = 8cm, c = 11cm

s = \(\frac{a + b + c}{2} = \frac{5 + 8 + 11}{2} \\ = \frac{24}{2} \\ \scriptsize = 12 \)

A = \( \scriptsize \sqrt{s(s \; – \; a)(s \; – \; b)(s \; – \; c)} \)

A = \( \scriptsize \sqrt{12(12 \; – \; 5)(12 \; – \; 8)(12 \; – \; 11)} \)

A = \( \scriptsize \sqrt{12(7)(4)(1)} \)

A = \( \scriptsize \sqrt{12 \; \times \; 28} \\ \scriptsize = \sqrt{336} \\ \scriptsize = 18.33 \)

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