MATRIX 1

FUNCTIONS 1

Given that F(x) = 3x  +  11. Find F(-2)

Solution

F(x) = 3x  +  11

F(-2) = 3(-2)  +  11

F(-2) = -6  +  11

F(-2) = 5

Hence  F(-2) = 5

TRY THIS………………..

Given that F(x) = 12x  +  78. Find F(-4)

UNITS OF VOLUME 1

Change 42.5 liters of water into milliliters

Solution

1L  =  1000mL

42.5L = ?

___________________________  

 = 42.5 x  1000

           1

= 42.5 x 1000

= 42500mL. Answer

TRY THIS...................................

Change 15.3 liters of milk into milliliters

PERFECT SQUARES 1

If 16x² + 24x + h is a perfect square, find h.

Solution

a = 16, b = 24, c = h.

b² = 4ac

(24)² = 4 x 16 x h

576 = 64h

576  =   64h

 64       64

           

h = 9

Hence h = 9

TRY THIS...............

If 4x² + 12x + w is a perfect square, find w.

EXPAND 1

Expand 8w(5w + 5 - w)

Solution

= 8w(5w + 5 - w)

= (8w x 5w) + (8w x 5) - (8w x w)

= 40w² + 40w - 8w²

= [40w² - 8w²] + 40w collecting like terms

= 32w² + 40w answer

TRY THIS………..

Expand 4a(9a+ 11 - a)

TRANSPOSE 1

BODMAS 1

Evaluate  70 + 6 – 5 – 7 – 9 + 15.

Solution

= 70 + 6 – 5 – 7 – 9 + 15

= 70 + 6 + 15 – 5 – 7 – 9

= 70 + 6 + 15 – ( 5 + 7 + 9)

= 91 – 21

= 70

TRY THIS………

Evaluate  55 + 6 – 7 – 3 – 13 + 6

EXPONENTIALS 1

Simplify (d⁴)⁸

solution

= (d⁴)⁸

=  d^4x8

=  d³²

TRY THIS........

Simplify  (k¹⁸)³

INEQUALITIES 1

Find x if 5x – 21 ≤ x + 15 ≤ 6x.

Solution

5x – 21 ≤ x + 15 and  x + 15 ≤ 6x

5x – x ≤ 21+ 15 and  15 ≤ 6x - x

4x ≤ 36 (divide by 4 both sides) and  15 ≤ 5x (divide by 5 both sides)

x ≤ 9 and  3 ≤ x

x ≤ 9 and  x ≥ 3 answer

TRY THIS……..

Find x if 6x – 35 ≤ x + 15 ≤ 2x.

SLOPE 1

Find the slope of a line which passes through (17, 13) and (6, 8)

Solution

x₁ = 17,  y₁ =13,  x₂ = 6,  y₂ = 8

m = y2 –y1

        x2 – x1

m =   8 –13

          6 –17

m =   -5

         -11

  

Hence the slope is ⁵/11

TRY THIS……..

Find the slope of a line which passes through (6, 13) and (9, -2)