ALGEBRA B2

If 3w² = 507; find w

Solution

3w² = 507

3w² = 507               [Dividing by 3 both sides]

3          3

 

w² = 169

w = 13          Because the square root of 169 is 13.   

 

Hence w = 13         

 

TRY THIS……………………….

 

If 5y² = 605; find y.

GEOMETRY B1

 

A regular polygon has 37 sides. Find the total interior angles of that polygon.

Solution

 

n = 37

 

Total angles = (n - 2)180⁰

 

                   = (37 – 2)180⁰

 

                   = 35 x 180⁰

 

                   = 6300⁰

 

Hence total interior angles = 6300⁰

 

TRY THIS……………………….

 

A regular polygon has 23 sides. Find the total interior angles of that polygon.

RELATIONS B1

 

Let R={(8,23), (0,1), (-2,-5), (14,-10)}. Find the domain and range of R.

 

solution

 

For domain, we check on the values of x in each point.

Domain={8, 0, -2, 14}

 

For range we check on the values of y in each point.

Range={23, 1, -5, -10}

 

Hence Domain={8, 0, -2, 14} and Range = {23, 1, -5, -10}

 

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

 

Let R={(12,7), (-33,13), (-18,-2), (29, -4)}. Find the domain and range of R.

VARIATIONS B1

 

x is directly proportional to y. x=32 while y=16. Find y when x is 720.

 

Solution

 

x ⍺ y

x = ky   [ We omit ⍺ by writing it as =k ]

 

32 = k x 16

 

32 = 16k    [dividing by 16 both sides]

16    16

 

k = 2

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

 

Now; k = 2, y= ? x = 720.

 

x = ky

 

720 = 2 x y

 

720 = 2y

 2       2

 

y = 360.

 

TRY THIS…………….

 

x is directly proportional to y. x=40 while y=4. Find y when x is 430.

MEASUREMENTS B1

 

Convert 83434m into km.

Solution

1km  = 1000m

  ?     = 83434m

 

After cross-multiplying;

= 1 x 83434

      1000

 

=   83434

     1000

 

= 83.434 km  [After dividing 83434 by 1000]

Hence 83434m = 83.434km

 

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

 

Convert 42428m into km.

QUADRATICS B1

 

Factorize completely qc + qr - cr - c².  

 

Solution

 

= qc + qe - cr - c².

 

= (qc + qr) – (cr - c²).      [Grouping ]

 

= q(c + r) - c(r + c).   [after factoring out q and c]

 

 = (c + r)(q - c).

 

  Hence qc + qr - cr - c². =  (c + r)(q - c).   

 

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

 

Factorize completely pe + pr - re - e². 

FUNCTIONS B2

 

Find a linear function f(x) with gradient -6 which is such that f(5)=14.

 

Solution.

 

m=-6, points = [5,14] and [x, f(x)]

 

m = y₂-y₁/x₂-x₁

 

-6 = [f(x) – 14]/x-5

 

f(x)-14=-6(x-5)  [after cross multiplying]

 

f(x)-14=-6x+30

 

f(x)=-6x+30+14

 

f(x)=-6x+44

 

Hence a linear function is f(x) = -6x + 44.

 

TRY THIS……….

 

Give out a linear function f(x) with gradient -7 and f(2)=12

SLOPE B1

 

Find the slope of a line which passes through (-3, -4) and (8,-13)

 

Solution

 

x1 = -3,  y1 =-4,  x2 = 8,  y2 = -13

 

m = y2 –y1

       x2 – x1

 

m =   -13 –(-4)

          8 –(-3)

 

m =   -13 + 4         [Since -(-4) = +4, and -(-3) = +3] 

          8 + 3

 

m =    - 9

          11

 

Hence the slope is -9/11

 

 

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

 

 

Find the slope of a line that passes through (-11, -2) and (4,-10)

LOGARITHMS B2

 

Simplify Log₂1024 - Log₃27

 

solution

 

= Log₂1024 - Log₃27

 

= Log₂2¹⁰ - Log₃3³    [Since 1024=2¹⁰  and 27=2³ after prime factorization]

 

= 10Log₂2 - 3Log₃3   [since log_aaⁿ  = nlog_aa]

 

= (10 x 1) - (3 x 1)    [since log_cc = 1]

 

= 10 - 3

 

= 7

 

Hence Log₂1024 - Log₃27 = 7

 

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

 

 

Simplify Log₂256 – Log₅125

FUNCTIONS B1

 

If f(x) = x⁴ + kx² + 6x + 7 has a remainder of 91 when divided by x+2; find k.

 

solution

 

f(x) = x⁴ + kx² + 6x + 7

 

x + 2 = 0

 

x = -2

 

f(x) = (-2)⁴ + k(-2)² + 6(-2) + 7 = 91

 

16 + 4k + (-12) + 7 = 91

 

16 + 4k - 12 + 7 = 91

 

16 + 4k - 5 = 91

 

4k + 16 - 5 = 91

 

4k + 11= 91

 

4k = 91 - 11

 

4k = 80

 

4k = 80

4      4

 

k = 20

 

hence k = 20

 

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

 

 

If f(x) = x⁴ - hx² + 2x - 13 has a remainder of 16 when divided by x-3; find h.