Mathematics MOCK revision with answers

Solve the following inequalities
3 – 2x < 5
4 – 3x > - 8.

-starting with the first part of the inequality, 3 - 2x < 5
-When we take 3 to the other side, we get -2x < 2
-Divide both sides by -2 (dividing by a negative number changes the inequality sign.)
-Therefore we get x > -1
-For the second part, 4 - 3x > -8
-Taking 4 to the other side -3x > -4
-Dividing both sides by -3   x < 1 1/3
-Therefore our inequalities become  -1 < x < 1 ⅓

Find the equation of the perpendicular line that passes through the mid – point X of C( - 7 , 8) and D ( 3 , - 8)

To get the equation of a line, we have to determine the point at which it passes
We have been given a hint that it is the mid point of the line C(-7 ,8) and D(3, -8)
To get the mid-point We take ((x1 + x2)/2 + (y1+y2)/2)
 = (( -7 + 3)/2 , (8 + -8)/2) = (-2,0)
Something else we know is that gradient of perpendicular lines are negative
So first we get the gradient of this line, which is change in y/ change in x
= (8 -- 8)/(-7-3) = 16/-10
To find the equation, we apply this formula

y - y1 = m(x - x1), where m is the gradient
y = 0 +-16/10( x - -2)
y = -16/10x - 16/5
5y = -8x -16

We know that the area of a triangle = 1/2(b x h)
Let's assume height = x
Base becomes x + 3
Therefore area of the triangle

1/2((x(x + 3)) = 35

X²+3x-70=0
X(x+10)-7(x+10) = 0
(X+10)(X-7)=0
X =-10 or x=7
:HEIGHT = 7cm

A certain two – digit number is equivalent to five times the sum of the digits. It is found to be 9 less than the number formed when the digits are interchanged. Find the number

Let x be the 10's digit and let y be the ones digit.

10x + y = 5 (x + y)
10x + y = (10y + x) - 9

5x - 4y = 0
9x - 9y = -9