Mathematics MOCK revision with answers

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  1. 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

  2. Determine the quartile deviation of the following data 4,9,5,4,7,6,2,1,6,7,8,3.

    -Quartile deviation = (upper quartile - lower quartile
    -To get the quartiles, we first arrange the data in ascending order
    -1, 2, 3, 4, 4, 5, 6, 6, 7, 7,8,9
    -Lower quartile = (3 +4)/2 = 3.5
    -Upper quartile = (7 + 7)/2 = 7
    -Quartile deviation is therefore (7 - 3.5)/2 = 1.75

  3. 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

  4. The base of a triangle is 3cm longer than its height. Given that the area of the triangle is 35cm2, determine the height of the triangle.

    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

  5. 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


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