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Science & Math for K6 - K12 Students

Home SAT Math Grid in Section Exercise-X , XI & XII
Exercises - X,XI &XII
Exercise-X
1. C is a point on such that AC = AD. If the length of CD = 3p + 6 and the length of AD is 60''. What is the value of p?
Sol:
  AC = AD
  AD = 60''
  AC = × 60''
  = 15''
  CD = 60'' – 15''
  = 45''
  CD = 3p + 6''
    = 45''
  3p + 6'' = 45''
  3p = 45 – 6
  3p = 39
  p = 13''
 
 
2. If 5x + 3y = 60 and Then the value of y is
Sol: 5x + 3y = 60 and
 
 
3. If = 4, what is the value of x?
Sol: = 4
  = 4
  = 4
  x – 6 = 4(x – 2)
  x – 6 = 4x – 8
  4x – x = 8 – 6
  3x = 2
  x =
  = 0.6666
  x = 0.67
 
 
4. 24 steel containers can contain 204 litres of water. What is the volume of water that can be stored in each steel container.
Sol: Number of steel containers = 24
  Total volume of water = 204litres
  volume of water in each container =
  =
  = 8.5 litres
 
 
5. f(x) = ax + b. If f(5) = 20, f(3) = 14, what is the volume of ?
Sol: f(x) = ax + b
  f(5) = a(5) + b
  5a + b = 20
  f(3) = a(3) + b
  3a + b = 14
 
 
 
6. In v = u + at, if v = 100, u = 64, t = 8 then the value of a is
Sol: v = u + at
  100 = 64 + a(8)
  100 – 64 = 8a
  8a = 36
  a =
  a =
  = 4.5
 
 
7.
The circumference of each circle is 14π''. What is perimeter of the square?
Sol: 2πr = 14π
  r = 7''
  side of each square = 2r
  = 2 × 7
  = 14''
  perimeter of square = 14'' × 4
  = 56''
 
 
8.
ABCD is a rectangle 2AB = 4BC = 28''. Find the perimeter of the given figure.
Sol: 2AB = 28''
  AB = 14''
  R = 7''
  4BC = 28''
  BC = 7''
  r =
  perimeter = πR × 4 + πr × 4
  =
  = 88'' + 44''
  = 132''
 
 
9.
Circumference of each circle is 88''. What is the altitude of ΔABC?
Sol: 2πr = 88
  r =
  r = 14''
  Side of ΔABC = 14 × 2
    = 28''
  Height of ΔABC =
    = √3 × 14
    = 1.7 × 14
    = 23.8''