Non Calculator Practice Questions

• Simplify: [3x/4]+[2x/5]

  [3xX5/20]+[2xX4/20]=[15x+8x/20]=[23x/20]
• Simplify: [5/sqrt(3)]​

  [5/sqrt(3)]X[sqrt(3)/sqrt(3)]=[5sqrt(3)/3]
• Simplify: sqrt(50)+sqrt(8)

  sqrt(50)=5sqrt(2)

  sqrt(8)=2sqrt(2)

  5sqrt(2)+2sqrt(2)=7sqrt(2)
• Solve for x: 3^[2x+1]=27

  3^[2x+1]=3^[3]

  2x+1=3

  2x=2

  x=1
• Complete the square for:x^[2]+6x-7

  (x+3)^[2]=x^[2]+6x+9

  (x+3)^[2]-16
• Find the gradient of a line through points A(2,3)and B(4,7)


  Gradient=[y2-y1/x2-x1]=[7-3/4-2]=[4/2]=2
• State the equation of a line parallel to y=3x+2 passing through the point (1,4).

  Parallel lines have the same gradient, so y=3x+c. Substitute (1,4) to find c: 4=3(1)+c

  c=1

  y=3x+1
• Simplify: (a^[3]b^[-2])X(a^[-1]b^[4])


  a^[3+(-1)]b^[-2+4]=a^[2]b^[2]
• What are the circle theorems for angles subtended by the same arc?


  • Angles subtended by the same arc are equal.
  • Angles in a semicircle are right angles (90°).
  • The angle at the center is twice the angle at the circumference.
• Given a is directly proportional to b^[2], write the equation for a in terms of b if a=50 when b=5.

  • Set up the proportional relationship: a=kb^[2]
  • Substitute to find k: 50=kx5^[2]

  k=2

  • Final equation: a=2b^[2]