Maths past paper questions

• What is the formula for the surface area of a sphere?

  Surface area of a sphere = $4\pi r^2$
• How do you calculate the total surface area of a solid hemisphere with radius $x$?


  • Total surface area = $2\pi x^2 +$$\pi x^2 =$$3\pi x^2$
• How do you calculate the total surface area of a solid cylinder with radius $3x$ and height $x$?


  • Total surface area = $2\pi(3x)^2 +$$2\pi(3x)(x) =$$18\pi x^2 +$$6\pi x^2 =$$24\pi x^2$
• What is the ratio of the total surface area of the hemisphere to the total surface area of the cylinder?

  The ratio is $1:8$
• If 3K = 4L, what is the relationship between K and L?

  K is equal to $\frac{4}{3}L$
• How many M weights are needed to balance one L weight if $1 K =$$L +$$2M$?


  6 M weights are needed to balance one L weight
• What is the equation for the angles EBD, ABE, and DBC in terms of x?

  • $EBD =$$x$
  • $ABE =$$5x$
  • $DBC =$$3x$
• What is the sum of angles EBD, ABE, and DBC on a straight line?

  The sum is $180^\circ$
• What is the value of angle EBD if $x +$$5x +$$3x =$$180^\circ$?


  Angle EBD is $100^\circ$
• What two prime numbers can be multiplied to get an even number between 50 and 60?

  2 and 29
• How do Andrew and Bruce share money in the ratio 5:6 if Bruce gets £96?

  • Bruce's share = £96
  • Andrew's share = $(96 \div 6) \times 5 =$$80$
• How much money does Carl receive from Andrew and Bruce?

  Carl receives £84
• What is the equation to find the value of $a$ in $2a \times 3 \times 5^2 =$$600$?


  $a =$$8$
• What is the mean of the ages of Sunita, Beth, and Joel if their mean age is 5?

  The total age is 15 years
• How old is Joel if Sunita is $x$ years old and Beth is one year younger?


  Joel is 8 years old
• What is the inequality for the value of $a$ in standard form?


  $1 \leq a < 10$
• How do you write 7200 in standard form?

  $7.2 \times 10^3$
• What is $b \times 10^{-n}$ if $b =$$7.2 \times 10^3$?


  $0.0072$
• How do you solve the simultaneous equations $2x - 5y =$$13$ and $3x +$$4y =$$8$?


  1. Multiply the first equation by 4: $8x - 20y =$$52$
  2. Multiply the second equation by 5: $15x +$$20y =$$40$
  3. Add the equations: $23x =$$92$
  4. Solve for $x$: $x =$$4$
  5. Substitute to find $y$: $y =$$1$
• What is the simplest form of $0.1333\ldots$ as a fraction?


  $\frac{4}{30} =$$\frac{2}{15}$
• How can you show that $4\sin 30^\circ - \tan 45^\circ \div 2 \cos 30^\circ$ can be written as $\tan x$?


  It simplifies to $\tan 30^\circ$
• What is the inverse function of $f(x) =$$\frac{1}{2}x$?


  • The inverse function is $f^{-1}(x) =$$2x$
• What is the value of $g(x) =$$x - x^2$ when $x =$$0$?


  g(0) = 0
• What is the value of $g(x)$ when $x =$$-6$?


  g(-6) = -6 - 36 = -42