common entrance

• If PQ is a straight line and some angles are marked in degrees as x, y, and 7x, what is the relationship between these angles?

  x + y + 7x = 180
• Given PQ is a straight line, and angles are marked as x, y and 7x degrees, where $x =$$20^\circ$, what is the size of angle y?


  $40^\circ$
• In a regular pentagon inscribed in a rectangle, what is being calculated in the diagram?

  The size of angle a
• A TV costs £650 and the price increases by 28%, how much is the increase in price?

  £182
• A TV costs £650, the price increased by 28%, and Martin buys it with a 28% discount on the new price; what does Martin pay?

  £665.64
• Karim sold his house in 2023 for £442,400, making a 12% profit, so how much did he originally pay?

  £395,000
• What shape is a tin of beans?

  A cylinder
• What shape is the label that exactly covers the curved surface of a cylindrical tin of beans?

  Rectangular
• A tin has a diameter of 7 cm and a height of 10 cm; what is the radius?

  3.5 cm
• A tin has a diameter of 7 cm and a perpendicular height of 10 cm; what is the area of the label that wraps around it?

  $220 cm^2$
• What volume is required on average per bean?

  0.83 cm$^3$
• What are the dimensions of the rectangular track Anthony and Beatrice run around?

  30 m long and 20 m wide
• A cylindrical tin has a diameter of 7 cm and height of 10 cm, and each bean requires 0.83 cm$^3$ volume; approximately how many beans are in the tin?


  Approximately 296 beans
• What is the perimeter of the rectangular track that Anthony runs around?

  100 m
• Anthony runs around a track with a perimeter of 100 m at 8 metres per second; how long does it take him?

  12.5 seconds
• Beatrice runs from A to B to D to A on a rectangular track 30 m long and 20 m wide; how far does she run?

  86.06 m
• Beatrice runs 86.06 m at 6.5 metres per second; how long does it take her?

  13.24 seconds
• Anthony runs a lap in 12.5 seconds and Beatrice runs a shorter distance in 13.24 seconds; who finishes first and by how much?

  Anthony by 0.74 seconds
• What are the dimensions of the metal cube's edges?

  7 cm
• What is the mass of 1 cubic centimetre of the metal cube?

  2.7 grams
• A metal cube has edges of length 7 cm; what is its volume?

  $343 cm^3$
• Tunnels with 1-cm square cross-sections are cut through a 7cm metal cube from each face to the opposite face; how many tunnels are there?

  Three
• Tunnels with 1-cm square cross-sections are cut through a 7cm metal cube; what is the volume of each tunnel?

  $7 cm^3$
• The volume of the metal cube is $343 cm^3$, and three tunnels of volume $7 cm^3$ are cut through it; what is the volume of the remaining metal?


  $322 cm^3$
• The volume of the remaining metal is $322 cm^3$, and 1 cm$^3$ of the metal has a mass of 2.7 grams; what is the mass of the remaining metal?


  869.4 grams
• A metal cube with tunnels cut through it is painted gold, inside and out; what is the area painted equal to?

  The total surface area
• A metal cube has edges of length 7 cm; what is the area of each face?

  $49 cm^2$
• A cube has faces of area $49 cm^2$; what is the total surface area of the cube?


  $294 cm^2$
• Tunnels with 1-cm square cross-sections are cut through a 7cm metal cube from each face to the opposite face; what is the internal surface area of each tunnel?

  $28 cm^2$
• Tunnels with 1-cm square cross-sections are cut through a cube creating three tunnels with surface area $28 cm^2$; what is the total internal surface area?


  $84 cm^2$
• A cube has a surface area of $294 cm^2$, and tunnels through it have surface area $84 cm^2$; what is the total surface area?


  $378 cm^2$
• How many atoms are there in a human body, according to the text?

  $7.3 \times 10^{27}$
• How many atoms are there in the Earth, according to the text?

  $1.3 \times 10^{50}$
• If a human has $7.3 \times 10^{27}$ atoms and the Earth has $1.3 \times 10^{50}$ atoms, approximately how many humans would have the same number of atoms as the Earth?


  $2 \times 10^{22}$
• How many years are there in a millennium?

  1000 years
• Approximately how many seconds are there in a millennium in standard form to 3 significant figures?

  $3.16 \times 10^{10}$
• If an equilateral triangle and a regular hexagon have equal perimeters, what does this imply about their side lengths?

  Hexagon sides are half triangle sides
• If an equilateral triangle and regular hexagon have equal perimeters, and the triangle has an area of $12 cm^2$, what must be calculated to find the hexagon's area?


  The area of the hexagon
• Solve the equation $2x(3x + 1) +$$3x(5 + 2x) =$$52$ for x.


  $x =$$2$
• An equilateral triangle and a regular hexagon have equal perimeters; the triangle has an area of $12 cm^2$; what is the area of the hexagon?


  $18 cm^2$