Math

• This paper consists of 11 pages
• Answer all questions in the booklet
• Show all working out on the test paper
• Write neatly and legibly
• Write in blue or black pen and drawings in pencil
• All the best!
• Properties


  • a(b+c) = ab + ac
  • p(r-q) = pr + pq
  • a + (b+c) = (a+b) + c
  • p × r × q = r × q × p
• Prime number


  A natural number greater than 1 that has no positive divisors other than 1 and itself
• Prime numbers between 10 and 20

  • 11
  • 13
  • 17
  • 19
• The value of any number divided by zero is undefined
• The quotient of 150 and 15 is 10
• Calculating LCM


  1. Identify all the prime factors of each number

  2. Find the highest power of each prime factor

  3. Multiply all the prime factors with their highest powers
• Calculating HCF


  1. Identify all the prime factors of each number

  2. Find the lowest power of each prime factor

  3. Multiply all the prime factors with their lowest powers
• The LCM of 144, 180 and 192 is 1440
• The HCF of 49, 91 and 112 is 7
• 8 1/2 - 1 1/8 + 2 1/4 = 9 5/8
• 525 × 4 + √1000^3 - 240 ÷ 48 + 35 = 2100 + 10 - 5 + 35 = 2140
• Solving word problem: Packing for holiday

  1. Find the total weight of the two suitcases

  2. Subtract the total weight from the 40kg limit

  3. The remaining weight is what can be packed in the third bag
• The total weight of the two suitcases is 22 1/2 kg + 14 2/5 kg = 36 7/10 kg
• The weight that can be packed in the third bag is 40kg - 36 7/10 kg = 3 3/10 kg
• Solving word problem: Fuel consumption

  1. Find the fuel consumption rate (litres per km)

  2. Multiply the fuel consumption rate by the distance to find the litres needed
• The fuel consumption rate is 10 litres per 50 km = 0.2 litres per km
• The litres needed to travel 60 km is 0.2 litres per km × 60 km = 12 litres
• Solving word problem: Sharing sweets

  1. Find the total number of parts in the ratio

  2. Divide the total number of sweets by the total parts to get the value of each part

  3. Multiply each person's part by the value per part to get their share
• The total parts in the ratio 2:3:4 is 2 + 3 + 4 = 9
• Each child will get 36 ÷ 9 = 4 sweets
• If the ratio is based on their ages of 3, 6 and 9 years, the ratio would be 3:6:9 = 1:2:3
• The total parts in the ratio 1:2:3 is 1 + 2 + 3 = 6
• Each child would get 36 ÷ 6 = 6 sweets
• √1 = 1, not √1^3
• √36 + 64 = √100 = 10, not √36 + √64
• 79 is not equal to 7 × 9
• 28/35 is not equal to 80%
• 9 is a perfect square, not a perfect cube
• 0.018 × 300 = 5.4
• 125 is a perfect cube
• 34 + 6 - 56 ÷ 7 × 3 = 16
• Acute angle PŜQ is 45°


  Reflex angle PŜQ is 315°
• Angles named by three letters

  B̂1, B̂3, B̂2, Reflex angle at B̂
• Angles named by single letter and subscript

  AB̂D, EB̂C