Algebra: formulae, sequences and missing numbers – Year 6 maths test answers to download as PDF

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1. Answer to Question 1 (3 marks)

   1. Replace \(h\) with 3: \(4\times3=12\) and \(8+12=\) £20. (1 mark)
   2. Set the formula equal to 28: \(8+4h=28\). Take away 8: \(4h=20\); divide by 4: \(h=\) 5 hours. Check: \(8+4\times5=28\). (1 mark)
   3. Two lengths and two widths: \(P=2l+2w\). With \(l=9\) and \(w=4\): \(18+8=\) 26 cm. (1 mark)

2. Answer to Question 2 (4 marks)

   1. Add 7 each time: 31, 38. (1 mark)
   2. The difference is 4. \(4n\) gives 4, 8, 12, 16, so add 2: \(4n+2\). (1 mark)
   3. \(4\times30+2=\) 122. (1 mark)
   4. \(4n+2=82\) gives \(4n=80\) and \(n=20\). Yes, 82 is the 20th term. (1 mark)

3. Answer to Question 3 (4 marks)

   1. Undo adding 14 by subtracting it: \(n=39-14=\) 25. Check: 25 + 14 = 39. (1 mark)
   2. \(5a\) means 5 times \(a\), so divide: \(a=65\div5=\) 13. (1 mark)
   3. Subtract 7 first: \(3x=27\); then divide by 3: \(x=\) 9. Check: \(3\times9+7=34\). (1 mark)
   4. Add 9 to both sides: \(4y=28\); divide by 4: \(y=\) 7. Check: \(28-9=19\). (1 mark)

4. Answer to Question 4 (4 marks)

   1. (12, 0), (11, 1), (10, 2), (9, 3), (8, 4), (7, 5). (1 mark)
   2. For example (0, 10), (2, 6), (4, 2), (1, 8), (3, 4), (5, 0). Any three of these. (1 mark)
   3. 1 part + 4 parts = 5 parts = 30, so 1 part = 6. The numbers are 6 and 24. (2 marks)

5. Answer to Question 5 (5 marks)

   1. \(C=60+25\times3=\) £135. (1 mark)
   2. The rule is \(C=25h+60\). The 25 is the cost for each hour, and the 60 is the fixed charge. (1 mark)
   3. \(60+25h=200\) gives \(25h=140\) and \(h=5.6\). The longest whole number of hours is 5 hours (or 5 hours 36 minutes). (2 marks)
   4. First company: \(60+25\times5=185\). Second company: \(40+30\times5=190\). The first company is £5 cheaper. (1 mark)

Total : 20 marks