Section 1: Integer addition
Answers are required to their full accuracy
1.
53 + 78
=
(1)
2.
38 + 31
=
(1)
3.
756 + 234
=
(2)
4.
509 + 821 + 716
=
(3)
5.
27848 + 79326
=
(4)
6.
8881 + 4402 + 6456 + 2875
=
(5)
7.
291582 + 792639 + 574881
=
(6)
8.
29760 + 837686 + 243313
=
(6)
9.
30361 + 58557 + 92139 + 91411 + 42374
=
(7)
10.
161551 + 459988 + 633486 + 490513 + 327218
=
(8)
11.
1361649467 + 8498272604 + 7951552797
=
(10)
12.
8810703481 + 9198624294 + 4111025673 + 7350258122 + 2375272822
=
(12)
(65)
Section 2: Integer subtraction
Answers are required to their full accuracy
1.
84 - 32
=
(2)
2.
46 - 28
=
(2)
3.
513 - 193
=
(3)
4.
5127 - 769
=
(4)
5.
97924 - 20285
=
(5)
6.
250635 - 84261
=
(6)
7.
438698 - 57853
=
(6)
8.
6987323 - 718500
=
(7)
9.
70552375 - 31901028
=
(8)
10.
8992480096 - 1753498538
=
(10)
11.
772922424705 - 331091127557
=
(12)
(65)
Section 3: Decimal addition and subtraction
Answers are required to their full accuracy
1.
1.5 + 6.4
=
(2)
2.
9.8 + 9.2 + 8.7
=
(3)
3.
6.8 + 8.5 + 1.1 + 1.3
=
(4)
4.
583.2 + 741.8 + 753.9
=
(5)
5.
100.31 + 221.76 + 5245.20 + 3041.70
=
(7)
6.
88.98 + 350.30 + 58.63 + 61.71 + 77.22 + 215.10
=
(8)
7.
180311.4770 + 16112.6943
=
(9)
8.
447239.70870 + 42639.14218 + 468498.35660 + 49681.19885
=
(12)
9.
4.7 - 2.2
=
(2)
10.
10.2 - 9.3
=
(3)
11.
8532.1 - 5707.4
=
(5)
12.
1649.05 - 835.84
=
(6)
13.
60136.53 - 39195.88
=
(7)
14.
86315.339 - 75446.732
=
(8)
15.
475665.836 - 383508.482
=
(9)
16.
5273145.892 - 4946090.095
=
(10)
(100)
Section 4: Integer multiplication
Answers are required to their full accuracy
1.
2 x 21
=
(2)
2.
9 x 85
=
(2)
3.
82 x 28
=
(3)
4.
53 x 591
=
(4)
5.
75 x 2096
=
(5)
6.
686 x 4413
=
(6)
7.
42 x 656953
=
(7)
8.
9237 x 98302
=
(8)
9.
1062 x 292247
=
(9)
10.
24776 x 427083
=
(10)
11.
4190844 x 77681704
=
(14)
12.
3x5x8
=
(2)
13.
6 x 13 x 92
=
(4)
14.
37 x 74 x 91
=
(5)
15.
71 x 679 x 176
=
(7)
16.
7994 x 3411 x 82685
=
(12)
(100)
Section 5: Integer division (exact)
Answers are required to their full accuracy
1.
63
/
9
=
(2)
2.
210
/
6
=
(3)
3.
5278
/
91
=
(4)
4.
94764
/
298
=
(5)
5.
721140
/
303
=
(6)
6.
5436376
/
4169
=
(7)
7.
49746165
/
7905
=
(9)
8.
448733628
/
7266
=
(10)
9.
12511245945
/
69
=
(11)
10.
49351259100
/
949062675
=
(13)
(70)
Section 6: Approximate multiplication
For Q1-5, give the answer to the nearest integer.
1.
1.4 x 3.2
=
(3)
2.
4.1 x 8.3
=
(4)
3.
9.8 x 373.3
=
(6)
4.
365.8 x 835.3
=
(8)
5.
40.53 x 2050618.1
=
(12)
For Q6-7, give the answer to four significant figures.
6.
7.4 x 8399.1
=
(7)
7.
70.1 x 717.3 x 457.2
=
(10)
For Q8-9, give the answer to five significant figures.
8.
95.4 x 2.66659
=
(9)
9.
579.2 x 881.6 x 299.5
=
(11)
(70)
Section 7: Approximate division
For Q1-7, give the answer to the nearest integer.
For example, 13 / 3 = 4 or 85 / 8 = 11
1.
74 / 9
=
(2)
2.
430 / 41
=
(3)
3.
6087 / 388
=
(5)
4.
28172 / 1264
=
(6)
5.
8503905 / 599
=
(8)
6.
520912914 / 377
=
(10)
7.
61332950958 / 86
=
(11)
For Q8-10, give the answer to four significant figures.
8.
80.14825 / 3.25
=
(8)
9.
79670.432 / 27.4
=
(9)
10.
88957.787 / 5675.5
=
(10)
For Q11-12, give the answer to six significant figures.
11.
251657.59367 / 36.622
=
(11)
12.
56103609 / 268321
=
(12)
(95)
Section 8: Factorisation
Specify each number as the product of prime factors. Factors must be recorded the relevant number of times, although the order does not
matter.
For example, 84 = 2, 2, 3, 7 or 7, 2, 3, 2 are both correct (but 2, 3, 7 is not)
1.
55
=
(2)
2.
56
=
(2)
3.
858
=
(3)
4.
7098
=
(4)
5.
85750
=
(5)
6.
626535
=
(6)
7.
5087250
=
(7)
8.
36722686
=
(8)
(37)
Section 9: Fractions (addition and subtraction)
Give all answers in their simplest form (3 3/4, 3 9/12 and 15/4 all represent the same number, but only the first is in its' simplest form).
1.
3 5/6 + 2 3/4
=
(2)
2.
6 1/8 + 11 2/9
=
(3)
3.
14 2/13 + 22 8/9
=
(5)
4.
8 14/15 + 16 13/14 + 14 8/11
=
(7)
5.
27 4/5 + 16 35/37 + 34 17/49
=
(8)
6.
41 31/59 + 56 72/139 + 46 47/127
=
(11)
7.
2 4/7 - 1 5/6
=
(2)
8.
22 12/19 - 11 16/37
=
(5)
9.
83 39/85 - 75 37/56
=
(7)
10.
321 62/109 - 269 41/134
=
(10)
(60)
Section 10: Fractions (multiplication and division)
Give all answers in their simplest form (3 3/4, 3 9/12 and 15/4 all represent the same number, but only the first is in its' simplest form).
1.
1 2/3 x 2 2/5
=
(2)
2.
12 1/5 x 6 2/13
=
(4)
3.
88 5/28 x 77 4/15
=
(6)
4.
123 7/12 x 129 31/81
=
(9)
5.
1 3/7 x 2 3/8 x 1 3/4
=
(5)
6.
16 1/2 x 8 3/11 x 6 3/5
=
(8)
7.
30 19/46 x 44 19/49 x 37 23/30
=
(11)
8.
7 19/35 / 2 2/7 x 1 1/11
=
(3)
9.
175 427/468 / 12 43/48
=
(7)
10.
2097 813/12995 x 48 88/113
=
(10)
(65)
Section 11: Calendar calculation
For Q1-10, enter the correct weekday (eg. Saturday or Sat).
=
(3)
1.
22 July 1642
(22/07/1642)
=
(3)
2.
1 May 1886
(01/05/1886)
=
(3)
3.
23 December 1596
(23/12/1596)
=
(3)
4.
22 September 2112
(22/09/2112)
=
(3)
5.
30 November 2281
(30/11/2281)
=
(3)
6.
6 December 1731
(16/12/1731)
=
(3)
7.
25 February 1924
(25/02/1924)
=
(3)
8.
14 June 1515
(16/06/1515)
=
(4)
9.
15 April 447
(15/04/0447)
=
(4)
10.
18 January 3761
(18/01/3761)
For Q11-14, insert any month for which the equation is correct (eg. October or Oct). The solution is not necessarily unique.
11.
21
1863
=
Tuesday
(6)
12.
14
1920
=
Wednesday
(6)
13.
26
1723
=
Thursday
(6)
14.
25
3456
=
Saturday
(6)
For Q15-18, inserrt the largest year less than or equal to 2140 (inclusive) for which the equation is correct. For example, if the equation
works with years 2131 and 2139, then only 2139 is the correct answer.
15.
14 August
=
Friday
(6)
16.
20 February
=
Thursday
(6)
17.
7 December
=
Tuesday
(6)
18.
30 January
=
Saturday
(6)
For Q19-22, give the time in seconds between the given dates and times.
19.
From 15:10:51 to 16:07:12
=
(3)
20.
From 16:02:21 on 07/05/1927 to 05:06:24 on 10/05/1927
=
(4)
21.
From 17:38:38 on 18/08/2017 to 21:16:00 on 24/10/2017
=
(8)
22.
From 11:35:03 on 18/05/2066 to 01:51:29 on 25/03/2067
=
(10)
(105)
Section 12: Miscellaneous (Algebraic, next squares, next cubes, remainders)
For Q1-3, A, B, C, D and E are constants with the following values:
A = 13.97
B = 0.49
C = 6.34
D = 32.56
E = -4.04
Evaluate the following expresions and give each answer to 2 decimal places.
1.
(A + B) x C
=
(6)
2.
D+E
3
=
(8)
3.
√ (A - E)2 - (B x D)
2
=
(12)
=
(8)
x (root 1)
=
(8)
x (root 2)
=
(8)
For Q4, give x to 4 significant figures.
4.
1/46 - 1/162 = 1/x
For Q5, give x to 3 decimal places. There are two valid answers; each is marked separately.
5.
√ x = 7 - 3x
For Q6-110, give the next exact square after the given number.
For example, the next exact square after 222 is 225 (which is 15₂); only the number is required, ie "225".
6.
Next exact square after 624
=
(2)
7.
Next exact square after 83570
=
(4)
8.
Next exact square after 2052971
=
(6)
9.
Next exact square after 295694171
=
(8)
10.
Next exact square after 5127347032373
=
(12)
For Q11-14, give the enxt exact cube after the given number.
For example, the next exact square after 222 is 343 (which is 7₃); only the number is required, ie "343".
11.
Next exact cube after 718
=
(2)
12.
Next exact cube after 669462
=
(5)
13.
Next exact cube after 336087352
=
(8)
14.
Next exact cube after 437260709723
=
(12)
For Q15-21, give the remainder after dividing the two integer values.
For example, the remainder of 553 / 6 is 1 (because 553 = {92 x 6} + 1).
15.
88 / 7
=
(2)
16.
738 / 78
=
(4)
18.
95084 / 13
=
(6)
19.
63646 / 3666
=
(8)
20.
888747 / 30627
=
(10)
21.
52823114992 / 21
=
(12)
(140)
Section 13: Exact roots
All the answers in this section are integers.
1.
2
√ 784
=
(2)
2.
2
√ 4624
=
(3)
3.
2
√ 99225
=
(4)
4.
2
√ 95316169
=
(7)
√ 90494477329
=
(10)
√ 6859
=
(3)
√ 571787
=
(4)
√ 1906624
=
(6)
√ 821603839896
=
(10)
√ 9834496
=
(4)
√ 570667270566300625
=
(10)
√ 2476099
=
(5)
5.
6.
7.
8.
9.
10.
11.
12.
2
3
3
3
3
4
4
5
13.
6
√ 7212549413161
=
(9)
14.
7
√ 7701771143776896
=
(11)
15.
7
√ 408429314978086912
=
(12)
(100)
Section 14: Inexact roots
For Q1-9, give the answer to the nearest integer.
2
3
For example, √28 = 5 or √47 = 4.
2
√ 44
=
(1)
√ 161
=
(2)
√ 82807
=
(3)
√ 601
=
(2)
5.
3
√ 61294
=
(3)
6.
4
√ 544983
=
(4)
7.
5
√ 5747210
=
(5)
8.
6
√ 7580358
=
(6)
9.
7
√ 32526369
=
(7)
1.
2.
3.
4.
2
2
3
For Q10-14, give the answer to 3 significant figures.
10.
2
√ 0.6597
=
(4)
11.
3
√ 43.19
=
(5)
12.
4
√ 2004.65
=
(6)
13.
5
√ 8.2672
=
(7)
14.
6
√ 682.1
=
(8)
For Q15-18, give the answer to 2 decimal places.
2
For example, √5200 = 72.11.
15.
4
√ 5084
=
(6)
16.
5
√ 33724
=
(8)
17.
5
√ 7598647
=
(10)
18.
6
√ 54880535
=
(12)
(110)
Section 15: Base conversions
Note, 1: A number in base N will be written as xyzN. For example, 11012 is a number in base 2 (which is equal to 1310 in base 10)
Note, 2: Numbers in bases larger than 10 should use capitalised letters with A = 10, B = 11 etc. For example, 1310 = D16. No base larger
than 16 is used in this section.
For Q1-5, convert the given number to the requested base.
1.
3345 to base 14
=
(3)
2.
5449 to base 6
=
(5)
3.
69411 to base 13
=
(6)
4.
C3413 to base 8
=
(7)
5.
BC7916 to base 5
=
(11)
=
(9)
=
(11)
=
(14)
=
(12)
=
(17)
For Q6-10, always give the answer in base 10.
6.
2447 + 52212
7.
362849 x 1337
8.
9132D14 - 3242105
9.
C2514 / 736
10.
550420036 - A044612 + 2463337
(95)
TOTAL FOR ALL SECTIONS (1-15) is 1335 POINTS