 There are 40 multiple choice questions in the challenge, each with 5 possible answers.
 Questions 1 – 25 each carry 2 marks, Questions 26 – 35 each carry 3 marks, and Questions 36 – 40 each carry 4 marks.
 The challenge is one hour long.
 Once you click on “Start” a clock will countdown and at the end of one hour your answers will be automatically saved and submitted.
 You can end the test before that by clicking on “Submit Test” on the final question.
 The grid of squares at the top will show you which questions you have answered.
 You can skip a question and come back to it later or revisit any question you have already answered by clicking on any question number in the grid.
 You will need paper for rough workings.
 You must not use a calculator or any other electronic device.
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Question 1 of 40
1. Question
2 point(s)Questions 125 each carry 2 marks
1. 5.0 − 0.5 + 0.05 − 0.005 + 0.0005

Question 2 of 40
2. Question
2 point(s)2. Which of the following is not divisible by 9?

Question 3 of 40
3. Question
2 point(s)3. When using Vertically and crosswise to calculate 367 × 482 , what is the result of the third step
before any carry digits are included? 
Question 4 of 40
4. Question
2 point(s)4. Given that 3× 37 =111 , calculate 999999÷37 .

Question 5 of 40
5. Question
2 point(s)5. What is the square root of 0.00005625?

Question 6 of 40
6. Question
2 point(s)6. One of the following shows the correct working for 329 × 989 using Nikhilam multiplication. Which
one? 
Question 7 of 40
7. Question
2 point(s)7. The devinculated form of 62 is 58. What is the devinculated form of 300237 4 8?

Question 8 of 40
8. Question
2 point(s)8. What are the final four digits of 99999999987² ?

Question 9 of 40
9. Question
2 point(s)9. Using Nikhilam division for 24219 ÷ 897, some workings are shown below. What are the three
missing digits for A, B and C? 
Question 10 of 40
10. Question
2 point(s)10. Which fraction is the largest?

Question 11 of 40
11. Question
2 point(s)11. Convert, the partially recurring decimal, 0.163636363…, to a fraction in lowest terms.

Question 12 of 40
12. Question
2 point(s)12. 78³

Question 13 of 40
13. Question
2 point(s)13. What are the last five digits of the recurring pattern in the decimal equivalent of 1 ? 39 
Question 14 of 40
14. Question
2 point(s)14. Find the integer remainder for 12345678 ÷ 89789

Question 15 of 40
15. Question
2 point(s)15. Which of the following is both a square and a cube?

Question 16 of 40
16. Question
2 point(s)16. What is the Lowest Common Multiple (LCM) of 38808 and 1320?

Question 17 of 40
17. Question
2 point(s)17. Which of the following is the square root of 123454321?

Question 18 of 40
18. Question
2 point(s)18. Which of the following can be expressed as the difference of two cubes and also the product of two
consecutive integers? 
Question 19 of 40
19. Question
2 point(s)19. In how many ways can 96 be expressed as the difference of two square integers?

Question 20 of 40
20. Question
2 point(s)20. Simplify,
(x +2y +1)² − (x −2y −1)²

Question 21 of 40
21. Question
2 point(s)21. What is the square root of, x⁴ − 6x³ +17x²− 24x +16 ?

Question 22 of 40
22. Question
2 point(s)22. Given that 3x² +3x − 5 is a factor of 6x⁴ − 9x³ − 7x² + 43x − 30 , which of the following is another
factor? 
Question 23 of 40
23. Question
2 point(s)23. What is the equation of the line which is perpendicular to 3x +2y = 7 and which passes through the
point with coordinates, (4, 3)? 
Question 24 of 40
24. Question
2 point(s)24. What is the radius of the circle with equation,
x² + y² + 4x −10y −167 = 0 ?

Question 25 of 40
25. Question
2 point(s)25. a, b and c are positive integers that satisfy,
What is the value of c?

Question 26 of 40
26. Question
3 point(s)Questions 26 – 35 each carry 3 marks
26. What are the values of A and B, given that Y and Z are linear functions of x?14x+ 4 = A + B 2x² +9x − 5 Y Z

Question 27 of 40
27. Question
3 point(s)27. A bee enters cell A in a honeycomb with the aim of reaching cell J. The bee cannot go back into any
cell with an earlier letter label. For example, to reach cell D, the bee can travel through ABCD or
ACD or ABD but not ACBD.
How many possible ways are there for it to reach cell J? 
Question 28 of 40
28. Question
3 point(s)28. Two identical triangles overlap. The area of the
overlapping region, B, is one sixth the area of the whole
shaded region.What fraction of the area of one triangle is the area B?

Question 29 of 40
29. Question
3 point(s)29. Given that f(x) = x −1 , what is the inverse function, f ^{1}(x) ? 3− x 
Question 30 of 40
30. Question
3 point(s)30. Simplify,

Question 31 of 40
31. Question
3 point(s)31. The equation, x²− 98x +k = 0 , has two distinct solutions. What value must k be less than?

Question 32 of 40
32. Question
3 point(s)32. A parallelogram, ABCD, is drawn on a graph with
vertices as shown. What is the numerical value
of the area of the parallelogram? 
Question 33 of 40
33. Question
3 point(s)33. A triangle has base, x − 7 cm , and height,
12 − 4x cm , where x is a variable. What is its
maximum area in cm² ? 
Question 34 of 40
34. Question
3 point(s)34. Two congruent isosceles triangles overlap
producing a hexagon in the middle. The areas
of the smaller triangles are 4 and the larger
triangels, 36, as shown.
What is the area of the hexagon? 
Question 35 of 40
35. Question
3 point(s)35. Angle Q is defined by the triple Q) 5 12 13. What is the triple for the angle 1 Q ? 2 
Question 36 of 40
36. Question
4 point(s)Questions 36 – 40 each carry 4 marks
36. Given that x<2 , what are the first three terms, in ascending powers of x, for the expansion of
4 ? (2+x)²

Question 37 of 40
37. Question
4 point(s)37. What is the area under the curve given by
y = 6 3x − 2 between the lines, x =1 and x = 9 ?

Question 38 of 40
38. Question
4 point(s)38. What is the gradient of the curve with equation, x² + y² = 12 , at the point (3, 6) ? 3 4 
Question 39 of 40
39. Question
4 point(s)39.Two corners of a square, with side length 2,
touch the circumference of a circle. One side of
the square is tangent to the circle.What is the circle’s circumeference?

Question 40 of 40
40. Question
4 point(s)40. How many rectangles of all types are there?