- 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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1. Question2 point(s)
Questions 1-25 each carry 2 marks
1. 5.0 − 0.5 + 0.05 − 0.005 + 0.0005
2. Question2 point(s)
2. Which of the following is not divisible by 9?
3. Question2 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?
4. Question2 point(s)
4. Given that 3× 37 =111 , calculate 999999÷37 .
5. Question2 point(s)
5. What is the square root of 0.00005625?
6. Question2 point(s)
6. One of the following shows the correct working for 329 × 989 using Nikhilam multiplication. Which
7. Question2 point(s)
7. The devinculated form of 62 is 58. What is the devinculated form of 30023748?
8. Question2 point(s)
8. What are the final four digits of 99999999987² ?
9. Question2 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?
10. Question2 point(s)
10. Which fraction is the largest?
11. Question2 point(s)
11. Which sutra is most appropiate for solving Question 10?
12. Question2 point(s)
13. Question2 point(s)
13. What are the last five digits of the recurring pattern in the decimal equivalent of 1 ? 39
14. Question2 point(s)
14. Find the integer remainder for 12345678 ÷ 89789
15. Question2 point(s)
15. Which of the following is both a square and a cube?
16. Question2 point(s)
16. What is the Lowest Common Multiple (LCM) of 38808 and 1320?
17. Question2 point(s)
17. Which of the following is the square root of 123454321?
18. Question2 point(s)
18. Which of the following can be expressed as the difference of two cubes and also the product of two
19. Question2 point(s)
19. In how many ways can 96 be expressed as the difference of two square integers?
20. Question2 point(s)
20. Two squares of side length 2 units and 6 units
touch a circle as shown. What is the radius of
21. Question2 point(s)
(x +2y +1)² − (x −2y −1)²
22. Question2 point(s)
22. What is the square root of, x⁴ − 6x³ +17x²− 24x +16 ?
23. Question2 point(s)
23. Given that 3x² +3x − 5 is a factor of 6x⁴ − 9x³ − 7x² + 43x − 30 , which of the following is another
24. Question2 point(s)
24. On the circle of nine points each number is
joined to every other number with a line.
The two numbers on the end of each line are
mutliplied. How many answers will be even?
25. Question2 point(s)
25. a, b and c are positive integers that satisfy,
What is the value of c?
26. Question3 point(s)
Questions 26 – 35 each carry 3 marks
26. A parallelogram, ABCD, is drawn on a graph with
vertices as shown. What is the numerical value
of the area of the parallelogram?
27. Question3 point(s)
27. Two identical triangles overlap. The area of the
overlapping region, B, is one sixth the area of the whole
What fraction of the area of one triangle is the area B?
28. Question3 point(s)
28. 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?
29. Question3 point(s)
30. Question3 point(s)
30. The equation, x² − 98x + k = 0 , has two distinct solutions. What value must k be less than?
31. Question3 point(s)
31. A triangle has base, x − 7 cm , and height,
12 − 4x cm , where x is a variable. What is its
maximum area in cm² ?
32. Question3 point(s)
32. Harry is tiling a floor with identical square tiles. When he forms a square of side n tiles has has 64
tiles left over. When he forms a square of side (n + 1) tiles he has 25 too few.
How many tiles does Harry have?
33. Question3 point(s)
33. Angle Q is defined by the triple Q) 5 12 13.What is the triple for the angle 1 Q ? 2
34. Question3 point(s)
34. Wajma folds a rectangular piece of paper in half
and then unfolds it so that it has a centre line.
She then folds one corner onto the centre line as
What is the value of angle x?
35. Question3 point(s)
35. What is the coefficient of the independent term in the binomial expantion of,
36. Question4 point(s)
Questions 36 – 40 each carry 4 marks
36. 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?
37. Question4 point(s)
37. Given that |x|<2 , what are the first three terms, in ascending powers of x, for the expansion of
4 ? (2+x)²
38. Question4 point(s)
38. 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?
39. Question4 point(s)
39. A cube has edge length 2. It has a single cut that
passes through points P, Q, R and S, which are
the midpoints of edges.
What is the area of cross-section?
40. Question4 point(s)
40. How many rectangles of all types are there?