Questions 1-25 each carry 2 marks

1.  5.0 − 0.5 + 0.05 − 0.005 + 0.0005

2. Which of the following is not divisible by 9?

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. Given that 3× 37 =111 , calculate 999999÷37 .

5. What is the square root of 0.00005625?

6. One of the following shows the correct working for 329 × 989 using Nikhilam multiplication. Which
    one?

7. The devinculated form of 62 is 58. What is the devinculated form of 30023748?

8. What are the final four digits of 99999999987² ?

9. Using Nikhilam division for 24219 ÷ 897, some workings are shown below. What are the three
    missing digits for A, B and C?

10. Which fraction is the largest?

11. Which sutra is most appropiate for solving Question 10?

12. 78³

14. Find the integer remainder for 12345678 ÷ 89789

15. Which of the following is both a square and a cube?

16. What is the Lowest Common Multiple (LCM) of 38808 and 1320?

17. Which of the following is the square root of 123454321?

18. Which of the following can be expressed as the difference of two cubes and also the product of two
consecutive integers?

19. In how many ways can 96 be expressed as the difference of two square integers?

20. Two squares of side length 2 units and 6 units
touch a circle as shown. What is the radius of
the circle?

21. Simplify,

(x +2y +1)² − (x −2y −1)²

22. What is the square root of, x⁴ − 6x³ +17x²− 24x +16 ?

23. Given that 3x² +3x − 5 is a factor of 6x⁴ − 9x³ − 7x² + 43x − 30 , which of the following is another
factor?

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. a, b and c are positive integers that satisfy,

What is the value of c?

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. 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?

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. Simplify,

30. The equation, x² − 98x + k = 0 , has two distinct solutions. What value must k be less than?

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. 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?

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
shown.
What is the value of angle x?

35. What is the coefficient of the independent term in the binomial expantion of,

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. Given that |x|<2 , what are the first three terms, in ascending powers of x, for the expansion of

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. 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. How many rectangles of all types are there?