Questions 1 – 25: Score 2 marks for each correct answer

1 − 0.2 + 0.03 − 0.004 + 0.0005

101214 ÷ 9

9876 × 9993

Which of the following is a multiple of 11?

What is the value of the digit A in the calculation, 83 × 87 = 7A21 ?

Including repetitions, how many prime factors does 2024 have?

What is the remainder for 256379 ÷ 12101 ?

Which is the most suitable sutra for the calculation in the previous question?

9988²

49³

What is the remainder when 2² × 4⁴ × 6⁶ × 8⁸ is divided by 9?

What is the mean value of the five answers to 91× 89, 94 × 86, 95× 85, 92 × 88 and 93× 87 ?

A sequence begins, 0    3    10    21    36
What is the 25th term in the sequence?

When using the Vertically and crosswise method to multiply 6734 × 2963 what is the result of the fourth step before any carry digits have been added?

Each shape is made of four identical right-angled isosceles triangles. Which shape has the smallest perimeter?

Which of the following is the equation of the straight line which passes through the point (7,−10) and and has gradient −2 ?

How many of the following points lie on the line with equation 3x − 2y =14 ?

               (4,−2)          (10,8)          (16,18)          (18,20)          (32,41)

Tile P has an area of 504 cm². Tile Q has an area of 2352 cm². A floor is to made with P tiles and another floor with Q tiles. What is the smallest area, in m², that can be made so that both floors have the same area?

Due to lack of babies being born, the population of South Korea is predicted to fall by 60% by the end of the century. The current population is 52 million. To the nearest million, what is the predicted population for 2100?

What is the common solution to the equations, x² −10x − 24 = 0 and x² − 8x − 48 = 0 ?

Two ice-cream cones, A and B, are mathematically similar. The surface areas are 16 square inches and 25 square inches, respectively. The volume of cone A is 6.4 cubic inches. What is the volume of cone B?

An equilateral triangle, a square and a regular heptagon are placed together as shown. What is the sum of the interior angles of the resulting shape?

Questions 26 – 35: Score 3 marks for each correct answer. -1 mark for each incorrect answer.

Which of the following is a factor of 6x³ +7x² + x − 28 ?

Given that a year is 365.24 days long, and a month, from new moon to new moon, is 29.53 days long, how many months will there be in 19 years?

A truncated icosahedron has 12 pentagon faces and 20 hexagon faces. Faces are joined along their edges. How many edges are there?

In the figure, QP and QRS are tangents to the circle with centre O.

PQ̂R = 58˚ and TR̂S = 68˚ .

What is the size of OP̂T ?

An irregular quadrilateral, has vertices A (2, 2), B (10, 0), C (12, 8) and D (6, 10). Midpoints of each side are joined to make quadrilateral PQRS.
What shape is PQRS?

In the figure, AB = 5 cm, BC = 2 cm, AD = 8 cm and ED = 7 cm.
What is the length of EC?

What is the 11th digit, after the decimal point in the recurring decimal equivalent for 4/39?

A regular p-sided polygon has exterior angle q˚ and a regular q-sided polygon has exterior angle p˚.
For how many possible pairs of numbers (p, q) is this possible?

Questions 36 – 40: Score 4 marks for each correct answer. -2 mark for each incorrect answer.

ABC is a right-angled triangle. AB is parallel to ED. The area of triangle EDC is 24 cm² and the area of triangle BED is 72 cm².
What is the area of triangle ABE?

What is the minimum value of x² + y² + 2xy + 8x + 8y + 12 ?

A square has side length 4. Four arcs have their centres at the midpoints of the sides of the square. What is the shaded area?

Points are placed one third of the way along each edge of a triangle as shown. What fraction of the whole triangle is shaded?

ABCD is a square with a quarter-circle centred at B and passing through A and C. The rectangle EFGD measures 9 units by 2 units. What is the edge length of the square?