UKMT Q11-20 Junior Maths Challenge 2016

Which of the following statements is false?

• 12 is a multiple of 2

• 123 is a multiple of 3

• 1234 is a multiple of 4

• 12 345 is a multiple of 5

• 123 456 is a multiple of 6

Tags

CCSS.4.OA.B.4

The musical Rent contains a song that starts 'Five hundred and twenty five thousand six hundred minutes'.

Which of the following is closest to this length of time?

• a week

• a year

• a decade

• a century

• a millennium

Tags

CCSS.6.RP.A.3D

The diagram shows five circles placed at the corners of a pentagon. The numbers 1, 2, 3, 4, 5 are placed in the circles shown, one in each, so that the numbers in adjacent circles always differ by more than 1.

What is the sum of the numbers in the two circles adjacent to the circle which contains the number 5?

• 3

• 4

• 5

• 6

• 7

In the diagram, AB=AC and D is a point on AC such that BD=BC. Angle BAC is 40°. What is angle ABD?

• 15°

• 20°

• 25°

• 30°

• 35°

Tags

CCSS.HSG.CO.C.11

How many of these four expressions are perfect squares?

1³ + 2³; 1³ + 2³ + 3³; 1³ + 2³ + 3³ + 4³; 1³ + 2³ + 3³ + 4³ + 5³

• 0

• 1

• 2

• 3

• 4

Tags

CCSS.HSA.SSE.B.4

Each of the nine small squares in this grid can be coloured completely black or completely white.

What is the largest number of squares that can be coloured black so that the design created has rotational symmetry of order 2, but no lines of symmetry?

• 4

• 5

• 6

• 7

• 8

In a group of 48 children, the ratio of boys to girls is 3:5.

How many boys must join the group to make the ratio of boys to girls 5:3?

• 48

• 40

• 32

• 24

• 8

In the addition sum shown, each letter represents a different non-zero digit.

What digit does X represent?

• 1

• 3

• 5

• 7

• 9

Three boxes under my stairs contain apples or pears or both. Each box contains the same number of pieces of fruit. The first box contains all twelve of the apples and one-ninth of the pears.

How many pieces of fruit are there in each box?

• 14

• 16

• 18

• 20

• 36

Tags

CCSS.7.EE.B.3

A cyclic quadrilateral has all four vertices on the circumference of a circle. Brahmagupta (598-670AD) gave the above formula for the area, A, of a cyclic quadrilateral whose edges have lengths a, b, c, d, where s is half the perimeter of the quadrilateral.

What is the area of the cyclic quadrilateral whose sides of length 4cm, 5cm, 7cm, 10cm?

• 6 cm²

• 13 cm²

• 26 cm²

• 30 cm²

• 36 cm²