Australian AMC 2010 - Upper Primary

What is one thousand and twenty-seven in numerals?

Jillian is standing inside a pet shop and looking out the window shown in the diagram.

What does she see?

Lee is 14 years old. Liz is 10 years old. Dad’s age is twice the sum of their ages. How old is Dad?

The midpoints of the sides of a square are joined as shown. A part of the original square is shaded as shown. What fraction of the original square is shaded?

In a queue in the school canteen, Sarah was behind Tim and Carl was between Sarah and Tim. Sarah was in front of Brett who was in front of George. Who was fourth in line?

When five numbers are added the total is 2010. One of the numbers is changed from 235 to 532. What is the total of the five numbers now?

Eight blocks are glued together as shown.

How many faces of these blocks are glued together?

What is the difference between the largest and smallest 3-digit numbers that can be made from the following 1-digit cards, if each card is to be used once only in each number?

My father won \$1000 in a lottery. He put one-fifth in the bank, spent one-quarter of what was left on me and gave the rest to my mother. How much did my mother receive?

Starting at A and walking around the figure back to A, how far do I walk?

This is Liam’s timetable for a normal school day.

Time — Activity

9:00 am – 9:10 am — Morning assembly

9:10 am – 11:00 am — Class time

11:00 am – 11:30 am — Recess

11:30 am – 1:00 pm — Class time

1:00 pm – 1:50 pm — Lunchtime

1:50 pm – 3:00 pm — Class time

3:00 pm — Home time

How many minutes of class time does Liam have every day?

The average of two numbers is 11. One of the numbers is 6 more than the other. Which is the larger number?

What fraction of the rectangle is shaded?

In a group of 55 students, exactly 39 are enrolled in mathematics and exactly 35 are enrolled in science. How many students are enrolled in both mathematics and science?

**Qualification for the checked intended answer:** Assume that all 55 students take at least one of the two subjects. This condition is missing from the original wording. Without it the answer is not unique; the solution gives the full range and a counterexample.

Jeremy decides to measure area in hexagonal units (instead of squares) using the hexagonal unit as shown.

What is the area of the triangle in Jeremy’s hexagonal units?

To make a quilt 120 cm by 90 cm for my baby’s cot, I add borders to a central panel as shown. If the borders are the same width all the way around, then the dimensions of the central panel, in centimetres, could be

Place the numbers 1, 2, 3, 4 and 5, one in each circle in the diagram so that no number is joined by a line to a consecutive number.

The sum of the numbers X and Y could be

Below is a diagram of a garden. Some of the garden is grass and some is a pathway made from square blocks.

The total area of the grass is 108 square metres.

What is the area, in square metres, of the pathway?

A shop has a sale and sells hats for \$12 each in the morning, taking \$720. After lunch, the price is dropped to \$9 each and the shop sells twice as many. What was the total amount taken on the day?

The areas, in square centimetres, of three rectangles are given.

What is the area, in square centimetres, of the shaded rectangle?