AMAZING GRACE ACADEMY PLACEMENT TEST TWO

Lungi and Kagiso are cousins, aged 10 and 34 respectively. How old will Lungi be when his age is exactly half of Kagiso’s age?

A box containing four Wits maths textbooks weighs 10kg, the same box with six Wits maths textbooks weighs 13kg. How much, in kg, does an empty box weigh, if all books have the same weight?

The large square below has an area of 16cm^2. It has been split into various smaller squares. Calculate the area, in cm^2, of the shaded region.

The first 56 odd numbers, starting from the number ’1’, are written. How many times does the digit ’7’ appear?

Along a highway, there are electric poles on one side of the highway and telegraph poles on the other side. The electric poles are separated by 15m and the telegraph poles are separated by 40m. If an electric and telegraph pole are both present at the point where the highway begins, after what distance, in m, will they be in front of each other again?

A water tank is 7/9 full. When 30 litres is released the tank is 5/9 full. What is the full capacity of the tank (in litres)?

A palindrome reads the same forwards and backwards. The number 202202 is a 6-digit palindrome. What is the difference of the palindrome directly before 202202 and the palindrome directly after 202202?

Tumelo makes a large cube from 27 small white cubes. She paints all the faces of the large cube (shaded in the picture below). She then removes a small cube from four corners, as shown. While the paint is still wet, she stamps each of the new faces onto a piece of paper. How many of the following stamps can Tumelo make?

A tower of rings (called the Tower of Hanoi) is shown below. What is the minimum number of moves required to reform the tower (in the exact order of biggest ring at the bottom and smallest ring at the top) on either the second or third pole? You can only move one ring at a time, and may only place a smaller ring on top of a larger ring.

A stand sells movie popcorn in only 2 sizes. Their prices are R4 and R7 per serving. What is the greatest popcorn sales value, in Rands, that is NOT POSSIBLE?