Printed positive marks are preserved per question. The source uses different blank-answer and incorrect-answer rules by section, including an optional bonus penalty; the import does not reproduce that complete official scoring scheme.
Given $2+0.5+0.06+0.002=a$ and $2+0.0+0.01+0.009=b$, what is the difference between a and b?
In the figure, ABCD and EFGH are squares. FG and HG are 4 cm from BC and DC respectively. The area of ABCD is 256 square centimetres. What is the perimeter of EFGH?
Step 1: Draw a square, divide it into four equal parts as shown, and paint one part red. Step 2: Repeat step 1 on the red part and paint the selected part yellow. Step 3: Repeat step 1 on the yellow part and paint the selected part green. What fraction of the whole square is green?
Triangle TMC has area 24 square centimetres, and PQRS is a parallelogram. The figure shows CM = 6 cm and SR = 11 cm, with the vertices on the same two parallel horizontal guides. What is the area of PQRS in square centimetres?
Let T, M and C be different digits from 0 to 9. The number $\overline{TMC7}$ is the largest four-digit number of this form divisible by 9. Find T + M − C.
A train leaves station A at 30 km/h. After 2 hours 30 minutes it reaches B and leaves B at 40 km/h. After another 3 hours 15 minutes it reaches C. Determine the distance between stations A and B in kilometres.
John takes a mathematics contest with three parts and 29 questions in total. Part 1: questions 1–12, 4 points per correct answer. Part 2: questions 13–24, 6 points per correct answer. Part 3: questions 24–29, 6 points per correct answer. In every part wrong or blank answers earn 0. John obtains 75% of the score in Part 1, 75% in Part 2 and 40% in Part 3. What is his total score?
There are 7 students. Each answers 7 questions. A correct answer earns 7 marks and a wrong answer earns nothing. Their total marks are “two times of 7 less than 70 marks”. How many correct answers could the student with the greatest possible score have?
A student goes to school and then returns home. Each trip may be by car, bus, school bus or motorcycle. In how many ways can the student make the outward and return trips?
Some birds are on a tree branch. After the first gunshot, half fly away. After the second, one third of the remaining birds fly away. After the third, half of those still remaining fly away. There are then 6 birds left. How many were there initially?
A rectangular box is 16 cm wide, 8 cm long and 12 cm high. It can contain exactly 192 equal-sized dice. What is the side length of each die in centimetres?
Mark leaves his office by car a little after 18:00, when the angle between the long and short hands of his watch is 110°. He reaches home before 19:00, when the angle between the hands is again 110°. How many minutes does his journey take?
