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.
How much is $0.1\times0.2\times0.3\times0.4\times0.5$ less than $0.2019$?
Consider this process. 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 chosen part yellow. Step 3: repeat step 1 on the yellow part and paint the chosen part green. Step 4: repeat step 1 on the green part and paint the chosen part blue. What fraction of the whole square is blue?
An envelope has size $10.8$ cm $\times16.5$ cm. In Fig. 1 it is opened to measure its size; in Fig. 2 it is closed. What is the area of the unshaded region in Fig. 2, in square centimetres?
A bakery has 7 chefs who make 100 pieces of cake in 8 hours. Today 2 chefs cannot come, so the remaining chefs make 100 pieces and finish in $a$ hours $b$ minutes. Find $a+b$.
$N$ is the least positive integer leaving remainder 2 when divided by 4, remainder 5 when divided by 7, and remainder 9 when divided by 11. What is the remainder when $4\times7\times11$ is divided by $N$?
There are four bags of number cards, one number per card. Bag 1 contains 1–10; bag 2 contains 12–20; bag 3 contains 23–30; bag 4 contains 24–35. Each bag has one card for each integer in its range, with no repeated number. From which bag should a student draw one card at random to have the greatest chance of an even number?
The table shows the number of students in each grade of a primary school. Let $a$ be the grade 5 enrolment, $b$ the grade 6 enrolment, and $c$ the total. Grade 6 has 2 fewer students than grade 5, and the average enrolment per grade is 249. Find $a+b+c$.
The fraction $\frac14$ is the decimal $0.25$, whose first digit after the decimal point is 2 and second digit is 5. When $\frac{2019}{2562}$ is written as a decimal, what is its fourth digit after the decimal point?
Uncle George has 50 chickens, ducks and geese altogether. There are 19 more chickens than ducks. Each day a chicken gives 3 eggs, a duck 2 eggs and a goose 1 egg. Today there are 115 eggs in total. How many ducks does he have?
Rectangle $ABCD$ contains seven equal shaded circles, tangent as shown. Each circle has radius 7 cm. Find the unshaded area in square centimetres, using $\pi=\frac{22}7$.
Joe has the two-storey rectangular container shown. A notebook is 12 cm wide, 17 cm long and 1 cm thick. A book is 12 cm wide, 17 cm long and 2 cm thick. He keeps notebooks in the top storey and books in the bottom storey. What are the greatest possible numbers of notebooks and books that fit?
A pattern of fractions is $\frac{11}{13},\frac{13}{24},\frac{15}{56},\frac{17}{72},\ldots,\frac ab$, where $\frac ab$ is the 15th term. It can be written as $\frac1x+\frac1y$. Find $(a+b)-(x+y)$.
