JMC 2021 Challenge

1. What is the value of $123-456+789$ ?

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2. Brianna has $\text{£}20$, all in $5\text{p}$ coins, and $\text{£}50$, all in $2\text{p}$ coins.

How many coins does she have in total?

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3. What is the value of $1-2\times3+4\div5$ ?

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4 .How many of the following numbers are multiples of $11$?

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5. When I have walked $20\%$ of the way to school, I have $1200$ metres more to walk than when I have $20\%$ of the walk remaining.

How far, in metres, is it from my home to my school?

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6. What is the value of $(2-\frac 12)(3-\frac13)(4-\frac14)$ ?

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7. In the diagram shown, $PT=QT=QR$

Also, $RT=RS$ and $\angle{PTQ}=36^\circ$

What is $\angle{PTS}$?

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8. What is the value of $1-(2-(3-(4-5)))$ ?

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9. Each cell in the cross number below contains a single non-zero digit.

The answer to each clue is a two-digit number.

What is the value of x?

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10. The diagram shows a rhombus formed by joining each vertex of a square to the midpoint of a side of the square.

What fraction of the area of the square has been shaded?

11. A particular prism has ten faces. How many edges does it have?

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12. The pupils in my class work very quickly. Jasleen answers four questions every $30$ seconds and Ella answers five questions every $40$ seconds.

Last week, Jasleen took exactly $1$ hour to answer a large set of questions.

How many minutes more than Jasleen did Ella take to answer the same set of questions?

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13. Five line segments coincide at a point as shown.

What is the sum of the marked angles?

14. I begin with a three-digit positive integer. I divide it by $9$ and then subtract $9$ from the answer.

My final answer is also a three-digit integer.

How many different positive integers could I have begun with?

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15. Alex has a pile of $2\text{p}$. She swapped exactly half of them for the same number of $10\text{p}$ coins. Now she had $\text{£}4.20$.

How much money did Alex have initially?

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