17. Jeroen writes a list of 2019 consecutive integers. The sum of his integers is 2019.

What is the product of all the integers in Jeroen's list?

18. Alison folds a square piece of paper in half along the dashed line shown in the diagram.
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After opening the paper out again, she then folds one of the corners onto the dashed line.

What is the value of α?

19. Which of the following could be the graph of y² = sin⁡ (𝑥²) ?

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20. The "heart" shown in the diagram is formed from an equilateral triangle ABC and two congruent semicircles on AB. The two semicircles meet at the point P. The point O is the centre of one of the semicircles. On the semicircle with centre O, lies a point X. The lines XO and XP are extended to meet AC at Y and Z respectively. The lines XY and XZ are of equal length.
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What is $\angle ZXY$ ?

21. In a square garden PQRT of side 10 m, a ladybird sets off from Q and moves along edge QR at 30 cm per minute. At the same time, a spider sets off from R and moves along edge RT at 40 cm per minute.

What will be the shortest distance between them, in metres?

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22. A function f satisfies the equation (n − 2019) f (n) − f (2019 − n) = 2019 for every integer n.

What is the value of f (2019) ?

23. The edge-length of the solid cube shown is 2. A single plane cut goes through the points Y, T, V and W which are midpoints of the edges of the cube, as shown.

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What is the area of the cross-section?

24. The numbers $x$, $y$ and $z$ are given by $x$ = $x=\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}$, $y=\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}$ and $z=\sqrt{2+\sqrt{3}}-\sqrt{2-\sqrt{3}}$

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What is the value of $xyz$ ?

25. Two circles of radius 1 are such that the centre of each circle lies on the other circle. A square is inscribed in the space between the circles.

What is the area of the square?