18. P, Q and R are the three angles of a triangle, when each has been rounded to the nearest degree.
Which of the following is the complete list of possible values of P + Q + R?
20. The diagram shows a semicircle of radius 1 inside an isosceles triangle. The diameter of the semicircle lies along the ‘base’ of the triangle, and the angle of the triangle opposite the ‘base’ is equal to 2θ.
Each of the two equal sides of the triangle is tangent to the semicircle.
What is the area of the triangle?
21. The graph of 𝙮 = $\frac{1}{𝑥}$ is reflected in the line 𝙮 = 1. The resulting image is reflected in the line 𝙮 = -𝑥.
What is the equation of the final graph?
22. The diagram shows two overlapping triangles; an isosceles triangle with an angle of 120° and an equilateral triangle with area 36. Two of the vertices of the equilateral triangle are midpoints of the equal sides of the isosceles triangle.
What is the total area of the shaded regions (inside the isosceles triangle but outside the equilateral triangle)?
23. For particular real numbers a and b, the function f is defined by f (x) = ax + b, and is such that f (f(f(x))) =27x−52.
Which of the following formulas defines the function g such that, for all values of x,g(f(x)) = x?
24.The diagram shows a circle with centre 0 which lies in a horizontal plane. The diameter AB has length 4. Point P lies vertically above 0 and P0 = 2$\sqrt2$. Point C lies on the semicircular arc AB such that the ratio of the lengths of the arcs AC and CB is 2 : 1.
What is the shortest distance from A to PC ?
25. A semicircle is inscribed in a quarter circle as shown.What fraction of the quarter circle is shaded?
