Unit 7

The graph of has an asymptote on the y-axis.

State the equation of this asymptote, and calculate the value of when .

State one property that two similar triangles always have.

A circle has a radius of 5 cm. The angle at the centre of a sector is 90°.

Calculate the length of the arc. Give your answer to 2 decimal places.

Explain, using reasoning, why the volume of a cylinder increases if the height is doubled but the radius stays the same.

The two pentagons below are similar. The side of the smaller pentagon is 4 cm. The side of the larger pentagon is 10 cm.

The table shows data for three sectors of a circle. The radius of all the sectors is 6 cm.

Calculate and complete the missing arc lengths for sectors A, B, and C. Enter your answers to 2 decimal places.

Write down the formula for the surface area of a sphere of radius .

Triangle PQR is similar to triangle XYZ. The length PQ = 7 cm and the corresponding side XY = 14 cm. If the area of triangle PQR is 25 cm², find the area of triangle XYZ.

A group of 40 students is surveyed. 18 students play tennis (set T), and 6 students play both tennis (T) and basketball (B). What is the number of students who play both tennis and basketball, n(T ∩ B)?

In a club of 50 members, 32 members play chess (set C), 19 members play cards (set D), and 7 members play both chess and cards. Use set notation to calculate the number of members who play only chess.