Review practice · Section 1 of 2

A cinema sells tickets at three different prices, depending on the age of the customers. The age categories are under 16 years, between 16 and 65 years, and over 65 years.

Three groups of people A, B and C go to the cinema on the same day.

The numbers in each age category for each group, together with the total cost of the tickets for each group, are given in the following table.

Write down and solve equations to find the cost of a ticket for each of the age categories.4 marks

Four housewives bought three different types of meat from the same meat seller. The mass of meat and the total each housewife paid are shown in the table below.

Find the value of $a$.4 marks

A shop selling biscuits gave the following offers. A customer who bought a total of 5 or more packets of biscuits was given a discount, regardless of the types of biscuits bought. A 10% discount was given if 5 to 8 packets were bought and a 20% discount if more than 8 packets were bought.

The following table shows the number of packets bought and the total amounts that three customers paid.

Calculate the price per packet for each type of biscuit before the discount.4 marks

Three brands of apple juice, A, B and C, each contain a certain percentage of pure juice and some artificial flavouring. The breakdown of the amount of juice and flavouring for each brand is summarised in the table below.

How many litres of each brand should be mixed to produce 300 litres of juice with 41.1% pure juice and 0.647% artificial flavouring?3 marks

In basketball, points are scored by a successful free throw or a field goal. A successful free throw is worth 1 point while a field goal is worth either 2 or 3 points. An attempt can either be a free throw attempt or a field goal attempt.

In the recently concluded basketball season, Stephen had 1695 attempts in total. 60% of these attempts were successful and he scored a total of 1917 points. 40% of his successful free throws and 25% of his field goal points were scored during the second half of the season, where Stephen scored a total of 534 points.

Calculate the number of 2-point field goals during the season.5 marks

The equation of a curve $C$ is given by $y=ax+b+c/x$, where $a,b,c$ are constants. The gradient of $C$ at the point $(1,1)$ is 3. It is also given that $C$ passes through the point $(2,2)$. Find the values of $a,b,c$. Hence state the equations of the asymptotes of $C$.4 marks