MOCK WEST LYCEUM 2020 | WIUT

For the geometric series  $a+ar+ar^2+…$ the sum of the first two terms is 24 and the sum to infinity is 27. Find  $r$  .

•  $\pm\frac{1}{3}$  

•  $\pm\frac{1}{2}$  

•  $\pm3$  

•  $\pm2$  

In the diagram AB is parallel to DE. Work out the value of x in the diagram below. All values are in cms. Give your answer to 2 decimal places.

• 8.60

• 8

• 9

• 8.57

The size of each exterior angle of regular polygon is 24º. What is the sum of the interior angles of this polygon?

• 2700º

• 2340º

• 2160º

• 1620º

In the figure M is the midpoint of OA, N is the midpoint of OC and OC=2AB. Write down BC in terms of a and b.

(a)  

Mukhammadbobur chooses three different integers between 1 and 50. The first number is a prime number. The second number is 4 times the first number. The third number is 6 less than the second number. The sum of the three numbers is greater than 57. Find the three numbers.

• 7, 28, 22

• 11, 44, 38

• 13, 52, 46

• 17, 68, 62

Find equation of a line which is parallel to the line with the equation 3x + y = 7 and which passes through the origin.

(a)  

A plumber charges a callout fee of $p plus $t for each 15 minutes he is working on a job. A job lasting 45 minutes costs $56.20. A job lasting 1.5 hours costs $98.50. What is the callout charge and the total cost of a job lasting 1.25 hours?

• charge: 14.10$ / total cost: 83.00$

• charge: 13.00$ / total cost: 84.40$

• charge: 14.10$ / total cost: 84.40$

• charge: 13.00$ / total cost: 83.00$

The letter ‘T’ on this square grid has an area of 200cm².

Calculate the perimeter of the ‘T’.

Give the correct units for the answer.

• 90 mm

• 90 cm

• 180 mm

• 180 cm

Find the equation of the given line

• $y=2x+7$

• $y=5x+3$

• $y=2x+3$

• $y=5x+7$

‘Sea Green paint is made by mixing yellow and blue paint in the ratio 3 : 1. ‘Azure Blue paint is made by mixing yellow and blue paint in the ratio 1 : 3. 1 litre of Sea Green paint is mixed with 500 millilitres of Azure Blue by mistake. How much yellow paint needs to be added to the mixture to make it Sea Green again?

(a)