GCSE High 5 Mathematics Conference

Session 1 Algebraic Arguments

Length - Perimeter 3b + 5 2a 2a 3b + 5 Why? Opposite sides in rectangle are equal Order does not matter

Length - Perimeter Find the value of x Perimeter = 48cm. 2x cm 3x cm

Show algebraically that the perimeters of these shapes are identical 2(5 + 2x) 12+ 20x 4(2x - 1) 5(x + 3) 2x

Find the values of a and b Length Find the values of a and b 3b + 5 5 2a 17

Find x in each of these triangles Length Find x in each of these triangles 4x + 8 3x + 12 2x − 9 x + 5 6x Equilateral – note that only choose 2 equations in order to solve for x.

Angles 6x (5y + 3)° Find x and y 127° 4x (10y + 7)° 88° 2x

What is special here about the angles? (14x + 6)° 2z 3z − 15 52° y° 2z 2z + 24 Parallelogram example – use this as an opportunity to review all of the angle facts. Note that for exam questions may need to use them in a particular order.

Here is a parallelogram. Work out the value of x and the value of y. (4y − 5x)°

Percentages Essentials Session 2 Percentages Essentials

Sort into two groups Loss Inflation Decline Dropped Increase Gain Rise Discount Depreciated Profit Increment Reduction Interest Marked down Decrease

Percentage Change Difference x 100 Original The price of a classic car increased from £50,000 to £70,000. What was the percentage increase? During June 2016 the number of people visiting Tower of London fell from 60,000 to 48,000. What was the percentage decrease?

Percentage Change Ben’s weekly salary is £250. He receives a 7% increase. What is his new weekly salary? A coat costs £30. The shop has a sale with 20% off all prices. On the final day they reduce all sale prices by 25%. What is the price of the coat on the final day?

Reverse Percentage Change Rachel’s monthly pay increased by 2.5% to £3895. What was Rachel’s pay before the increase? In a sale, normal prices are reduced by 20%. Jane buys a road bike for £440. What is the normal price of the bike?

Compound Increase & Decrease No of years Original Amount × 1.(the percentage as a decimal) = New Amount Miss Smith invests £7300 for 4 years in a savings account. She gets 2.7% per annum compound interest. How much money will Miss Smith have in her savings account at the end of 4 years?

Compound Increase & Decrease Raj purchased a new laptop for £550. Each year the value of his laptop depreciated by 2%. Calculate the number of years after which the value of his laptop was less than £500.

Session 3 Shape Combo Questions

Perimeter: found by adding together all lengths BUT we may have some missing lengths to find first… Draw on lines with coloured pens/highlighters 11m 7m 4m

Areas: need to correctly apply formulae You need to learn all of these formulae Area of a rectangle = b × h b h Area of a triangle = b × h 1 2 b h Area of a parallelogram = b × h b h h b a Area of a trapezium = (a + b)h 1 2 r Area of a circle = π × r2 Perpendicular height

Areas: practice (round to 3 significant figures where appropriate) 7cm 16cm 4cm 10cm 3.6cm 3cm 6cm 5cm 8cm 3.8cm 18cm 10cm 12cm 8cm 14cm 10cm 12cm

Volumes: practice (round to 3 significant figures where appropriate)   cross-section Volume of a prism = area of cross-section × length length 3cm 10cm 4cm 8cm 4cm 5cm 8cm

Applications The diagram shows a patio in the shape of a rectangle Matthew is going to cover the patio with paving slabs. Each paving slab is a square of side 60cm. Paving slabs are sold in packs of 10. Price per pack is £12. However, if you are buying 3 or more packs there is a 10% discount. How much does it cost to buy enough paving slabs to cover the patio? 3 m 3.6 m

Applications The diagram shows a container for oil. The container is in the shape of a cuboid. The container is empty. Sally has to fill the container with oil. A bottle of oil normally costs £3.50 but prices have just been increased by . There is 3000cm3 of oil in each bottle. Sally must not spend more than £82 buying the oil. Can Sally buy enough oil to fill the container? 1 5

Applications The diagram shows part of a field. A farmer wants to put a fence all the way around the edge of this part of the field. The shop sells fencing in 3 metre panels. The price per panel is £57. The farmer will have to take a loan to purchase the fencing from the bank. The bank will charge 2% compound interest per year. Calculate the amount owed to the bank after 3 years. 14m 11m 4m Final answer is rounded 725.866272

Session 5 Ratio and proportion

Paul and Katie share some sweets in the ratio 3 : 8. Katie gets 32 sweets. How many sweets does Paul get?

Sandra has a piece of string 150cm long. She cuts the string into three lengths, in the ratio 5:2:3. Work out the length, in cm, of each piece of string. Visualiser

Pat and Julie share some money in the ratio 2:7. Julie gets £45 more than Pat. How much money did Pat get?

Talil is going to make some concrete mix. He needs to mix cement, sand and gravel in the ratio 1:3:5 by weight. Talil wants to make 180 kg of concrete mix. Does he have enough cement, sand and gravel? Talil has 45kg of cement, 45kg of sand and 150 kg of gravel.

300ml milk 120g flour 2 eggs Recipe for 10 pancakes Matthew makes 32 pancakes. Work out how much flour he uses. Tara makes some pancakes. She uses 750ml of milk. Work out how many pancakes she makes

A car uses 16 litres of petrol to travel 95 miles. In this question, assume that the car uses the same amount of petrol for each mile it travels. A car uses 16 litres of petrol to travel 95 miles. How far would the car travel on 80 litres of petrol? How much petrol would the car use on a trip of 380 miles? P1XL