GCSE High 5 Mathematics Conference Session 1 Algebraic

GCSE High 5 Mathematics Conference

Session 1 Algebraic Arguments

Length - Perimeter 3 b + 5 2 a 2 a 3 b + 5

Length - Perimeter = 48 cm. Find the value of x 2 x cm 3 x cm (x + 9) cm

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

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

Length 2 x − 9 4 x + 8 3 x + 12 x+5 6 x Find x in each of these triangles

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

Angles (14 x + 6)° 3 z − 15 52° y° 2 z 2 z + 24 2 z What is special here about the angles?

Here is a parallelogram. Work out the value of x and the value of y. (2 x + 43)° (5 x − 20)° (4 y − 5 x)°

Session 2 Percentages Essentials

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

Percentage Change The price of a classic car increased from £ 50, 000 to £ 70, 000. What was the percentage increase? Difference x 100 Original 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… 16 m 4 m 10 m 14 m 7 m 11 m 4 m

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

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

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

Applications 3 m 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 60 cm. 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. 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 1. There is 3000 cm 3 5 of oil in each bottle. Sally must not spend more than £ 82 buying the oil. Can Sally buy enough oil to fill the container?

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. 14 m 11 m 4 m

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 150 cm 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.

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

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

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? P 1 XL