Maths Department Mental Agility

Transcription

1 Maths Department Mental Agility

2 Denny High School Mental Agility Level Developing Exercise (Adding: break up and find compatible numbers OR balancing.) Example : = = 70: or = Exercise (subtracting by balancing) Example: = = Exercise (Money Subtracting) Example = p = Exercise 4 (Decimal adding) [ Eg =.5] Page

3 Exercise 5 (Multiplication - Trailing zeros) Example 6000 x 40 = (6 x 4)0000 =40000 (do the number multiplication then add the zeros at the end). 40 x x x x x x x x x x 0 x 0 Exercise 6 (Division cancel common trailing zeros) Example add the zeros at the end) = = (560 8) = (56 8)0 (do the number division then Exercise 7 (Half-and-double/ compatible pairs) Example x 7 x 5 = 5 x x 7 = (5 x 4) x ( x 7) = 00 x 5 = 500. x x 5. x9 x 5. 8 x 5 x 4. x 9 x x 9 x x x x x x x x x x x 50 Exercise 8 (Money: Halving and Doubling) Example Find the cost of 4 packets of crisps at 5p each; = 4 x 5p = 7 x 70p = 490p = 4.90 Find the cost of:. packets of crisps at 45p each. 6 packets of sweets at 5p each. 4 packets of sweets at 5p each 4. chocolate bars at 5p each 5. 8 ice-creams at 45p each 6. 8 apples at 5p each 7. toffee bars at 55p each 8. 4 ice creams at 45p each 9. 4 packets of crisps at 5p each 0. 6 packets of sweets at 55p each

4 Exercise 9 ( Addition of Fractions) Example / + /4 = 8 / + / = /. / 4 + / 5. / + /. /8 + / 4. /4 + / 5. / + /5 6. / + /4 Exercise 0 ( Subtracting Fraction ) Example 5 6 = = 5 0 = Exercise (Dividing money) Example Four fish suppers cost 5.0, how much does one cost? = 5.0 (half, then half your answer, can be a way to divide by four) = 7.60 =.80. Four tickets cost 5, how much does each ticket cost?. Dad shares.90 between his six children, how much does each child get?. A meal for four people costs, how much is that per person? 4. A pack of four computer games cost 96, how much does each one cost? 5. A flat screen computer monitor costs, if the cost is paid in four weekly instalments, how much would it cost each week? 6. James and his three friends pay 08 for tickets to a theme park, how much is each ticket? 7. Six tins of soup cost.86, how much does one tin cost? 8. Jacqueline and her three friends share out a lottery win of 76, how much does each receive? 9. Forty CD s cost 60, how much does each CD cos? 0. Eight people go for a meal, costing a total of 84, if they share the cost equally, how much does each person pay?

5 Exercise ( Speed ) Example A car travels 50 miles in hours. Find the speed the car was travelling at. Speed = distance/time 50 = 5mph. Find the speed of a car which travels 50 miles in hours. Find the speed of a lorry which travels 70 miles in 6 hours.. Find the speed of a bike which travels 8 miles in 7 hours. 4. Find the speed of a train which travels 60 miles in 5 hours. 5. Find the speed of a car which travels 704 miles in hours. Exercise (Time) Example We leave Denny at 4 and arrive in Doune at 5. How long did the journey take? 4 00 = 8 mins 00 5 = 5mins Total = 4 mins How long did these journeys take?:. Leaves Denny at 094 and arrives in Inverness at 04. Leaves Glasgow at 5 and arrives in Denny at 09. Leaves Stirling at 67 and arrives in Dingwall at 4. Leaves Lanark at 85 and arrives in Wishaw at Leaves Glasgow at 79 and arrives in Edinburgh at 8 6. Leaves Inverness at 47 and arrives in Perth at 7. Leaves Cumbernauld at 5 and arrives in Lanark at Leaves Easterhouse at 6 and arrives in Stirling at Leaves Pollock at 7 and arrives in Shawlands at Leaves Denny at and arrives in Selkirk at 444 Exercise 4 (Percentages) Example Find 0 % of 8 = of 8 = 8 0 =.80 0 Find 0% of 4.50 = of 4.50 = x = 45pence x = 5p =.5 0. Find 0 % of. Find 5 % of 8. Find 40 % of 5 4. Find 70 % of 90 pence 5. Find 0 % of 5 kg 6. Find 0 % of 4 km 7. Find 5 % of 70 litres 8. Find 0 % of 9. Find 90 % of 8 0. Find 60 % of 45

6 Exercise 5 (Write a percentage as a fraction, in simplest form) Example Express 40 % as a fraction, in simplest form. 40% = 40 = 4 = Express the following percentages as a fraction, in simplest form:. 0%. 70%. 60% 4. 5% 5. 55% 6. 4% 7. 95% 8. 90% 9. 5% 0. % Execise 6 (Multiplying money) Example Find the cost of 9 kg of apples at.98 per kg = 9 x.98 = 9 x - 9 x pence = 8 8 pence = 7.8 Find the cost of the following;. 6 kg of apricots at.99 per kg. 5 kg of apples at.95 per kg. 7 kg of peaches at 4.95 per kg 4. 7 kg of Nectarines at.95per kg 5. 8 kg of strawberries at 5.95 per kg 6. 6 kg of raspberries at 7.98 per kg 7. 4 kg of bananas at.97 per kg 8. 7 kg of apples at.96per kg 9. 9 kg of cauliflower at.97 per kg 0. 4 kg of onions at.90 per kg Exercise 7 (fractions of quantities) Example ; 5 /8 of 48 /8 is 6 : 5 x 6 = 0. /5 of 5. 5 /6 of 4. /7 of 8 4. /9 of 6 5. /0 of /9 of 7 7. / of /7 of /8 of /4 of 4 Exercise 8 [ Rounding to / decimal places] [ Eg Round.678 to dec. place ]. 4.9 [ dec. place]..56 [ dec. place]. 4. [ dec. place] [ dec. place] [ dec. place] [ dec. place]

7 Exercise 9 [ Area : Halving & Doubling] [ area = L x B = 85 x 40 = 70 x 0 = 40 x 0 400] Find the areas of the fields with the following dimensions :. length = 60m, breadth = 40m. length = 80m, breadth = 5m. length = 70m, breadth = 50m 4. length = 75m, breadth = 40m 5. length = 90m, breadth = 60m 6. length = 85m, breadth = 60m Exercise 0 [ Prime Numbers] [ Eg Find the sum of the first prime numbers = 0]. Find the sum of the prime numbers between 4 and 0. Find the sum of the prime numbers between 6 and 6. Find the difference between the rd and 4 th prime numbers. 4. Find the sum of the prime numbers between 0 and 0 5. Find the product of the nd and rd prime numbers 6. Find the difference between the 5 th and 6 th prime numbers. Page 6

8 Answers Mental Agility Level Developing Exercise Exercise Exercise Exercise Exercise Exercise 9. 9/0. 7/6. 7/8 4. 7/ 5. 9/0 6. 7/ Exercise Exercise Page 7 Exercise Exercise Exercise Exercise. 50mph. 45mph. 6mph 4. 4mph 5. 64mph

9 Exercise. hrs mins. 6 minutes. 5hrs 46 mins 4. 8 minutes minutes 6. hr 6 mins. 7. hr 45 mins 8. hr 45 mins minutes 0. hrs mins Exercise p 5..5 kg km l Exercise 5. /5. 7/0. /5 4. /5 5. /0 6. 6/5 7. 9/0 8. 9/0 9. /0 0. / Exercise Exercise Exercise Exercise m². 000m². 500m² m² m² m² Exercise Page 8