General Exam Paper 1 Solutions 2003

Transcription

1 General Exam Paper 1 Solutions (a) Given (b). Given 6.37 x 60 Step 1 : 6.37 x 10 = 63.7 Step 2 : (c). Given Page 1 of 7

2 General Exam Paper 1 Solutions 2003 (d) Step 1 : Make denominator (bottom) the same Step 2 : Add the numerators + = Given the diagram the tree figure bearing is: Base West 21 o N 270 o 21 o = 249 o South 3. Given there are 9 wooden ball in a bag numbered 1 to 9. The chance that a number is more than 7 is: number over 7 2 P(> 7) = = total number 9 Page 2 of 7

3 General Exam Paper 1 Solutions Given the ram of the letter A. Increasing it by a factor of 2 we get. Page 3 of 7

4 General Exam Paper 1 Solutions Given the stem leaf diagram for the amount of sunshine each day in June: Hours of Sunshine n = 21 Key 3 2 means 3.2hours (a) The range is given by: = 7.1 (b) The median number of hours is: Median is the middle number after data has been sorted 5.2 hours Page 4 of 7

5 General Exam Paper 1 Solutions Given information on Pizza Restaurant bill the correct service charge is: 15% of 33 = = 4.95 Total charge = = Bill is wrong by 1 7. Given the rules for the True or false game. True = +3 False = -1 (a) Given Ann got 2 questions correct and 8 wrong her score is: 2 x 3 8 = -2 (b) Given David answered 10 questions and scored 18 points. To work out how many questions he got right: R W T Page 5 of 7

6 General Exam Paper 1 Solutions Given the paper sizes information and looking at the pattern the sizes for A10 will be: A3 297 x 420 A4 210 x 297 A5 148 x 210 A6 105 x 148 A7 74 x 105 A8 52 x 74 A9 37 x 52 A10 26 x Given the planet Pluto is approximately 7364 million miles from the Sun. In scientific notation the number is: = Remember scientific notation a x 10 n a must be between 1 < a < 10 n is an integer Page 6 of 7

7 General Exam Paper 1 Solutions Given Centre O AC is a tangent line to the circle at B Angle DBA = 70 o D O E Angel BOE is given by: A 70 o B C Since AC is a tangent to the circle, angle ABO is right-angled. Angle DBO is 90 o 70 o = 20 o ODB is an isosceles triangle so angle ODB = 20 o and angle BOD = 140 o. Finally, DOE is a straight line therefore angle BOE is: 180 o 140 o = 40 o Page 7 of 7

8 1. Given the distance between Verona and Milan is 158 km and the time taken is 1 hours and 40 mins, then the average speed is : mins in hours is = 60 3 average speed is = = 98.8km/hr 2. Given Alice gets a basic rate of pay of 6.50, her overtime rate is time and a half and she got paid last week which included 4 hours overtime. To calculate how much time she worked at normal rate we have: Overtime rate = = 9.75 Overtime pay = = 39 Basic pay = = Hours worked = 15 hours Page 1 of 10

9 3 Completing the table and finding the mean we have: Number of letters Frequency Number of letter x frequency x 5 = x 12 = x 18 = x 26 = x 18 = x 11 = x 7 = x 3 = 24 Totals Mean = = = 4.2 (to 1 decimal place) 4. Given Book prices and Dyna must spend between and does not buy more than one copy of any one book. All possible combinations are: Book Title Book Title Book Title Total Cost Pasta Chicken Pasta Soups Puddings Chicken Puddings Chicken Soups Fish Puddings Fish Soups Page 2 of 10

10 5. Completing the table and drawing the line y = 2x - 1 we get. x y y 10 5 C(4,7) x B(0,-1) -5 A(-4,-9) -10 Page 3 of 10

11 6. Following the instructions: Start with a multiple of 4 Move to a prime number Finish with a square number Start Finish First Number is 24 Second number is 43 Third number 36 Page 4 of 10

12 7. Given the diagram and measurements, the total goal height is: 3m Goal Height 4m 9m Real : Shadow Scale 3 : 4 Real goal height is : 3 of 9 = = 6.75m 4 Page 5 of 10

13 8. Given the diagram and that the candle is a cuboid. From a tub of 10 litre of wax we can make: 1 candle has volume: Volume = l b h = = 540cm 3 15cm 6cm 6cm 10 litres = cm 3 3 So for cm we can get: = candles. 540 Page 6 of 10

14 9. (a) Multiplying out the brackets and collecting terms we get: (b) Solving the inequality we get: 3(2w+ 1) + 2(8 w) 6w w 4w + 19 (Remember change side change sign) 3x x x 15 x x Page 7 of 10

15 10. Given the cost c pounds of carpet varies directly as it length l m. A carpet of length 5m costs 340: (a) A carpet of length 8m will cost: c = k l 340 = k k = = 5 68 Formula is: c = 68 l For 8m we have c = 68 8 = 544 (b) The length of the carpet that cost 238 will be: He will be able to paint his desk: c = 68 l 238 = 68 l 238 l = = m Page 8 of 10

16 11. Given the climbing frame is cylindrical in shape, the surface area is 75.5m 2 and the radius 1.5m. To find the height we have: A = 2π r h 75.5 = 2π 1.5 h Height h 75.5 = = 8.01 m 3π 1.5m 12. Given the diagram of the aircraft landing at Glasgow Airport we can calculate the height of the aircraft by: 7 o 5km o A o By (S H)(C H)(T A) x o sin(7 ) = 5 o x = 5sin(7 ) = km = 609m Page 9 of 10

17 12. Given the diagram of the isosceles triangular banner hanging from a building and knowing the dimensions. We can calculate the area of the banner by: 20cm 1 Area = bh h = vertical height 2 26cm By Pythagoras h= (26-10) = 576 =24m 1 Area = =120m 2 Page 10 of 10