Practice Unit Assessment (1) for National Applications 1. A farmer wishes to spread fertiliser on a triangular plot of ground. The diagram gives the dimensions of the plot. 3 m 8 o 44 m Calculate the area of this plot.. The diagram shows the paths taken by two runners, Barry and Charlie. Barry runs 30 metres from point S to position R. Charlie runs 300 metres to position T. 300 m T S 1 o 30 m R ` What is the shortest distance between the two runners? Pegasys 013
3. On an orienteering course there are three checkpoints at points U, V and W as shown in the diagram below. N U 400 km V 1 o 0 km W W is 0 kilometres from V and 400 kilometres from U. W is on a bearing of 1 from V. Calculate the bearing of W from U. Pegasys 013
Pegasys 013 4. The diagrams below show directed line segments u and v. Draw the resultant of 3u+ v.. The diagram below shows a square based model of a glass pyramid of height 8 cm. Square OPQR has a side length of 6 cm. The coordinates of Q are (6, 6, 0). R lies on the y-axis. Write down the coordinates of S. 6. The forces acting on a body are represented by three vectors a, b and c as given below. = a = 7 3 b = 6 1 c Find the resultant force. O R Q (6, 6, 0) P S x y z u v
1 7. Vector p = and vector q =. 3 3 Calculate p + q 8. Kashef bought a new car for 4 000. Its value decreased by 1% each year. Find the value of the car after years. 9. A desk top has measurements as shown in the diagram. 3 7 m 1 3 m Calculate the exact area of the desk top (in m ). 10. A man invested some money in a Building Society last year. It has increased in value by 1% and is now worth 760. Calculate how much the man invested. 11. The cost of a set menu meal in 7 different café style restaurants were as follows: 14 17 13 14 11 19 17 (a) Calculate the mean and standard deviation of these costs. (b) In 7 up market restaurants the mean cost of a meal was with a standard deviation of. Using these statistics, compare the profits of the two companies and make two valid comparisons. Pegasys 013
1. A primary teacher took a note of the results in a spelling test and the number of hours of TV that some of her pupils watched in a week. She then drew the following graph. (10,.) Spelling Test (S) 0 1 10 (40, 7.) 0 0 10 0 30 40 0 Hours spent watching TV, (H) (a) (b) (c) Determine the gradient and the y-intercept of the line of best fit shown. Using these values for the gradient and the y-intercept, write down the equation of the line in terms of H and S. Estimate the mark in the spelling test if the pupil spent hours watching television. Joe thought that for hours of watching television a good estimate for the score would be 10. Is he correct? Use your equation to explain your answer. End of Question Paper Pegasys 013
Practice Unit Assessment (1) for Applications: Marking Scheme Points of reasoning are marked # in the table. Question 1 Main points of expected responses substitute into formula 1 3 44 sin 8 63 m use correct formula selects cosine rule substitute correctly s = 300 + 30 300 30 cos1 3 process to s take square root 3 #.1 uses correct strategy 3 7 089 84 1 metres (rounding not required) 0 sin1 #.1 sinu = then valid 400 steps below finds angle U 6 8 4 draws 3u 3 states bearing from U applies head-to-tail method when adding v draws resultant from tail of 3u to head of v. 13 o (rounding not required) v 3u 3u + v correct point (3, 3, 8) Pegasys 013
6 add to get resultant 7 correct scalar multiplication then addition 3 1 + 7 + 6 3 1 6 10 1 11 + = 6 3 3 3 calculate magnitude 11 + 3 3 130 8 start calculation process calculation 3 Note: repeated subtraction method can be used 9 area calculation 10 #.1 appropriate strategy 0 88 4 000 0 88 3 1 66 7 equivalent 17 7 3 8 1 4 1 1 #.1 eg 1 + 0 1 x = 760 400 11 (a) mean for A 10 7 = 1 calculates ( x x) 1, 4, 4, 1, 16, 16, 4 3 substitute into formula 3 46 6 correct standard deviation 77 (rounding not required) (b) #. Compares mean and standard deviation in a valid way for data #. On average up market prices more expensive because > 1 There is less of a spread in up market restaurants because. <.77 Pegasys 013
1 (a) chooses distinct points and substitutes into gradient formula calculates gradient 7 m = 10 40 1 m = 3 finds intercept 3 c = 7 (b) writes down equation S = 1 H + 7 (c) #. estimate mark #. Equation gives approximately 1 hours so he is incorrect. Pegasys 013
Practice Unit Assessment () for National Applications 1. A children s play park, which is triangular in shape, has to be covered with a protective matting. The diagram gives the dimensions of the plot. m 4 m 6 o Calculate the area of protective matting needed.. The diagram shows the courses followed by two ships, the Westminster and the Bogota, after they leave Port A. The Westminster sails 0 metres to position W and the Bogota 80 metres to position B. W 0 m A 14 o 80 m B ` How far apart are the ships? Pegasys 013
3. On a radar screen, three planes, P, Q and R are at the positions shown in the diagram. N P 40 km Q 13 o 300 km R R is 300 kilometres from Q and 40 kilometres from P. R is on a bearing of 13 from Q. Calculate the bearing of R from P. Pegasys 013
Pegasys 013 4. The diagrams below show directed line segments a and b. Draw the resultant of a + b.. The diagram below shows a square based model of a glass pyramid of height 10 cm. Square OPQR has a side length of 8 cm. The coordinates of R are (0, 8, 0). P lies on the x-axis. Write down the coordinates of S. 6. The forces acting on a body are represented by three vectors k, l and m as given below. = 4 3 k = 1 4 l = 4 0 3 m Find the resultant force. O Q P S x y z a b R (0, 8, 0)
3 7. Vector a = and vector b =. 6 Calculate a + b 8. Due to inflation, house prices are expected to rise by 3 6% each year. What will the average house price be in 3 years if it is 14,000 today? 9. A room has dimensions as shown in the diagram. 3 4 m 8 3 4 m Calculate the exact amount of carpet that would have to be bought for the room. 10. A woman bought an antique painting last year. It has increased in value by 3% and is now worth 3 10. Calculate how much the woman paid for the painting. 11. A quality control examiner on a production line measures the weight, in grams, of cakes coming off the line. In a sample of eight cakes the weights were 10 147 148 13 149 143 14 149 (a) Find the mean and standard deviation of the above weights. (b) On a second production line, a sample of 8 cakes gives a mean of 148 and a standard deviation of 6 1. Using these statistics, compare the profits of the two companies and make two valid comparisons. Pegasys 013
1. The diagram below shows the connection between the thickness of insulation in a roof and the heat lost through the roof. The line of best fit has been drawn. Thickness of insulation in centimetres (T) 0 1 10 0 (1., 0) (3., 10) 0 1 3 4 Heat loss from roof in kilowatts (H) (a) (b) (c) Determine the gradient and the y-intercept of the line of best fit shown. Using these values for the gradient and the y-intercept, write down the equation of the Line in terms of H and T Estimate the thickness of insulation for a heat loss of kilowatts. Frank thinks that a good estimate for thickness when the heat loss is. kilowatts would be 1cm. Is he correct? Use your equation to explain your answer. End of Question Paper Pegasys 013
Practice Unit Assessment () for Applications: Marking Scheme Points of reasoning are marked # in the table. Question 1 Main points of expected responses substitute into formula 1 4 sin 6 19 m use correct formula selects cosine rule substitute correctly a = 0 + 80 0 80 cos14 3 process to a 3 117 take square root 146 7 metres (rounding not required) 3 #.1 uses correct strategy 300sin13 #.1 sin P = then valid 40 steps below v finds angle P 9 7 4 draws a states bearing from P 10 3 o applies head-to-tail method when adding b a b 3 draws resultant from tail of a to head of b a + b correct point (4, 4, 10) Pegasys 013
6 add to get resultant 7 correct scalar multiplication then addition 3 3 + 4 + 0 4 1 4 1 6 6 3 4 1 + = 6 10 4 3 calculate magnitude ( 1) + ( 4 ) 3 17 8 start calculation process calculation 3 Note: repeated addition method can be used 9 area calculation 10 #.1 appropriate strategy 1 036 14 000 1 036³ 3 17 894 equivalent 3 11 8 4 38 1 1 3 3 #.1 eg 1 + 0 3 x = 310 600 11 (a) mean for A 1184 8 = 148 calculates 4, 1, 0,, 1,, 9, 1 3 substitute into formula 3 66 7 correct standard Deviation 3 07 (rounding not required) (b) #. Compares mean and standard deviation in a valid way for data #. On average weights the same because 148 = 148. Wider spread on second line because 3.07 < 6.1. Pegasys 013
1 (a) chooses distinct points and substitutes into gradient formula 0 10 m = 1 3 calculates gradient m = 3 finds intercept 3 c = 7 (b) writes down equation T = H + 7 (c) #. estimate mark #. Equation gives approximately 1 cm so yes, he is correct. Pegasys 013
Practice Unit Assessment (3) for National Applications 1. Turf has to be laid on a triangular plot of garden. The diagram gives the dimensions of the plot. 7 m 10 o m Calculate the area of turf that is required.. Billy and Peter are bowlers. They are playing a game and after they each throw their first bowl they are in the positions shown in the diagram. B 4 m P 6 m 17 o T ` How far apart are the bowls after this first throw? Pegasys 013
3. The positions of three players, K, L and M are shown in this diagram. N K 40 m L 1 o 30 m M Player M is 30 metres from player L and 40 metres from player K. M is on a bearing of 1 from L. Calculate the bearing of player M from player K. Pegasys 013
Pegasys 013 4. The diagrams below show directed line segments k and l. Draw the resultant of k + l.. The diagram below shows a square based model of a glass pyramid of height cm. The base OPQR is a square. The coordinates of S are (,, ). P lies on the x-axis and R lies on the y axis. Write down the coordinates of Q. 6. The forces acting on a body are represented by three vectors x, y and z as given below. = 1 3 4 x = 0 7 y = 1 z Find the resultant force. k l O Q P S x y z R (,, )
3 7. Vector x = and vector y =. 6 Calculate 3x y 8. Chocolate fountains have become very popular at parties. At one party 3% of the remaining chocolate was used every 0 minutes. If kg of melted chocolate was added to the fountain at the start of the night, how much would be left after 1 hour? 9. Calculate the area of this piece of ground which has dimensions as shown in the diagram. 1 10 m 1 6 4 m 10. I bought a car three years ago. Since then it has decreased in value by 4% and is now worth 687. How much did I pay for the car? 11. A set of Maths test marks for a group of students are shown below. 3 7 43 18 36 39 (a) Find the mean and standard deviation. (b) Another group had a mean of 37 and a standard deviation of 8 6. Compare the test marks of the two classes and make two valid comparisons. Pegasys 013
1. A selection of the number of games won and the total points gained by teams in the Scottish Premier League were plotted on this scattergraph and the line of best fit was drawn. P 80 70 60 0 Points 40 30 (1, 40) 0 (6, 0) 10 4 8 1 16 0 Wins W (a) (b) (c) Determine the gradient and the y-intercept of the line of best fit shown. Using these values for the gradient and the y-intercept, write down the equation of the line in terms of W and P. Use your equation to estimate the number of points gained by a team who win 7 games. Anne thinks that a good estimate for a team who won 7 games would be 90 points, is she correct? End of Question Paper Pegasys 013
Practice Unit Assessment (3) for Applications: Marking Scheme Points of reasoning are marked # in the table. Question 1 Main points of expected responses substitute into formula 1 7 sin10 330 m use correct formula selects cosine rule substitute correctly t = 4 + 6 4 6 cos17 3 process to t 3 8 3 take square root 7 7 metres (rounding not required) 3 #.1 uses correct strategy 30sin1 #.1 sin K = then valid 40 steps below finds angle K 38 4 draws k states bearing from K 14 o applies head-to-tail method when adding l l 3 draws resultant from tail of k to head of l k correct point (4, 4, 0) Pegasys 013
6 add to get resultant 7 correct scalar multiplication then addition 4 3 + 7 + 1 1 0 0 6 9 4 = 18 10 8 3 calculate magnitude + 8 3 89 8 start calculation process calculation 3 Note: repeated addition method can be used 9 area calculation 10 #.1 appropriate strategy 0 77 000 0 77³ 3 913g equivalent 3 1 4 3 = 63 m² 4 4 #.1 eg (1 0 4) x = 6 87 1 00 11 (a) mean 198 6 = 33 calculates 4, 36, 100,, 9, 36 3 substitute into formula 3 410 correct standard deviation 9 (rounding not required) (b) #. Compares mean and standard deviation in a valid way for data #. On average second group had higher marks because 37 > 33. Second group s marks less spread out because 8.6 < 9. Pegasys 013
1 (a) chooses distinct points and substitutes into gradient formula calculates gradient 40 0 m = 1 6 10 m = 3 3 finds intercept 3 c = 0 (b) writes down equation P = 10 W 3 (c) #. estimate mark #. Equation gives 90 points so yes, she is correct. Pegasys 013