National 5 Mathematics

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Elmer Wilkinson
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1 St Andrew s Academy Mathematics Department National 5 Mathematics UNIT 1 ASSESSMENT PREPARATION St Andrew's Academy Maths Dept

2 Practice Unit Assessment 1A for National 5 1. Expand and simplify where appropriate: (a) d(4d e) (g + 4)(g + 9) 2. Factorise: (a) y² 6y t² 49 x² + 7x Express x² + 6x + 7 in the form (x + p)² + q. 4. Kashef bought a new car for Its value decreased by 12% each year. Find the value of the car after 5 years. 5. A desk top has measurements as shown in the diagram m 2 1 m 3 Calculate the exact area of the desk top (in m 2 ). 6. A man invested some money in a Building Society last year. It has increased in value by 15% and is now worth Calculate how much the man invested. St Andrew's Academy Maths Dept

3 7. The cost of a set menu meal in 7 different café style restaurants were as follows: (a) Calculate the mean and standard deviation of these costs. In 7 up market restaurants the mean cost of a meal was 22 with a standard deviation of 2 2. Using these statistics, compare the profits of the two companies and make two valid comparisons. 8. 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 Spelling Test (S) R l Hours spent watching TV, (h) (a) 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. Estimate the mark in the spelling test if the pupil spent 25 hours watching television. End of Question Paper St Andrew's Academy Maths Dept

4 Practice Unit Assessment 1B for National 5 1. Expand and simplify where appropriate: (a) g(6g h) (d + 3)(d 7) 2. Factorise: (a) k² 7k x² 81 z² + 10z Express x² 8x + 1 in the form (x + p)² + q. 4. 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 142,000 today? 5. A room has dimensions as shown in the diagram. 3 4 m m Calculate the exact amount of carpet that would have to be bought for the room. 6. A woman bought an antique painting last year. It has increased in value by 35% and is now worth Calculate how much the woman paid for the painting. St Andrew's Academy Maths Dept

5 7. 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 (a) Find the mean and standard deviation of the above weights. 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. 8. 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) Heat loss from roof in kilowatts (H) (a) 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. Estimate the thickness of insulation for a heat loss of 2 5 kilowatts. End of Question Paper St Andrew's Academy Maths Dept

6 Practice Unit Assessment 1C for National 5 1. Expand and simplify where appropriate: (a) m(3m n) (p + 5)(p + 8) 2. Factorise: (a) h² 11h q² 144 a² 12z Express x² + 7x + 9 in the form (x + p)² + q. 4. Chocolate fountains have become very popular at parties. At one party 23% of the remaining chocolate was used every 20 minutes. If 2kg of melted chocolate was added to the fountain at the start of the night, how much would be left after 1 hour? 5. Calculate the area of this piece of ground which has dimensions as shown in the diagram m 1 10 m 5 6. I bought a car three years ago. Since then it has decreased in value by 45% and is now worth How much did I pay for the car? St Andrew's Academy Maths Dept

7 7. A set of Maths test marks for a group of students are shown below (a) Find the mean and standard deviation. Another group had a mean of 37 and a standard deviation of 8 6. Compare the test marks of the two classes. 8. 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 Points (a) W Wins 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. Use your equation to estimate the number of points gained by a team who win 27 games. End of Question Paper St Andrew's Academy Maths Dept

8 Practice Unit Assessment 1A Marking Scheme Points of reasoning are marked # in the table. Question Main points of expected responses 1 multiply out brackets multiply out the brackets collect like terms 2 factorise expression factorise difference of two squares start to factorise trinomial expression complete factorisation 3 start of process complete process 4 start calculation process calculation correct answer Note: repeated subtraction method can be used 5 area calculation correct answer 6 #2.1 appropriate strategy 4d 2 de g 2 + 4g + 9g + 36 g g + 36 y(y 6) (t + 7)(t 7) (x 3)(x 4) ie evidence of brackets, x, 3 and 4 (x + 3)(x + 4) (x + 3) 2 (x + 3) equivalent #2.1 eg x = (a) correct answer mean for A = 15 calculates 2 ( x x) 1, 4, 4, 1, 16, 16, 4 substitute into formula 46 6 correct standard deviation 2 77 (rounding not required) (Equivalent calculations can be used) #2.2 Compares mean and standard deviation in a valid way for data #2.2 On average up market prices more expensive There is less of a spread in up market restaurants St Andrew's Academy Maths Dept

9 8 (a) chooses 2 distinct points and substitutes into gradient formula calculates gradient m m (or based on gradient line 2 of best fit finds intercept writes down equation # 2.2 estimate mark c = 27 5 (approximately or by calculation or from graph) 1 S = h (or equivalent) #2.2 Approximately 15 hours St Andrew's Academy Maths Dept

10 Practice Unit 1B: Marking Scheme Points of reasoning are marked # in the table. Question 1 (a) 2 (a) Main points of expected responses multiply out brackets multiply out the brackets collect like terms factorise expression factorise difference of two squares start to factorise trinomial expression completefactorisation 6g 2 gh d 2 7d + 3d 21 d 2 4d 21 k(k 7) (x + 9)(x 9) (z 3)(z 7) ie evidence of brackets, z, 3 and 7 (z + 3)(z + 7) 3 start of process complete process 4 start calculation process calculation correct answer Note: repeated addition method can be used 5 area calculation correct answer 6 #2.1 appropriate strategy (x 4) 2 (x 4) ³ equivalent #2.1 eg x = 3510 correct answer (a) mean for A = 148 calculates 4, 1, 0, 25, 1, 25, 9, 1 substitute into formula 66 7 correct standard Deviation 3 07 (rounding not required) (Equivalent calculations can be used) #2.2 Compares mean and standard deviation in a valid way for data #2.2 On average weights the same Wider spread on second line. St Andrew's Academy Maths Dept

11 8 (a) chooses 2 distinct points and substitutes into gradient formula calculates gradient finds intercept m m 5 (or based on gradient line of best fit c = 27 5 (approximately or by calculation or from graph) writes down equation T = 5 H (or equivalent) # 2.2 estimate mark #2.2 Approximately 15 cm St Andrew's Academy Maths Dept

12 Practice Unit 1C: Marking Scheme Points of reasoning are marked # in the table. Question Main points of expected responses 1 (a) multiply out brackets multiply out the brackets collect like terms 2 (a) factorise expression factorise difference of two squares start to factorise trinomial expression complete factorisation 3 start of process complete process 3m 2 mn p 2 + 8p + 5p + 40 p p + 40 h(h 11) (q + 12)(q 12) (a 4)(a 8) ie evidence of brackets, a, 4 and 8 (a 4)(a 8) (x + 3 5) 2 (x + 3 5) start calculation process calculation correct answer Note: repeated addition method can be used 5 area calculation correct answer 6 #2.1 appropriate strategy ³ 913g equivalent #2.1 eg (1 0 45) x = correct answer (a) mean = 33 calculates 4, 36, 100, 225, 9, 36 substitute into formula correct standard deviation 9 (rounding not required) (Equivalent calculations can be used) #2.2 Compares mean and standard deviation in a valid way for data #2.2 On average second group had higher marks Second group s marks less spread out St Andrew's Academy Maths Dept

13 8 (a) chooses 2 distinct points and substitutes into gradient formula calculates gradient finds intercept 40 0 m m (or based on gradient line 3 of best fit) c = 0 (approximately or by calculation or from graph) writes down equation 10 P = W 3 (or equivalent) # 2.2 estimate mark # points St Andrew's Academy Maths Dept

HIGH-LOW METHOD. Key Terms and Concepts to Know

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