National 4 Expressions and Formulae Unit

1. National 4 Expressions and Formulae Unit Practice Assessment Split into Topic Areas 1.1 Applying Algebraic Skills to Manipulating Expressions and Formulae Q1 Expand the brackets: 6(2a – 3) Q2 Expand the brackets and simplify: 5e + 3(e – 9) Q3 Factorise: 12x – 20 Q4 Simplify: 2a² - 4a + 3a² + 6a Q5 In a car hire shop they calculate the price of a car using the formula: C = 0.9M + 30D Where C is the cost, M is the number of miles and D is the number of days. How much would it cost to hire a car for a week going 350 miles?

2. Q6

3. Q7 The difficulty of a ski run is given by it’s gradient. Green run – Gradient between 2.7 and 11.25 Blue run – Gradient between 11.25 and 18 Black run – Gradient greater than 18. The following run needs to be given a difficulty. What colour of run would you give it? Justify your answer. 1000m 280m

4. 1.2 Applying Geometric Skills to Circumference, Area and Volume Q1 The following clock has a diameter of 30cm. Calculate: a.) The circumference of the clock b.) The area of the clock Q2 What is the surface area of this triangular prism? Q3 Calculate the area of this trapezium: Q4 What is the volume of this cylinder with a height of 15cm and radius of 4cm? 10cm

5. 1.3 Applying Statistical Skills to Representing and Analysing Data and to Probability Q1 The following data was collected of number of hours first year pupils spend on their homework a week. 12, 7, 5, 2, 3, 10, 8, 6, 5, 2 a.) Calculate the mean number of hours spent on homework b.) Calculate the range c.) For pupils in fourth year their mean was 7.8 and their range was 8. Comment on the differences. Q2 You roll a dice. What is the probability that it will land on a number less than 2? Q3 Complete the following frequency table of these results collected about the weight of animals in a zoo (in kg): 12, 8, 3, 25, 30, 56, 44, 16, 59, 50, 42, 18, 25, 33, 34, 40, 15, 35, 36, 45, 38, 15

6. Q4 The following table shows the results of a survey taken on how pupils get to school. Fill in the table to complete the pie chart:

7. 2.1 Interpreting a Situation and Identifying a Valid Strategy Q1 Q2 If the formula for calculating the nth term of a sequence is given by s = 3n – 2, what is n when s = 10?

8. 2.2 Explaining a solution and/or relating it to context Q1 To meet profit targets in a company the juice container used must have a surface area less than 500cm². Does this container satisfy the target? Juice 14cm 5cm 10cm

9. Next Steps • 1.1 Applying Algebraic Skills to Manipulating Expressions and Formulae • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Brackets_Factorising_TJ_Chapter15.pps • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Multiplying_Out_And_Factorising_TJ.xls • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Past_Paper_Algebra.xls • http://www.bbc.co.uk/bitesize/ks3/maths/algebra/formulae2/revision/4/ • http://www.bbc.co.uk/bitesize/ks3/maths/algebra/formulae2/revision/2/ • http://www.bbc.co.uk/bitesize/ks3/maths/algebra/formulae2/revision/5/ • 1.2 Applying Geometric Skills to Circumference, Area and Volume • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Surface_Area_TJ_Chapter7.pps • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Volume_TJ_Chapter8.pps • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_3_General_Volume_Surface_Area_TJ.xls • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_The_Circle_TJ_Chapter10.pps

10. 1.3 Applying Statistical Skills to Representing and Analysing Data and to Probability • http://www.bbc.co.uk/bitesize/ks2/maths/data/mode_median_mean_range/read/1/ • http://www.youtube.com/watch?v=81zcjULlh58 • http://www.mathsteacher.com.au/year8/ch17_stat/03_freq/freq.htm • http://www.mathsisfun.com/data/pie-charts.html • http://www.mathgoodies.com/lessons/vol6/intro_probability.html • http://www.mathsrevision.com/index_files/Maths/Presentations/S3_Presentations/S3_General_Chapter18_TJ_Probability.pps • http://www.mathsrevision.com/index_files/Maths/Presentations/S3_Presentations/S3_General_Probability_Statistics_Practice.xls • 2.1 Interpreting a Situation and Identifying a Valid Strategy • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Symmetry_TJ_Chapter3.pps • http://www.mathsisfun.com/geometry/symmetry-rotational.html • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Formulae_TJ_Chapter14.pps • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Past_Paper_Patterns.xls • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_3_General_Harder_Integer_Practice.xls

11. 2.2 Explaining a solution and/or relating it to context • http://www.mathsisfun.com/gradient.html • http://www.math.com/tables/geometry/surfareas.htm • http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_General_Past_Papers_Volume_Surface_Area.xls • http://www.mathsrevision.com/index_files/Maths/Presentations/S3_Presentations/S3_General_Statistics_Practice.xls