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?

Q6

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

10cm

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 clockb.) 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?

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, 2a.) Calculate the mean number of hours spent on homeworkb.) Calculate the rangec.) 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

Weight Tally Frequency

0 - 9

10 - 19

20 - 29

30 - 39

40 - 49

50 - 59

Total =

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:

Travel Method Number of Pupils Angle of Pie Chart

Walk 130

Cycle 26

Bus 54

Driven 60

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?

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?

10cm5cm

14cm

Next Steps1.1 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

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

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