Transcript National 4 Expressions and Formulae Practice Assessment with

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
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?
10cm
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, 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
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
Walk
130
Cycle
26
Bus
54
Driven
60
Angle of Pie Chart
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?
14cm
5cm
10cm
Next Steps
1.1 Applying Algebraic Skills to Manipulating Expressions and Formulae
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_G
eneral_Brackets_Factorising_TJ_Chapter15.pps
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_G
eneral_Multiplying_Out_And_Factorising_TJ.xls
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_G
eneral_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_G
eneral_Surface_Area_TJ_Chapter7.pps
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S4_G
eneral_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_G
eneral_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/S
3_General_Chapter18_TJ_Probability.pps
•http://www.mathsrevision.com/index_files/Maths/Presentations/S3_Presentations/S
3_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/S
4_General_Symmetry_TJ_Chapter3.pps
•http://www.mathsisfun.com/geometry/symmetry-rotational.html
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S
4_General_Formulae_TJ_Chapter14.pps
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S
4_General_Past_Paper_Patterns.xls
•http://www.mathsrevision.com/index_files/Maths/Presentations/S4_Presentations/S
4_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/S
4_General_Past_Papers_Volume_Surface_Area.xls
•http://www.mathsrevision.com/index_files/Maths/Presentations/S3_Presentations/S
3_General_Statistics_Practice.xls