Key Stage 4

 Assessment 2

Intent

The intention of this unit is build on and increase the level of rigour in students' mathematical understanding from Key Stage 3, whilst introducing new Key Stage 4 concepts.

Implementation

To develop students as independent learners this unit of work covers three terms with a period of revision before a substantial assessment in term 6. This requires students to take ownership of their mathematical understanding and engage in a process of identifying gaps and improving ahead of the tests.

From the 3rd week of the unit students will complete a weekly knowledge check so they can measure how their knowledge and expertise is building. The content of the knowledge checks updates as more concepts are covered, to provide a rolling check of what students can recall.

During this unit there will also be several longer written homework tasks which include a knowledge check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work on these homework tasks.

Impact

The impact of this unit of work will be measured through a Two 90 minute written assessments in term 6

The assessment will cover every aspect of the unit of work and using the knowledge organiser together with this website is a great way to prepare for the tests.

Topics covered in this unit:

Core

32n Use a written method to multiply decimals

30n Estimate answers by rounding including word problems

43n Comparing value for money by finding the cost of comparable amounts and work with unit prices

60n Adjust a recipe or check it there are enough ingredients to make a given number

24n Put decimals in order and  round to decimal places

44n Using a calculator correctly with powers, roots and division

58n Rounding to significant figures

34a Using BIDMAS to evaluate numerical expressions (without powers and roots)

35a Using BIDMAS to evaluate numerical expressions including powers and roots Inserting brackets into a calculation

47n Using the three index laws with whole numbers

72n Evaluate negative powers or reciprocal of whole numbers

47a Using the three index laws to simplify expressions

66a Simplifying expressions by applying index laws more than once or to several terms

31a Take readings from conversion graph for units or currency

41a Use a conversion graph to convert larger numbers and solve extended problems

44s Solve speed-distance-time problems (including converting minutes to hours when necessary)

36a Read and plot distances and times from distance-time graphs

45a Calculate speed or use speed to complete a distance-time graph

28a Using a two-step formula written in words both forwards and backwards

38a Using an algebraic formula both forwards and backwards

49a Write algebraic formulae from a written description

43a Listing integers that satisfy inequalities and representing inequalities on a number line

48a Solve equations with x on both sides and solving inequalities by algebraic manipulation

73a Addition, subtraction and resultants of 2D column vectors

74a Writing a vector in terms of the free vectors on a diagram

34s Converting between metric units (and to imperial given the conversion factor)

67s Solve density-mass-volume or pressure-force-area problems

27s Calculate the area and perimeter of a rectangle

35s Calculate the area of a parallelogram or a triangle

42s Calculate the area of a trapezium or a compound shape involving trapeziums

39s Calculate the area of a compound shape

54a Forming and solving  equations arising from shape, measure or word problems

50s Calculating the area or circumference of a circle giving answers approximately or in terms of π

55s Calculating the area or perimeter of a semi-circle or quadrant or work with circular measure in context

64s Calculating the arc length or area of a sector

49s Calculate the volume of a prism or the surface area of a cuboid

57s Calculate the volume of a cylinder giving answers approximately or in terms of π

69s Calculating the surface area of a cylinder (or half-cylinder or quadrant) giving answers approximately or in terms of π

72s Use the volume or surface area formulae for cones and spheres

65s Calculate lengths in similar 2D shapes

35d Draw and read from combined bar charts

47d Draw and read from stacked bar charts

36d Draw and read from a vertical line chart for discrete data

28d Recognise the mode from a list of data or a bar chart

30d Calculate the range from a list of data or a bar chart

31d Calculate the median from an odd or even list of data

42d Calculate the mean from a list of data and compare which is the best average to use

64d Compare distributions of data by referring to averages and spread

52d Identify possible outliers from a list of data and omit them in calculating range

60d Use averages to work out the values of missing data 

38d Draw a stem and leaf diagram and use it to find mode, median or range 

29d List the possible outcomes of an experiment

39d Calculate probability based on equally likely outcomes

45d List possible combinations and use your list to calculate probabilities

44d Use the fact that probabilities sum to 1

50d Define mutually exclusive and calculate the probability of either event happening

53d Calculate probability based on relative frequency

54d Work out the expected number of successes given the probability and number of trials

57d Understand that by increasing sample size outcomes will tend towards theoretical probabilities

46d Sort sets of numbers into a Venn diagram

61d Use set notation including {},A´, Ø, ∩ and U to refer to Venn diagrams

67d Define independent and calculate the probability of independent events both happening 

68d Complete a tree diagram with independent probabilities and use it to calculate probabilities

Plus / Plus+

78n Use the product rule for counting combinations

58a Know the difference between an equation and an identity and show algebraic expressions are equivalent

90n Provide algebraic proof for statements about divisibility

91n Provide algebraic proof for statements about odd, even, consecutive numbers

77n Evaluate 1/n fractional powers of whole numbers

79n Evaluate positive or negative fractional powers of whole numbers

84n Evaluate fractional negative powers of fractions or mixed numbers

94n Solve an index equation by first making the bases match

85a Use function notation and substitute values and expressions into functions

97a Obtain an inverse function by rearranging formulae and express this in the form f¯¹(x) = 

98a Obtain a composite function by substituting the output expression of one function into another

43a Listing integers that satisfy inequalities and representing inequalities on a number line

77a Shade a region or mark integer coordinates satisfied by 2D Inequalities

96a Find approximate solutions to equations using an iterative formula

99a Form an iterative scheme for a given equation and understand that it may converge or diverge

100a Solve quadratic inequalities giving solutions in set notation 

88a Recognise or form the equation for a circle around (0,0)

89a Recognise and form equations for exponential growth or decay

87s Calculate and interpret the gradient of a distance-time or velocity-time graph

88s Calculate and interpret the area under a distance-time or velocity-time graph

96s Know that the gradient at a point on a curve describes an instantaneous rate of change

97s Use a chord to estimate the average rate of change of a non-linear graph

98s Use a tangent to estimate the instantaneous rate of change of a non-linear graph

99s Find the equation of a tangent to a circle at a given point

100s Estimate the area under a non-linear graph eg using trapezium rule

87a Prove that two vectors are parallel

92a Prove that three points are colinear using vectors

44s Solve speed-distance-time problems (including converting minutes to hours when necessary)

76a Solve quadratic equations that require rearranging first or arise from geometry problems

77s Determine and use area or volume scale factors for similar 2D and 3D shapes

68s Convert between compound measures and units of area and volume

89s Calculate the volume of a frustum using similar triangles or find the height of a cone formed from a given sector

66d Use data from a sample to estimate properties of the population and explain how bias might influence these estimates

78d Find the quartiles from a list of data and calculate and compare inter-quartile range

79d Plot a cumulative frequency graph

80d Read median and frequency above or below a given value from a cumulative frequency graph

81d Read quartiles from a cumulative frequency graph and calculate and compare inter-quartile range

82d Draw a box plot from summary statistics or a list of data

83d Compare distribution of data shown in box plots

84d Read bivariate data from a scatter graph and use it to draw and compare box plots

86d Calculate frequency density and draw a histogram

87d Read and use frequencies from a histogram

91d Use a partial frequency table and partial histogram to complete both

94d Use a histogram to estimate median, quartiles or frequency above or below a value that isn't a class boundary

72d Use a Venn diagram to calculate probabilities of combined events

73d Solve a two-event probability problem by drawing up a tree diagram

74d Know and use the addition rule for probability

88d Know and use the multiplication rule for conditional probability

77d Calculate conditional probabilities from Two-way tables

75d Complete a tree diagram with conditional probabilities and use it to calculate probabilities

85d Use a tree diagram or binomial reasoning to find probabilities of three or more events

92d Solve algebraic conditional probability problems

90d Draw up and populate a Venn diagram for 3 events and use it to calculate probabilities

93d Calculate conditional probabilities of combined events from a Venn diagram

95d Solve probability problems by introducing an unknown into a Venn diagram and using Addition and Multiplication rules