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Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics (1MA1)
Higher tier diagnostic document
For first teaching from September 2015
Contents
Introduction 5Higher course overview 6Higher units 7
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
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Introduction
This Higher tier diagnostic document is intended to support students in accessing the Higher tier of the new GCSE (9–1) Mathematics specification.
This document lists the units in the Higher tier scheme of work, suggests questions to establish whether a student has the required prior knowledge, and provides a mapping of references to the Foundation scheme of work (and occasionally the Access to Foundation tier scheme of work) should the student need to refresh their understanding or develop a particular skill. Teachers can then turn to the relevant unit(s) in the Foundation scheme of work for additional support, including objectives, possible success criteria, opportunities for reasoning and problem-solving, and common misconceptions.
For later Higher tier units, prior knowledge has sometimes not been covered in the Foundation scheme of work. In these instances, a reference to an earlier Higher tier unit is provided, along with diagnostic questions to check that this knowledge has been acquired.
Our free support for the GCSE Mathematics specification (1MA1) can be found on the Edexcel mathematics website (http://qualifications.pearson.com/en/home.html) and on the Emporium (www.edexcelmaths.com).
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Unit Title
1a Calculations, checking and roundingb Indices, roots, reciprocals and hierarchy of operationsc Factors, multiples, primes, standard form and surds
2a Algebra: the basics, setting up, rearranging and solving equationsb Sequences
3 a Averages and rangeb Representing and interpreting data and scatter graphs
4 a Fractions and percentagesb Ratio and proportion
5 a Polygons, angles and parallel linesb Pythagoras’ Theorem and trigonometry
6a Graphs: the basics and real-life graphsb Linear graphs and coordinate geometryc Quadratic, cubic and other graphs
7a Perimeter, area and circlesb 3D forms and volume, cylinders, cones and spheresc Accuracy and bounds
8 a Transformationsb Constructions, loci and bearings
9 a Solving quadratic and simultaneous equationsb Inequalities
10 Probability11 Multiplicative reasoning 12 Similarity and congruence in 2D and 3D
13 a Graphs of trigonometric functionsb Further trigonometry
14 a Collecting datab Cumulative frequency, box plots and histograms
15 Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics
16 a Circle theorems b Circle geometry
17Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof
18 Vectors and geometric proof
19a Reciprocal and exponential graphs; Gradient and area under
graphsb Direct and inverse proportion
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20165
Foundation tier
UNIT 1: Powers, decimals, HCF and LCM, positive and negative, roots, rounding, reciprocals, standard form, indices and surds
Return to OverviewSUB-UNITS
a Calculations, checking and roundingb Indices, roots, reciprocals and hierarchy of operationsc Factors, multiples, primes, standard form and surds
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
understand place value, order integers and decimals and use the four operations
Given the digits 2, 5, 7 and 9, make all the possible three-digit number with one decimal place and put them in order.
Addition, subtraction, multiplication and division questions with up to three digits and one decimal place
Foundation Unit 1: Number, powers, decimals, HCF and LCM, roots and rounding
find integer complements to 10 and to 100
46 + = 100 Foundation Unit 1a: Integers and place value
See also Access Unit 5: Addition and subtraction 2
recall multiplication facts to 10 × 10
Quick-fire multiplication and division questions. e.g.6 × 7 =8 × 9 =35 ÷ 5 =132 ÷ 12 =
Foundation Unit 1a: Integers and place value
multiply and divide by 10, 100 and 1000
Multiply 24.75 by 10, 100, 1000
Divide 72430 by 10, 100, 1000.
Foundation Unit 1a: Integers and place value
recall and identify squares, square roots, cubes and cube roots
Which of these numbers is a square number? Which is a cube? Explain your answers.2, 5, 8, 12, 16, 20, 28
Foundation Unit 1c: Indices, powers and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 2: Expressions, substituting into simple formulae, expanding and factorising, equations, sequences and inequalities, simple proof
Return to OverviewSUB-UNITS
a Algebra: the basics, setting up, rearranging and solving equationsb Sequences
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
use negative numbers with the four operations, recall and use the hierarchy of operations and understand inverse operations
4 – (–6) =
–6 × 3 =
18 ÷ = –3
4 × 7 – 16 ÷ 2 =
Foundation Unit 1a: Integers and place value
Foundation Unit 1c: Indices, powers and roots
deal with decimals and negatives on a calculator
Use a calculator to calculate:
–6.5 × –4.2 =
Foundation Unit 1c: Indices, powers and roots
use index laws numerically
43 × 45 =
67 ÷ 62 =
Foundation Unit 1c: Indices, powers and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20167
Foundation tier
UNIT 3: Averages and range, collecting data, representing data
Return to OverviewSUB-UNITS
a Averages and rangeb Representing and interpreting data and scatter graphs
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
read scales on graphs, draw circles, measure angles and plot coordinates in the first quadrant
On cm-squared paper, draw axes for x and y from 0 to 8. Plot these points: (1, 0), (2, 6), (7, 8). Join to make a triangle. Measure the angles.
On the same coordinate grid, use a pair of compasses to draw a circle centre (5, 4), radius 4 cm. What are the coordinates of the point where the circle touches the x-axis?
Foundation Unit 3a: Tables, charts and graphs
Foundation Unit 3b: Pie charts
Foundation Unit 6a: Properties of shapes, parallel lines and angle facts
Foundation Unit 15a: Plans and elevations
use tally charts What number does this represent?
Write 24 in tallies.
Foundation Unit 3: Drawing and interpreting graphs, tables and charts
See also Access Unit 22: Data handling 2
use inequality notation Take a pair of two-digit numbers and use < and > correctly. e.g. 46 and 78 or 62 and 35
Foundation Unit 1a: Integers and place value
find the midpoint of two numbers
What number is in the middle of 3 and 9? 42 and 50?
Foundation Unit 7: Statistics, sampling and the averages
See also Access Unit 22: Data handling 2
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 4: Fractions, percentages, ratio and proportion
Return to OverviewSUB-UNITS
a Fractions and percentagesb Ratio and proportion
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
use the four operations of number
See questions for Unit 1 Foundation Unit 1a: Integers and place value
find common factors What factor is common to 8 and 12? To 14 and 35?
Foundation Unit 1d: Factors, multiples and primes
understand fractions as being ‘parts of a whole’
Shade of
Shade of
Foundation Unit 4a: Fractions, decimals and percentages
See also Access Unit 11: Fractions, decimals and percentages 2
understand percentage as ‘number of parts per hundred’ and recognise that percentages are used in everyday life
Shannon got the questions
in a test correct. What is as a percentage?
In a sale, prices are reduced by 10%. What is 10% as a fraction?
Foundation Unit 4b: Percentages
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20169
30°x
45°y
Foundation tier
UNIT 5: Angles, polygons, parallel lines; Right-angled triangles: Pythagoras and trigonometry
Return to OverviewSUB-UNITS
a Polygons, angles and parallel linesb Pythagoras’ Theorem and trigonometry
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
rearrange simple formulae and equations
If t = 6h – 3, write an expression for h
Foundation Unit 2: Expressions, substituting into simple formulae, expanding and factorising
recall basic angle facts On squared paper, draw a right-angled triangle with one acute and one obtuse angle.
Find the size of the angles marked x and y.
Foundation Unit 6a: Properties of shapes, parallel lines and angle facts 6b - G3, G6
understand that fractions are more accurate in calculations than rounded percentage or decimal equivalents
≈ 0.3Which of the following give the most accurate answer?
× 50 = 16
0.3 × 50 = 15
Foundation Unit 4a: Fractions, decimals and percentages
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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12 cm
5 cm x cm
3 cm
6 cm
7 cm
Foundation tier
UNIT 6: Real-life and algebraic linear graphs, quadratic and cubic graphs, the equation of a circle, plus rates of change and area under graphs made from straight lines
Return to OverviewSUB-UNITS
a Graphs: the basics and real-life graphsb Linear graphs and coordinate geometryc Quadratic, cubic and other graphs
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
identify coordinates of given points in the first quadrant or all four quadrants
Draw axes for values of x and y from –5 to +5.
Plot the points (2, 3), (–3, 2) and (–2, –3), which form three corners of a square. What are the coordinates of the fourth corner?
Foundation Unit 9a: Real-life graphs
use Pythagoras’ Theorem Find the length of the unknown side.
Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometry
calculate the area of compound shapes
Find the area of this shape. Foundation Unit 8: Perimeter, area and volume
use and draw conversion graphs for common units
5 miles ≈ 8 kilometresDraw axes with scales from 0 to 80 km on the horizontal axis and 0 to 50 miles on the vertical axis. Plot a line to show the relationship between miles and kilometres.
Estimate 20 km in miles.Estimate 40 m in kilometres.
Foundation Unit 9a: Real-life graphs
use function machines Find y when x = 3. Foundation Unit 1a: Integers and Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 2016
×2 +511
Foundation tier
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
and inverse operations x → → = y
Find x when y = 11.x → → = y
place value
Foundation Unit 5a: Equations and inequalities
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
×3 –4
12
1.7 cm
Foundation tier
UNIT 7: Perimeter, area and volume, plane shapes and prisms, circles, cylinders, spheres, cones; Accuracy and bounds
Return to OverviewSUB-UNITS
a Perimeter, area and circlesb 3D forms and volume, cylinders, cones and spheresc Accuracy and bounds
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
name and identify the properties of 3D forms
Sketch a cuboid, a cylinder and a square-based pyramid.
How many faces does each shape have? How many vertices? How many edges?
Foundation Unit 15a: Plans and elevations
find perimeter and area by measuring lengths of sides
Measure the sides of this rectangle. Find its perimeter and area.
Foundation Unit 8: Perimeter, area and volume
substitute numbers into an equation and give answers to an appropriate degree of accuracy
Use the formula A = πr2 to find the area of this circle. Give your answer to an appropriate degree of accuracy.
Foundation Unit 5a: Equations and inequalities
Foundation Unit 1b: Decimals
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201613
Foundation tier
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
understand the various metric units
Match each item to the most appropriate unit you could use to measure it.
mm capacity of an egg cupcm capacity of a bathm length of a pencil km diameter of a coin g mass of a horsekg journey from London
to Edinburghml mass of a mousel length of a room
Foundation Unit 8: Perimeter, area and volume
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 8: Transformations; Constructions: triangles, nets, plan and elevation, loci, scale drawings and bearings
Return to OverviewSUB-UNITS
a Transformationsb Constructions, loci and bearings
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
recognise 2D shapes Make different shapes using two congruent right-angled triangles by matching equal sides, and name the shapes produced. (There are six: rectangle, kite, two parallelograms, two isosceles triangles.)
Foundation Unit 6: Angles, polygons and parallel lines
plot coordinates in four quadrants
See questions for Unit 6. Foundation Unit 9a: Real-life graphs
plot linear equations parallel to the coordinate axes
On cm-squared paper, draw axes for x and y from 0 to 8. Plot the lines x = 4 andy = –2.
Foundation Unit 9b: Straight-line graphs
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201615
Foundation tier
UNIT 9: Algebra: Solving quadratic equations and inequalities, solving simultaneous equations algebraically
Return to OverviewSUB-UNITS
a Solving quadratic and simultaneous equationsb Inequalities
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
understand the ≥ and ≤ symbols
List the positive integers that satisfy the inequality 10 > x ≥ 6.
List the integers that satisfy the inequality 10 < y ≤ 14.
Foundation Unit 1a: Integers and place value
substitute into, solve and rearrange linear equations
What is the value of h in this formula, if C = 10?C = 5h + 20
Foundation Unit 2b: Expressions and substitution into formulae
factorise simple quadratic expressions
Factorise x2 – x – 6, Foundation Unit 16a: Quadratic equations: expanding and factorising
recognise the equation of a circle
Which of these equations is the equation of a circle?y = x2 + 16x2 + y2 = 52
x + y = 25
Higher Unit 6c: Quadratic, cubic and other graphs
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 10: Probability
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
distinguish between events which are impossible, unlikely, even chance, likely, and certain to occur
Match to events to how likely they are to occur.
1 Christmas will fall on 25 December this year.
2 The sun will rise at midnight tonight.
3 You will score an even number if you roll an ordinary, fair dice.
4 The next person you meet likes chocolate.
5 If you buy a lottery ticket, you will win the jackpot.
A Impossible B UnlikelyC Even chance D LikelyE Certain
Foundation Unit 13: Probability
understand that a probability is a number between 0 and 1 and mark events and/or probabilities on a probability scale of 0 to 1
A bag contains 20 marbles. Tessa picks a marble at random.
Mark these probabilities on the number line.
P(blue) = P(red) =
P(green) = P(pink) = P(black) = 0 P(marble) = 1
0 1
Foundation Unit 13: Probability
add and multiply fractions and decimals
+ = × =
0.35 + 1.7 = 0.2 × 0.6 =
Foundation Unit 4a: Fractions, decimals and percentages
express one number as a fraction of another number
What is 15 as a fraction of 25?
Foundation Unit 4a: Fractions, decimals and percentages
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201617
Foundation tier
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 11: Multiplicative reasoning: direct and inverse proportion, relating to graph form for direct, compound measures, repeated proportional change
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
find a percentage of an amount and relate percentages to decimals
What is 45% of 300?
What is the decimal equivalent of 6%?
Foundation Unit 4b: Fractions and percentages
rearrange equations and use these to solve problems
A square has sides of d + 3. A rectangle has sides of 3d + 1 and d – 3. They have the same length perimeter. Find d.
Foundation Unit 5a: Equations and inequalities
understand speed = distance/time, density = mass/volume
A car travels 70 miles in 2 hours. What is its average speed?
Cobalt has a density of 8.9 gm/cm3. What is the mass of a cm cube of cobalt?
Foundation Unit 14: Multiplicative reasoning
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201619
6 cm40° 35°
x ya
Foundation tier
UNIT 12: Similarity and congruence in 2D and 3D
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
recognise and enlarge shapes and calculate scale factors
Enlarge this triangle by a scale factor of 2.
Shape B is an enlargement of shape A. What is the scale factor?
B
A
Foundation Unit 10: Transformations
calculate area and volume in various metric measures
What is the area of a rectangle that measures 4.5
m by 6 m?
What is the volume of a cuboid that measures 2 mm by 5 mm by 7 mm?
Foundation Unit 8: Perimeter, area and volume
measure lines and angles and use compasses, ruler and protractor to construct standard constructions
Use compasses and a ruler to construct this triangle accurately.
Measure the length of sides x and y and the size of angle a.
Foundation Unit 3b: Pie charts
Foundation Unit 6a: Properties of shapes, parallel lines and angle facts
Foundation Unit 8: Perimeter, area and volume
Foundation Unit 15b: Constructions, loci and bearings
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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a cm32°
11 cm
Foundation tier
UNIT 13: Sine and cosine rules, ab sin C, trigonometry and Pythagoras’ Theorem in 3D, trigonometric graphs, and accuracy and bounds
Return to OverviewSUB-UNITS
a Graphs of trigonometric functionsb Further trigonometry
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
use axes and coordinates to specify points in all four quadrants
See questions for Unit 6. Foundation Unit 9a: Real-life graphs
recall and apply Pythagoras’ Theorem and trigonometric ratios
See questions for Unit 6.
Use the cosine rule to find the value of a.
Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometry
substitute into formulae See questions for Unit 9. Foundation Unit 5a: Equations and inequalities
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201621
Foundation tier
UNIT 14: Statistics and sampling, cumulative frequency and histograms
Return to OverviewSUB-UNITS
a Collecting datab Cumulative frequency, box plots and histograms
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
understand the different types of data: discrete/continuous
Sort the following data into two groups: discrete and continuous.
A Heights of 10 studentsB Number of pets owned by
30 studentsC Favourite colours of 15
studentsD Mass of 20 apples
Foundation Unit 3a: Tables, charts and graphs
use inequality notation See questions for Unit 3. Foundation Unit 1a: Integers and place value
multiply a fraction by a number
What is of 48?
Foundation Unit 4a: Fractions, decimals and percentages
understand the data handling cycle
Put these four steps in the correct order.
A Analyse the data.B Draw conclusions.C Collect data.D Specify the problem and
plan an investigation.
Foundation Unit 7: Statistics, sampling and the averages
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 15: Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
solve quadratics and linear equations
Solve these equations.3(x – 6) = 6x2 – 3x – 28 = 0
Foundation Unit 5a: Equations and inequalities
Foundation Unit 16: Algebra: quadratic equations and graphs
solve simultaneous equations algebraically
Solve these simultaneous equations:3x – y = 232x + y = 7
Foundation Unit 20: Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201623
Foundation tier
UNIT 16: Circle theorems and circle geometry
Return to OverviewSUB-UNITS
a Circle theorems b Circle geometry
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
draw circles with compasses
See questions for Unit 3. Foundation Unit 15a: Plans and elevations
recall the words, centre, radius, diameter and circumference
Use the following words to fill in the gaps.
centre circumference diameter radius
The ___ of a circle is a straight line from the ___ to the ___. It is half the length of the ___.
Foundation Unit 17: Circles, cylinders, cones and spheres
recall the relationship of the gradient between two perpendicular lines
Line A has gradient 2.Line B is perpendicular to Line A.Write down the gradient of Line B.
Higher Unit 6b: Linear graphs and coordinate geometry
find the equation of the straight line, given a gradient and a coordinate
Find the equation of the line with gradient 3 that passes through the point (2, 4).
Foundation Unit 20: Rearranging equations, graphs of cubic and reciprocal functions and simultaneous equations
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 17: Changing the subject of formulae (more complex), algebraic fractions, solving equations arising from algebraic fractions, rationalising surds, proof
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
simplify surds Simplify .
Higher Unit 1c: Factors, multiples, primes, standard form and surds
use negative numbers with all four operations
See questions for Unit 2. Foundation Unit 1a: Integers and place value
recall and use the hierarchy of operations
See questions for Unit 2. Foundation Unit 1a: Integers and place value
Foundation Unit 1c: Indices, powers and roots
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201625
Foundation tier
UNIT 18: Vectors and geometric proof
Return to OverviewPRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
use vectors to describe translations
Write as a column vector the transformation that maps shape A onto shape B.
Foundation Unit 10: Transformations
use Pythagoras’ Theorem See questions for Unit 6. Foundation Unit 12: Right-angled triangles: Pythagoras and trigonometry
identify properties of triangles and quadrilaterals
See questions for Unit 8. Foundation Unit 6a: Properties of shapes, parallel lines and angle facts
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 20156
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Foundation tier
UNIT 19: Direct and indirect proportion: using statements of proportionality, reciprocal and exponential graphs, rates of change in graphs, functions, transformations of graphs
Return to OverviewSUB-UNITS
a Reciprocal and exponential graphs; Gradient and area under graphsb Direct and inverse proportion
PRIOR KNOWLEDGE
Students will be able to: Possible diagnostic questions
Students will need to work on the objectives covered in:
draw linear and quadratic graphs
Sketch the following graphs.y = 2x – 3y = x2
Foundation Unit 9: Real-life and algebraic linear graphs
Foundation Unit 16b: Quadratic equations: graphs
calculate the gradient of a linear function between two points
A line passes through the points (1, 2) and (7, 5).Find the gradient of the line.
Foundation Unit 9a: Real-life graphs
recall transformations of trigonometric functions
Sketch the graph of y = sin x.On the same axes, sketch the graph of y = 2 sin x.
Higher Unit 13a: Graphs of trigonometric functions
write statements of direct proportion and form an equation to find values
a is directly proportional to b.a = 18 when b = 1.5.Form an equation involving a and b and solve it to find the value of a when b = 7.
Foundation Unit 11b: Proportion
Pearson Edexcel Level 1/Level 2 GCSE (9 – 1) in Mathematics Higher tier diagnostic document – Issue 1 April 2016 © Pearson Education Limited 201627
Issue 1 – April 2016
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