Foundation Tier GCSE: Unit 1

Foundation Tier GCSE: Unit 1

Topic Skill Corbett Maths

worksheet and video number

Exam style questions

Solutions

N1 Number System

I can understand digits and place value 222 Factors, Multiples and Primes

Product of Prime Factors, HCF & LCM

Multiples in context

Factors, Multiples and Primes

Product of Prime Factors, HCF & LCM

Multiples in context

I can read, write and order positive and negative integers

221

I can interpret a number line I can add and subtract integers without a calculator

6 304

I can multiply integers without a calculator 199 I can divide integers without a calculator 98 I can add and subtract negative numbers 205 I can multiply negative numbers 206 I can divide negative numbers 207 I can recognise factors, multiples and primes 216 I can recognise multiples 220 I can recognise primes 225 I can write a number as a product of its prime factors

223

I can find the HCF 219 I can find the LCM 218 I can understand and find square numbers and their roots

227 228

I can understand and find cube numbers and their roots

212 214

A1 Expressions

I use the order of operations 211 BIDMAS, Powers and Roots

Simplifying and Expanding

BIDMAS, Powers and Roots

Simplify and Expanding

I can collect like terms 9 I can simplify expressions by multiplying terms 18 I can simplify expressions by dividing terms 11 I can expand single brackets 13 I can factorise an expression by using a single bracket

117

I can insert brackets to make a true statement 211 I know the difference between terms, expressions, equations and formulae I can substitute values into an expression 20 I can use the rules of indices to simplify an expression

17

I can simplify expressions involving the law of indices including negative and zero powers

174 175

I can form an algebraic term or expression from words

16





Solutions

N2 Decimals

and Rounding

I can write decimal numbers in size order 95 Number Problems

Rounding and Bounds

Standard Form

Number Problems

Rounding and Bounds

Standard Form

I can understand and use the inequality sign 176 I can add and subtract decimals 90 & 91 I can multiply decimals 94 I can divide decimals 92 & 93 I can round to nearest 10, 100, 1000 277a & 277b I can round to a given number of decimal places 278 I can round to a given number of significant figures 279a

I can estimate the answer to a calculation using significant figures 215

I can use known facts to derive unknown facts. 222a I can apply and interpret limits of accuracy 183 & 184 I can use inequality notation to express error intervals due to truncation or rounding 377

I can convert between ordinary numbers and standard form 300

I can calculate numbers in standard form 301, 302 & 303

G1 Measures

I can read and estimate dials and scales 284 Reading Scales

Timetables Q1-Q8

Reading Scales

Timetables Q1-Q8

I can convert between 12 hour and 24-hour clock

I can work out durations of time 322

I can solve problems involving time and timetables

320 & 322

I can choose an appropriate unit of measure 347

I can convert between metric units of length, mass and capacity

349a, 349b & 349c

N3 Fractions

I can understand fractions, including diagrams 143 Fractions

FDP

Fractions

FDP

I can find equivalent fractions 135 I can find fractions of an amount 137 I can order fractions, percentages and decimals 131 I can convert between improper fractions and mixed numbers

139 & 140

I can multiply fractions 142 I can divide fractions 134 I can add and subtract fractions 132 & 133 I can convert between fractions, decimals and percentages

130





Solutions

N4 Using a

Calculator

I can recognise terminating and recurring decimals Use of a

Calculator

Use of a Calculator

I can find reciprocals 145 I can interpret a calculator display

352 I can work out powers and roots using a calculator I can use a calculator to work out complex calculations (including standard form)

R1 Percentages

I can convert between fractions, decimals and percentages (review from fractions unit)

121 - 128

Percentages

FDP

Reverse Percentages

Percentages

FDP

Reverse Percentages

I can find a percentage of an amount, including percentages greater than 100% 234

I can express a quantity as a percentage of another 237

I can increase and decrease amounts by a percentage without a calculator 238

I can increase and decrease amounts using a multiplier 239

I can calculate reverse percentages 240 I can calculate a percentage change 233 I can calculate simple interest I can calculate compound interest 236 I can solve real life problems involving percentages and fractions (e.g which deal is better, investments)

I can solve problems involving repeat percentage change 236

I can solve problems involving percentage change where no values are given 233

S1 Averages

and Range

I can find the mode, median and mean of a set of data 56, 50, 53 Averages

Averages

I can discuss the advantages and disadvantages of different averages

I can calculate the range of a set of data 57 I can compare data sets using the averages and range

I can draw a stem and leaf diagram 169 I can use stem and leaf to find the mode and median of a set of data 170

I can calculate averages from an ungrouped frequency table 51, 54

I can calculate modal class and median from a grouped frequency table 52

I can estimate the mean from a grouped frequency table 55





Solutions

G2 2D Shapes

I can identify types of different triangles 327 Area of Compound Shapes Intro Area and Perimeter Circles Intro

Circles 2

Area of Compound Shapes Intro Area and Perimeter

Circles Intro

Circles 2

I know the properties of quadrilaterals 2 I can draw and identify line of symmetry on 2D shapes

316

I can identify the order of symmetry of a 2D shape 317 I can identify congruent and similar shapes 66 & 291 I can find the perimeter of simple shapes 242 I can find the perimeter of compound shapes 241 I can find the area by counting squares 43 I can find the area of a rectangle 45 I can find the area of a triangle 49 I can find the area of a parallelogram 44 I can find the area of a trapezium 48 I can find the area of compound shapes 41 & 42 I can identify and name part of a circle 61 I can draw a circle and arc with a given radius and angle

I can find the circumference of a circle 60 I can find the area of a circle 59 I can find the area and perimeter of half and quarter circles

62

I can find the area of a sector of a circle 63

I can find the arc length of a circle 58

R2 Ratio and

Proportion 1

I can simplify a ratio 269 Ratio

Ratio 2 Proportion

Ratio

Ratio 2 Proportion

I can write a ratio as a fraction and vice versa 269a

I can scale ratios to find unknown quantities 270

I can divide in a given ratio either given the whole amount, given the value of one part of the ratio or given the value of the difference

271, 271a & 271b

I can express a multiplicative relationship between two quantities as a ratio or a fraction. 271c

I can use the unitary method to solve direct proportion and best buy problems 255a

I can solve calculations involving exchange rates 214a





Solutions

A2 Equations

I can solve a one step linear equation

110

Solving Equations

Forming & Solving Equations

Solving Equations

Forming & Solving Equations

I can solve a two step linear equation

I can solve a linear equation with brackets

I can solve linear equations that have unknowns on both sides

113 I can solve linear equations with negative coefficients

I can set up and solve linear equations from words or practical situations 114, 115

A3 Formulae

I can substitute values into expressions including brackets and powers

20

Substitution, solving & rearranging equations

Substitution, solving & rearranging equations

I can substitute into algebraic formulae

I can change the subject of a formula 7

G3 Angles 1

I can estimate the size of an angle 29 Basic Angles

Angles

Angles in Parallel Lines

Basic Angles

Angles

Angles in Parallel Lines

I can use a protractor to accurately measure angles 31

I can use a protractor to accurately draw angles 28

I can find missing angles of special triangles 37 In can find missing angles using angle facts up to

180 degrees I can find missing angles of a straight line, around a point and vertically opposite 39

I can find missing angles in a quadrilateral 33

I can identify parallel and perpendicular lines 232, 233

I can identify corresponding angles

25 I can identify alternate angles




Exam-style Questions

Solutions

S2 Data and

Graphs

I can classify data as being qualitative or quantitative

342

Bar Charts

Pie Charts

Two Way Tables

Bar Charts

Pie Charts

Two Way Tables

I can classify quantitative data as being discrete or continuous

343

I can design and use a data collection sheet 268 I can understand and use a tally 321 I can group data into class interval of equal width

I can complete two-way tables 319 I can interpret and extract data from tables I can interpret distance charts 318 I can interpret and complete a pictogram I can draw a pie chart 163 I can interpret a pie chart 164 I can read and interpret simple bar charts and line diagrams

147 & 148

I can read and interpret comparative and composite bar charts

I can represent grouped continuous data of equal class widths as a histogram

157

I can draw a frequency polygon 155 I can interpret simple trends from a frequency polygon

156

I can identify mistakes in graphs and tables

P1 Probability

I can place events on a probability scale 251 Probability & Relative Freq

Basic Probability

Harder Probability

Probability & Relative Freq

Basic Probability

Harder Probability

I can use words to describe probabilities 245 I can use a number to represent a probability 245 I can work out the probability of something not happening

250

I can use the fact that sum of exhaustive probabilities is 1

I can list outcomes in a systematic way 253 I can draw a sample space diagram and use it to find probabilities

246

I can estimate the probability from an experiment

248

I can compare experimental and theoretical probabilities

I can find probabilities from a two way tables 319 I can design a two way table 319

I can use probabilities to predict results 248


Topic Skill Corbett Maths worksheet and video number

Problem solving and

exam questions

Solutions

G4 3D Shapes

I can recognise and name 3D shapes 3 2D Shapes &

3D Forms

Volume of Prisms etc.

Plans & Elevations

2D Shapes &

3D Forms

Volume of Prisms etc.

Plans & Elevations

I can count the vertices, faces and edges of 3D shapes

5

I can draw nets and recognise solids from their nets

4

I can draw and interpret plans and elevations

354

I can find the volume of shapes made from cuboids

355

I can find the volume of prisms 356 I can find the surface area of prisms 310 – 312 I can find the volume & surface area of a cylinder

357

I can use the volume of a prism to calculate unknown lengths

356

I can interpret functional problems involving volume and capacity

I can understand the effect of enlargement for perimeter, area and volume of 2D and 3D shapes

I can convert between area measures 350 I can convert between volume measures 351

I can convert between units of volume and capacity

351

A4 Sequences

I can continue a sequence using the term to term rule

286 – 287

Sequences

Sequences

I can use an input/output machine 386 I can recognise and use sequences of triangular, square and cube numbers

212, 226, 229,

I can recognise and generate Fibonacci-type sequences

287a

I can find terms in a linear sequence using position to term rule

286 – 287

I can use a position to term rule to reason whether specific numbers are part of the sequence

286 – 287

I can find the nth term of a linear sequence

288 – 289

I can find the nth term from a picture pattern

290

I can recognise and generate quadratic and simple geometric progressions

A5 Graphs 1

I can plot co-ordinates in the first quadrant

84, 85

Coordinates

Equation of a Straight Line

Coordinates

Equation of a Straight Line

I can plot co-ordinates in all four quadrants

84, 85

I can find the midpoint of a line segment 198 I can draw and name horizontal and vertical lines

192, 193

I can plot a straight-line graph from a table of values

186

I can plot a straight-line graph without a table of values

187, 188

I can interpret the line y = mx + c to find the gradient and y-intercept

189 – 191

I can give the equation of a straight line drawn on a co-ordinate grid

189 – 191

I can use the form y = mx + c to identify parallel lines

196

I can find the equation of a line from two given points or one point and a given gradient

194, 195




Problem solving and exam questions

Solutions

G5 Trigonometry

1

I can find the hypotenuse of a right-angled triangle

257 Pythagoras’

Theorem Pythagoras’

Theorem I can find the shorter side of a right-angled triangle

257

I can apply Pythagoras' theorem to check if a triangle is right angled or not

257

I can find the length of a line segment between two co-ordinates

258, 263

I can use Pythagoras' Theorem in context 257

R3 Rates of Change

I can draw and interpret conversion graphs 151, 152 Speed, Distance & Time

Compound Measures

Speed, Distance & Time

Compound Measures

I can interpret the gradient of a straight line as a rate of change (such as rates of pay and speed)

390a, 390b

I can write a ratio as a linear function and use ratios to draw linear graphs I can convert and order metric units of time, length, mass and capacity (recap from measures)

348 – 349

I can calculate speed, distance and time and solve problems involving multiple stages of a journey

299, 171

I can calculate compound units of density and pressure

384, 385

G6 Angles 2

I can recognise regular polygons 32

Angles in Polygons

Angles in Polygons

I can find the sum of the interior angles of a polygon

32

I can calculate the interior angle of a polygon

32

I can calculate the exterior angle of a polygon

32

I can calculate angles at the centre of a regular polygon

32

I can solve problems involving bearings 26 – 27 I can construct accurate scale drawings 283

P2 Tree

Diagrams

I can draw frequency trees and use them to calculate probabilities

376 Frequency Trees

Probability & Tree Diagrams

Frequency Trees

Probability & Tree Diagrams

I can draw frequency trees when the information is given as a combination of ratios, percentages and fractions

376

I can draw probability tree diagrams and use them to calculate probabilities of combined independent events (with replacement)

252

I can draw probability tree diagrams and use them to calculate probabilities of combined independent events (without replacement)

252




Just Maths problem solving

practice questions

Solutions

A6 Further Equations and

Inequalities

I can expand and simplify double brackets

14 Quadratics

Quadratics

I can factorise quadratic expressions

118

I can solve quadratics equations using factorisation

266

I can represent inequalities on a number line

177 Inequalities

Inequalities

I can solve inequalities

178, 179

I can solve simultaneous equations

295 Simultaneous Equations

Simultaneous Equations

G7

Transformations and Vectors

I can reflect and describe a reflection of a shape

272,273,274 Mixed Transformations

Rotations

Mixed Transformations

Rotations

I can translate and describe a translation of a shape

325, 326

I can rotate and describe a rotation of a shape

275

I can enlarge and describe an enlargement of a shape

104, 105, 106

I can enlarge and describe an enlargement of a shape using a fractional and negative scale factor

107, 108

I can perform and describe the combination of all four transformations

I can use vector notation 353a

Mathswatch clip 174

Vectors

Vectors

I can apply addition, subtraction and multiplication to column vectors

I can represent column vectors graphically

S3 Line Diagrams and Scatter Graphs

I can draw and estimate values from a line graph

Time Series

Time Series

I can draw and interpret line graphs for time series data

382

I can draw and describe the relationship in a scatter graph

165, 166 Scatter Diagrams

Scatter Diagrams

I can describe the correlation in a scatter graph I can draw a line of best fit on a scatter graph

167

I can use the line of best fit to make predictions I can identify when it is reliable to use a line of best fit on a scatter graph (extrapolation)

G8 Constructions, Loci and Similarity

I can construct an angle 68,69,70,71 Loci and constructions

Loci and constructions

I can construct an accurate drawing of a triangle and a quadrilateral

81,82,83

I can bisect an angle 72 I can bisect a line 78 I can construct a perpendicular line to a given line

79

I can construct a perpendicular line from a point on a given line

80

I can construct the locus of a point that moves according to a simple rule.

75

I can construct and shade regions that follow more than one rule

76, 77

I can use scale factors, scale diagrams and maps

283 Similarity

Similarity

I can find missing lengths in similar shapes

292




Problem solving practice

questions

Solutions

P3 Sets and Venn

Diagrams

I can work out probabilities from a basic Venn diagram 380

Venn diagrams

Venn Diagrams

I can define a set and list elements of a set, using proper notation and use a simple Venn diagram to show elements in a set

379

I can list the union and intersection of two or three sets using proper notation and represent them on a Venn diagram

380 Mathswatch

Clip 127b I can draw and use Venn diagrams of three sets to calculate probabilities

Mathswatch Clip 185

I can use a Venn diagram to calculate conditional probability

G9 Trigonometry

2

I can use SOHCAHTOA to find missing lengths of right angled triangles 330 Trigonometry

Trigonometry

I can use SOHCAHTOA to find missing angles of right angled triangles 331

I can recall the exact values of sin and cos 30°, 45°, 60°, and 90° 341

R4 Ratio and Proportion 2

I can solve problems involving direct proportion algebraically 254 Graphs

Reasoning

Graphs

Reasoning

I can solve simple inverse proportion problems

Link

I can solve problems involving inverse proportion algebraically 255

I can identify graphs that illustrate direct and inverse proportion

Mathswatch Clip 199

A7 Graphs 2 I can interpret and draw line graphs 160 Distance time

Distance time

I can draw and interpret graphs of water filling different shaped containers

Mathswatch Clip A21b

2:19 I can draw and interpret distance-time graphs 171

I can draw a quadratic graph from a table of values 264

Quadratic Graphs

Quadratic Graphs

I can draw a quadratic graph without a table of values 265

I can use the graph of a quadratic function to solve equations 267c

I can identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically.

Mathswatch clip 160

I can plot cubic and reciprocal graphs Mathswatch clip 161

Foundation Tier GCSE: Unit 1

Documents

Transcript of Foundation Tier GCSE: Unit 1