# HYC Stage 8

**Stage 8 Unit 1 – Numbers and the number system - Hegarty Maths**

Recall prime numbers up to 100. 28

Understand the meaning of prime factor. 29

Write a number as a product of prime factors. 30

Use a Venn diagram to sort information. 379

Use prime factorisations to find HCF and LCM. 32, 35

Identify any significant figure in a number. 130

Write and interpret large and small numbers in standard form. 122, 123

**Stage 8 Unit 2 - Calculating**

Add/subtract and Multiply/Divide Fractions 41

Improper and mixed fractions 63, 64

Add/subtract improper Fractions 65, 66

Multiply/Divide improper fractions 68, 70

Add/subtract/multiply/divide mixed fractions 155, 278

Using BIDMAS with powers (indices) 24, 120

**Stage 8 Unit 3 – Visualising and Construction**

Measuring and drawing lines and angles 458, 461

Explore enlargement of 2D shapes. Vocabulary. Finding and using scale factors 609, 642, 644

Use and identify a centre of enlargement 643

Interpret plans and elevations

Scale drawings, scale factors and maps 679

**Stage 8 Unit 4 – Understanding risk**

Work out probabilities using words 349

Working out probabilities – the probability scale 350

Understand theoretical probability 351, 352

Compare with experimental probability 356

Work out probabilities for all outcomes (two-way tables) 359, 423

Construct simple probability trees 361

**Stage 8 Unit 5 – Algebraic Proficiency**

Create algebraic expressions with products and fractions 151, 153, 155

Simplify an expression with complex terms 156

Understand formulae and substitution. Common scientific formulae 155

Expand and simplify and expression 160, 161

Factorise an expression Single brackets 168, 169

Changing the subject of a formula 280

**Stage 8 Unit 6 – Exploring fractions, decimals and percentages**

Investigate the relationship between fraction, decimals and percentages terminating and recurring fractions 149

Simplify fractions by cancelling common factors 61

Equivalent Fractions. Scaling by 10ths and 100ths 59

Use a calculator to convert between decimals, fractions and percentages. 74, 75

**Stage 8 Unit 7 – Proportional reasoning**

Write a ratio to describe a real life situation 329

Finding proportion. Using proportion in real life 739

Solving problems using ratio and proportion. Real life problems and exam questions 332

Use fractions in situations involving ratio and proportion 330

Solve problems involving speed, distance and time 716, 719

**Stage 8 Unit 8 – Pattern Sniffing**

Generate a sequence using a term-to-term rule 197

Find terms of a sequence from a position to term rule 198

Deduce the nth term rule of a linear sequence 198

Find a given number in a sequence using the nth term 198

Generate sequences using a spread sheet 198

**Stage 8 Unit 9 – Investigating angles**

Identify alternate and corresponding angles and know their properties. 480 - 483

Use alternate and corresponding angles to solve problems. 481, 483

Establish the angle sum of a triangle. 484

Use the triangle angle sum to calculate the interior angle sum of any polygon. 561

Establish the size of an interior angle in a regular polygon. 562

Know the total of the exterior angles in any polygon. 563

Establish the size of an exterior angle in a regular polygon. 564

**Stage 8 Unit 10 – Calculating fractions, decimals and percentages**

Recognise when a fraction or percentage should be interpreted as a number or an operator. 66, 68, 70, 91

Identify the multiplier for a percentage increase or decrease when the percentage is greater than 100%. 89

Use a calculator to increase an amount by greater than 100%. 90

Solve problems involving percentage change. 97

Solve original value problems when working with percentages. 96

Solve financial problems involving simple interest. 93

Understand the meaning of giving an exact solution.

**Stage 8 Unit 11 – Solving equations and inequalities**

Solve equations with positive and negative solutions. 179

Solve equations with unknowns on both sides. 184

Solve equations with unknowns on both sides when the solution is negative or fractional. 184

Solve equations with unknowns on both sides and brackets. 185

Recognise that the point of intersection on a graph corresponds to the solution. 217

**Stage 8 Unit 12 – Calculating Space**

Know the vocabulary of circles and recall π to 2dp. 592

Know and use the formula for circumference of a circle. 534, 535

Calculate the perimeter of composite shapes that include sections of a circle. 563, 537

Know and use the formula for area of a circle. 539

Calculate the area of composite shapes that include sections of a circle. 541

Calculate the volume of a cylinder. 572

**Stage 8 Unit 13 – Algebraic proficiency: visualising**

Know how graphs of functions of the form y=mx+c will look. 207

Identify the gradient and y-intercept of a straight line. 204, 208

Sketch a linear graph from the intercept and gradient. 206

Know the general shape of quadratic graphs (containing x2). 251

Sketch and plot graphs of the form y=x2+c. 251

Plot and interpret distance-time graphs and use them to solve kinematic problems. 711, 716

**Stage 8 Unit 14 – Understanding risk 2**

Use Venn diagrams to list all elements in a combination of sets. 379

List the outcomes of an event systematically, including using a sample space diagram. 358, 359

Use theoretical or experimental probability to calculate expected outcomes. 355 Use frequency trees to record outcomes of probability experiments. 368, 369 Calculate probabilities using a possibility space. 358, 359

**Stage 8 Unit 15 – Presentation of data**

Know the meaning of continuous data. 393

Construct and interpret grouped frequency tables for continuous data. 418

Construct and interpret histograms for grouped data with equal class intervals. 445, 446

Plot a scatter graph. 453

Identify and interpret correlation in a scatter graph. 453, 454

**Stage 8 Unit 16 – Measuring data**

Find the modal class for a set of grouped data. 415

Find the class containing the median for a set of grouped data. 416

Calculate the estimated mean from a grouped frequency table. 418

Analyse and compare sets of data. 415 - 418

Appreciate the limitations of different statistics (mean, median mode and range). 413

Justify choice of statistics to describe a set of data. 413