# HYC Stage 9

**Stage 9-Unit 1 Calculating - Hegarty maths**

Interpret numbers in standard form. Convert a “near miss” into standard form. 122, 123

Multiply/divide numbers written in standard form. Also using a calculator. 125, 126, 128

Add/subtract numbers in standard form. Also using a calculator. 127, 128

Rounding with d.p. and significant figures. Accuracy of measurement. 56, 130

Estimation. Using inequality notation. 131

Minimum and maximum values of an amount that has been rounded. 137

**Stage 9 Unit 2 – Visualising and Constructing**

Construct perpendicular lines and perpendicular bisectors. 660

Perpendicular from point to a line. 662

Perpendicular from a point on a line. 663

Construct angle bisectors. Construct angles of 30, 45, 60, 90 degrees 661, 664, 665

Draw parallel lines, circles and arcs given a radius and construct a regular hexagon inside a circle. 659, 667, 668

Using loci to define a region. Distance from a point, a line, equal distance from 2 points, 2 line segments. Regions defined “nearer to”/ “greater than”. Relate to construction techniques. 674 - 679

Interpreting and constructing plans and elevations. Use in planning and representing 3D shapes.

**Stage 9 Unit 3 - Algebraic Proficiency**

Multiply two linear expressions of the form (x+a)(x+b). 162

Multiply two linear expressions of the form (x±a)(x±b). 163

Square a bracket. 162, 163

Factorise into a single bracket. 168, 169

Factorise into a double bracket. 223

Identifying an equation, expression, formula and identity. 154

Create a mathematical argument to show to expressions are equal.

Form expressions and formula to describe a situation. 155, 325

**Stage 9 Unit 4 – Proportional reasoning**

Explain the difference between direct and inverse proportion. 339, 342

Represent direct or inverse proportion graphically. 348

Represent direct or inverse proportion algebraically. 344, 345

Identify congruent or similar shapes. 608, 680

Solve problems in similar shapes. 312

Solve problems involving compound units. 716, 718, 719, 725, 729

**Stage 9 Unit 5 – Pattern Sniffing**

Investigate the Fibonacci sequence and other sequences. 263

Substitute numbers into formula including terms in x squared. 155, 189

Generate terms in a quadratic sequence. 249

Find the nth term rule of a quadratic sequence. 248, 249

**Stage 9 Unit 6 – Solving equations and inequalities**

Understand inequalities. 14, 265

Represent inequalities on a number line. 265

List a range of values that solve an inequality. 267

Solving equations with all unknowns on one side. 177, 179, 180

Solve equations with unknowns on both sides. 184

Solve inequalities. 269 - 272

**Stage 9 Unit 7 – Calculating Space**

Know the vocabulary of circles. 592

Calculate area and circumference of circles. 534, 539

Investigate arcs. 544 Investigate sectors. 546, 547

Calculate the volume and surface area of 3D shapes, including cylinders. 570, 572, 586

Recall and use Pythagoras’ Theorem. 497 - 499

Apply Pythagoras’ Theorem to solve problems. 502

**Stage 9 Unit 8 - Conjecturing**

Know the criteria for triangles to be congruent. 682

Identify congruent triangles. 682

Use known facts to form conjectures about lines and angles in geometrical situations. 684

Use known facts to create simple proofs. 325, 484

Explain why the base angles in an isosceles triangle must be equal. 685

**Stage 9 Unit 9 – Algebraic Proficiency- Visualising**

Investigate the equation of a straight line y=mx+c. 207, 208

What is the same in parallel lines? 207, 208 Rearrange equations into the form y=mx+c 210

Find the equation of a line through a given point (s). 213

Explore graphs of quadratic form. 251

Sketch graphs of a quadratic, cubic and reciprocal functions. 257, 299, 300

Plot and interpret graphs in real life contexts. 712, 713

Plot and interpret graphs to find solutions of kinematic problems involving distance, speed and acceleration. 716

**Stage 9 Unit 10 – Solving Equation and Inequalities 2 **

Understand why simultaneous equations are required to solve ax+by=c.

Use graphs to estimate the solutions of simultaneous equations. 218

Solve simultaneous equations using elimination. 190 - 192

Balance coefficients to target a variable to eliminate. 193

Form simultaneous equations to model situations. 195

**Stage 9 Unit 11 – Understanding Risk **

List outcomes of combined event using a tree diagram. 361

Label a tree diagram with probabilities, including when events are dependent. 361 - 363

Use a tree diagram to calculate the probabilities of independent combined events. 361 - 363

Use a tree diagram to calculate the probabilities of dependent combined events. 361 - 363

Know when to add or multiply probabilities. 360

Understand that relative frequency tends towards theoretical probability as sample size increases. 355, 356

**Stage 9 Unit 12 – Presentation of Data**

Construct and interpret graphs of time series. 450 - 452

Construct and interpret compound bar charts. 425

Draw accurate scatter graphs. 453

Describe correlation and draw a line of best fit. 453

Uses a line of best fit to estimate values. 454

Know when it is appropriate to use a line of best fit to estimate values. 454