Higher Supported Study

Slides:

Advertisements

Similar presentations

Higher Outcome 1 Higher Unit 1 Distance Formula The Midpoint Formula Gradients Collinearity Gradients of Perpendicular.

Advertisements

Let Maths take you Further…

Digital Lesson on Graphs of Equations. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The graph of an equation in two variables.

Notes Over 10.3 r is the radius radius is 4 units

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

10 Trigonometry (1) Contents 10.1 Basic Terminology of Trigonometry

Higher Maths Strategies Click to start The Wave Function.

Revision Logarithms & Exponentials Higher Mathematics Next.

Straight Line Higher Maths. The Straight Line Straight line 1 – basic examples Straight line 2 – more basic examplesStraight line 4 – more on medians,

The Straight Line All straight lines have an equation of the form m = gradienty axis intercept C C + ve gradient - ve gradient.

Higher Outcome 1 Higher Unit 1 Distance Formula The Midpoint Formula Gradients Collinearity Gradients of Perpendicular.

Click to Start Higher Maths Unit 3 Chapter 3 Logarithms Experiment & Theory.

APP NEW Higher Distance Formula The Midpoint Formula Prior Knowledge Collinearity Gradients of Perpendicular.

Higher Maths Question Types. Functions & Graphs TYPE questions (Trig, Quadratics) Sketching Graphs Composite Functions Steps : 1.Outside function stays.

Quadratic Theory Introduction This algebraic expression: x 2 + 2x + 1 is a polynomial of degree 2 Expressions like this in which the highest power of x.

Term 3 : Unit 2 Coordinate Geometry

Circles, Tangents and Chords

Circles Notes. 1 st Day A circle is the set of all points P in a plane that are the same distance from a given point. The given distance is the radius.

EXAMPLE 1 Write an equation of a line from a graph

Straight Lines Objectives: B GradeExplore the gradients of parallel straight line graphs A GradeExplore the gradients of perpendicular straight line graphs.

Session 1 Paper 2 Questions and Answers Calculator Harris Academy Supported Study.

1Higher Maths Quadratic Functions. Any function containing an term is called a Quadratic Function. The Graph of a Quadratic Function 2Higher Maths.

Higher Unit 1 Distance Formula The Midpoint Formula Gradients

Distance and Midpoint Graphing, Symmetry, Circles Solving.

coordinates, lines and increment

Higher Maths Strategies Click to start The Circle.

2.2: Do Now: Determine if the following point is on the graph. 1.) 2.)

Scholar Higher Mathematics Revision Session Thursday 18 th May 7:30pm You will need a pencil, paper and a calculator for some of the activities.

Application of Derivative - 1 Meeting 7. Tangent Line We say that a line is tangent to a curve when the line touches or intersects the curve at exactly.

Mathematics. Session Three Dimensional Geometry–1(Straight Line)

Session 1 Paper 1 Questions and Answers Non Calculator Harris Academy Supported Study.

Straight Line Applications 1.1

Finding a Quadratic Equation from Three Coordinates.

Section 3.2 Connections to Algebra.  In algebra, you learned a system of two linear equations in x and y can have exactly one solution, no solutions,

Higher Outcome 1 Higher Unit 1 Distance Formula The Midpoint Formula Gradients Collinearity Gradients of Perpendicular Lines The Equation of a Straight.

Next Quit Find the equation of the line which passes through the point (-1, 3) and is perpendicular to the line with equation Find gradient of given line:

DMO’L.St Thomas More C3: Starters Revise formulae and develop problem solving skills

Higher Maths 2 4 Circles1. Distance Between Two Points 2Higher Maths 2 4 Circles The Distance Formula d =d = ( y2 – y1)²( y2 – y1)² + ( x2 – x1)²( x2.

Summary of Chapter 2 (so far). Parallel lines  y = mx + c y = mx + d Perpendicular lines  y = mx + cy = nx + dm x n = -1 Length of a line using Pythagoras’

Calculus Continued Tangents and Normals Example Find the equations of the tangent and normal to the graph of at the point where.

Digital Lesson Graphs of Equations.

The equation of a circle

Drawing a sketch is always worth the time and effort involved

Using The Discriminant

Lesson 5 Equation of a Line.

DIFFERENTIATION APPLICATIONS 1

Notes Over 10.3 r is the radius radius is 4 units

Co-ordinate Geometry for Edexcel C2

BHASVIC MαTHS Skills 1 A1 DOUBLES ASSIGNMENT 14B

Question 1 A curve has equation (a) Express in the form where k > 0

Differentiate the function. {image}

The gradient of a tangent to a curve

Higher Supported Study

Coordinate Geometry in the (x,y) plane.

BHASVIC MαTHS Skills 1 A1 DOUBLES ASSIGNMENT 13B

r > 0 Does circles touch externally or internally ? radius = (a,b)

Tuesday, December 04, 2018 Geometry Revision!.

The Circle x2+y2+2gx+2fy+c = 0 (x-a)2 + (y-b)2 = r2 x2 + y2 = r2

Higher Supported Study

TEST 1-4 REVIEW 381 Algebra.

Writing the Equation of a Line

Completing the square Tuesday, 23 April 2019.

TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST

Higher Maths The Circle Strategies Click to start

Higher Maths The Straight Line Strategies Click to start

Higher Maths The Wave Function Strategies Click to start

TEST 1-4 REVIEW 381 Algebra.

Parallel and Perpendicular Lines

Digital Lesson Graphs of Equations.

BHASVIC MαTHS 1 A1 DOUBLES AssIGNMENT 2A

Presentation transcript:

Higher Supported Study May 2015 Session 2 Paper 1

Question 1 Solve the equation for rearrange to = 0 factorise solve equations 23 April 2017

Question 2 D, E and F have coordinates (10,- 8, -15), (1,-2,-3) and (-2,0,1) respectively. (a) (i) Show that D, E and F are collinear. (ii) Find the ratio in which E divides DF (b) G has coordinates (k,1,0). Given that DE is perpendicular to GE, find the value of k.    so EF and DE are parallel E is a common point so D, E and F are collinear   23 April 2017

Question 3 The diagram shows a sketch of the function y = f (x) Copy the diagram and on it sketch the graph of y = f (2x) (b) On a separate diagram sketch the graph of y = 1 - f (2x). 23 April 2017

Question 4 Two variables, x and y, are connected by the law log 4 y The graph of log 4 y against x is a straight line passing through the origin and the point A(6,3). Find the value of a A(6,3) O x 23 April 2017

Question 5a The diagram shows a sketch of and the tangent to the curve at x = 2 Show that the equation of the tangent to the curve at x = 2 is y = 5x - 8

Question 5a Find algebraically the coordinates of the point where this tangent meets the curve again 2 1 -2 -4 8 - 8

Question 6a Angle x is acute and is such that (a) Show clearly that the exact value of is

Question 6b (b) Hence show that

Question 7 Two identical circles touch at the point P(9,3) as shown in the diagram. One of the circles has equation Find the equation of the other circle. x y O P (9, 3) 23 April 2017

Question 8 Solve the equation 23 April 2017

Question 9 y x y x (–4, 0) (12, 0)

Question 10 -1 1 -13 -12 12 remainder = 0 so x + 1 is a factor

Question 11

Question 12

Question 13

Question 14 Sketch the graph of