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Higher Maths Strategies www.maths4scotland.co.uk Click to start The Straight Line.

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Presentation on theme: "Higher Maths Strategies www.maths4scotland.co.uk Click to start The Straight Line."— Presentation transcript:

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2 Higher Maths Strategies Click to start The Straight Line

3 Maths4Scotland Higher The Straight Line The following questions are on Non-calculator questions will be indicated Click to continue You will need a pencil, paper, ruler and rubber.

4 Maths4Scotland Higher Hint PreviousNext 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: Find gradient of perpendicular: Find equation:

5 Maths4Scotland Higher Hint PreviousNext Quit Find the equation of the straight line which is parallel to the line with equation and which passes through the point (2, –1). Find gradient of given line: Gradient of parallel line is same: Find equation:

6 Maths4Scotland Higher Hint PreviousNext Quit Table of exact values Find gradient of the line: Use table of exact values Use Find the size of the angle a° that the line joining the points A(0, -1) and B(3  3, 2) makes with the positive direction of the x-axis.

7 Maths4Scotland Higher Hint PreviousNext Quit A and B are the points (–3, –1) and (5, 5). Find the equation of a)the line AB. b)the perpendicular bisector of AB Find gradient of the AB: Find mid-point of AB Find equation of AB Gradient of AB (perp): Use gradient and mid-point to obtain perpendicular bisector AB

8 Maths4Scotland Higher Hint PreviousNext Quit Table of exact values The line AB makes an angle of radians with the y-axis, as shown in the diagram. Find the exact value of the gradient of AB. Find angle between AB and x-axis: Use table of exact values Use (x and y axes are perpendicular)

9 Maths4Scotland Higher Hint PreviousNext Quit A triangle ABC has vertices A(4, 3), B(6, 1) and C(–2, –3) as shown in the diagram. Find the equation of AM, the median from A. Find mid-point of BC: Find equation of median AM Find gradient of median AM

10 Maths4Scotland Higher Hint PreviousNext Quit P(–4, 5), Q(–2, –2) and R(4, 1) are the vertices of triangle PQR as shown in the diagram. Find the equation of PS, the altitude from P. Find gradient of QR: Find equation of altitude PS Find gradient of PS (perpendicular to QR)

11 Maths4Scotland Higher Hint PreviousNext Quit The lines and make angles of a  and b  with the positive direction of the x-axis, as shown in the diagram. a)Find the values of a and b b)Hence find the acute angle between the two given lines. Find supplement of b Find gradient of Find a° Find b° Angle between two lines Use angle sum triangle = 180° 72°

12 Maths4Scotland Higher Hint PreviousNext Quit Triangle ABC has vertices A(–1, 6), B(–3, –2) and C(5, 2) Find: a) the equation of the line p, the median from C of triangle ABC. b) the equation of the line q, the perpendicular bisector of BC. c) the co-ordinates of the point of intersection of the lines p and q. Find mid-point of AB Find equation of p Find gradient of p (-2, 2) Find mid-point of BC (1, 0) Find gradient of BC Find gradient of q Find equation of q Solve p and q simultaneously for intersection (0, 2)

13 Maths4Scotland Higher Hint PreviousNext Quit Triangle ABC has vertices A(2, 2), B(12, 2) and C(8, 6). a) Write down the equation of l 1, the perpendicular bisector of AB b) Find the equation of l 2, the perpendicular bisector of AC. c) Find the point of intersection of lines l 1 and l 2 d) Hence find the equation of the circle passing through A, B and C. Mid-point AB Find mid-point AC (5, 4) Find gradient of AC Equ. of perp. bisector AC Gradient AC perp. Point of intersection (7, 1) This is the centre of circle Find radius (intersection to A) Equation of circle: Perpendicular bisector AB

14 Maths4Scotland Higher Hint PreviousNext Quit A triangle ABC has vertices A(–4, 1), B(12,3) and C(7, –7). a) Find the equation of the median CM. b) Find the equation of the altitude AD. c) Find the co-ordinates of the point of intersection of CM and AD Mid-point AB Equation of median CM Gradient of perpendicular AD Gradient BC Equation of AD Gradient CM (median) Solve simultaneously for point of intersection (6, -4)

15 Maths4Scotland Higher Hint PreviousNext Quit A triangle ABC has vertices A(–3, –3), B(–1, 1) and C(7,–3). a) Show that the triangle ABC is right angled at B. b) The medians AD and BE intersect at M. i) Find the equations of AD and BE. ii) Hence find the co-ordinates of M. Gradient AB Product of gradients Gradient of median AD Mid-point BC Equation AD Gradient BC Solve simultaneously for M, point of intersection Hence AB is perpendicular to BC, so B = 90° Gradient of median BE Mid-point AC Equation AD

16 Maths4Scotland Higher Previous Quit You have completed all 12 questions in this presentation Back to start

17 Maths4Scotland Higher Return 30°45°60° sin cos tan1 Table of exact values


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