Announcing the release of VERSION 5 •950+ MB of Presentations •575 files (Double CD) •15 000+ slides •1000’s of example/student questions •100’s of worksheets •1200 interactive SAT/GCSE Boosters •5000 Mental Maths Questions •Huge Enrichment Area This Demo shows just 20 of the 15,000 available slides andtakes 7 minutes to run through. Please note that in the properpresentations the teacher controls every movement/animation by use of the mouse/pen. Click when ready→
Conditional Probability: Dependent EventsWhen events are not independent, the outcome of earlierevents affects the outcome of later events. This happens insituations when the objects selected are not replaced.
Conditional Probability: Dependent EventsA box of chocolates contains twelve chocolates of three different types.There are 3 strawberry, 4 caramel and 5 milk chocolates in the box. Samchooses a chocolate at random and eats it. Jenny then does the same.Calculate the probability that they both choose a strawberry chocolate. P(strawberry and strawberry) = 3/12 x
Conditional Probability: Dependent EventsA box of chocolates contains twelve chocolates of three different types.There are 3 strawberry, 4 caramel and 5 milk chocolates in the box. Samchooses a chocolate at random and eats it. Jenny then does the same.Calculate the probability that they both choose a strawberry chocolate. P(strawberry and strawberry) = 3/12 x 2/11 = 6/132 (1/22)
Enlargements from a Given PointCentre of Enlargement To enlarge the kite by B scale factor x3 from the point shown. A Object C B/ 1. Draw the ray lines through vertices. D 2. Mark off x3 distances C/ along lines from C of E. A / Image 3. Draw and label image.No Grid 2 D/
Loci (Dogs and Goats) Q2Billy the goat is tethered by a 15m long chain to a tree at A. Nanny the goat istethered to the corner of a shed at B by a 12 m rope. Draw the boundary locusfor both goats and shade the region that they can both occupy. Wall Scale:1cm = 3m A Shed B Wall1. Draw arc of circle of radius 5 cm2. Draw ¾ circle of radius 4 cm3. Draw a ¼ circle of radius 1 cm 4. Shade in the required region.
Investigate some Properties ofPascal’s Triangle
A 3 rd Pythagorean TripleIn a right-angled triangle, the square on the 625 hypotenuse is equal to the sum of the squares 7, 24, 25 on the other two sides. 25 49 7 24 576 7 2 + 24 2 = 25 2 49 + 576 = 625
The Theorem of Pythagoras: A Visual Demonstration In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Henry Perigal (1801 – 1898)Perigal’sDissection Gravestone Inscription Draw 2 lines through the centre of the middle square, parallel to the sides of the large square This divides the middle square into 4 congruent quadrilaterals These quadrilaterals + small square fit exactly into the large square
Look at one of the 6 proofs of the Theorem from the Pythagorean Treasury.
President James Garfield’s Proof(1876) To prove that a2 + b2 = c2 We first need to show that the angle between angle x and angle y is a right angle. •This angle is 90o since x + y = 90o (angle sum of a triangle) and angles on a straight line add to 180o Draw line:The boundary shape is a trapezium Area of trapezium = ½ (a + b)(a + b) = ½ (a2 +2ab + b2) yo Area of trapezium is also equal to the areas of the 3 right-angled triangles. = ½ ab + ½ ab + ½ c2 c b So xo ⇒ ½ (a2 +2ab + b2) = ½ ab + ½ ab + ½ c2 ca ⇒ a2 +2ab + b2 = 2ab + c2 yo xo ⇒ a 2 + b2 = c2 QED b aTake 1 identical copy of this right-angled triangle and arrange like so.
Sample some materialfrom the Golden section presentation.
THE GOLDEN SECTIONConstructing a Golden Rectangle.1. Construct a square and the 2. Extend the sides as shown.perpendicular bisector of a sideto find its midpoint p. L M Q 3. Set compass to 1 length PM and draw an arc as shown. O P N R 4. Construct aLQRO is a Golden Rectangle. perpendicular QR.
THE GOLDEN SECTION"Geometry has two great treasures: one is the Theorem ofPythagoras, and the other the division of a line into extremeand mean ratio; the first we may compare to a measure ofgold, the second we may name a precious jewel." Johannes Kepler 1571- 1630