Use this as an opportunity for practical work. Probabilities written in fraction form should be cancelled to their simplest form. 13b. Probability II (N5, P1, P2, P3, P5, P7, P8) Teaching time 8–10 hours OBJECTIVES By the end of the sub-unit, students should be able to: Find the probability of an event happening using relative frequency; Estimate the number of times an event will occur, given the probability and the number of trials – for both experimental and theoretical probabilities; List all outcomes for combined events systematically; Use and draw sample space diagrams; Work out probabilities from Venn diagrams to represent real-life situations and also ‘abstract’ sets of numbers/values; Use union and intersection notation; Compare experimental data and theoretical probabilities; Compare relative frequencies from samples of different sizes; Find the probability of successive events, such as several throws of a single dice; Use tree diagrams to calculate the probability of two independent events; Use tree diagrams to calculate the probability of two dependent events. POSSIBLE SUCCESS CRITERIA Understand the use of the 0–1 scale to measure probability. List all the outcomes for an experiment. Know and apply the fact that the sum of probabilities for all outcomes is 1. Draw a Venn diagram of students studying French, German or both, and then calculate the probability that a student studies French given that they also study German. COMMON MISCONCEPTIONS Not using fractions or decimals when working with probability trees. NOTES Probability without replacement is best illustrated visually and by initially working out probability ‘with’ replacement. Encourage students to work ‘across’ the branches working out the probability of each successive event. The probability of the combinations of outcomes should = 1. Emphasise that were an experiment repeated it will usually lead to different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics. Probabilities written in fraction form should be cancelled to their simplest form.
Use and interpret maps and scale drawings; Estimate lengths using a scale diagram; Make an accurate scale drawing from a diagram; Use three-figure bearings to specify direction; Mark on a diagram the position of point B given its bearing from point A; Give a bearing between the points on a map or scaled plan; Given the bearing of a point A from point B, work out the bearing of B from A; Use accurate drawing to solve bearings problems; Solve locus problems including bearings. POSSIBLE SUCCESS CRITERIA Sketch the locus of point on a vertex of a rotating shape as it moves along a line, i.e. a point on the circumference or at the centre of a wheel. COMMON MISCONCEPTIONS Correct use of a protractor may be an issue. NOTES Drawings should be done in pencil. Relate loci problems to real-life scenarios, including mobile phone masts and coverage. Construction lines should not be erased. UNIT 16: Algebra: quadratic equations and graphs SPECIFICATION REFERENCES A4 simplify and manipulate algebraic expressions by: … expanding products of two binomials; factorising freturn to overview expressions of the form x2 + bx + c, including the difference of two squares; … A11 identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically A12 recognise, sketch and interpret graphs of … quadratic functions; … A18 solve quadratic equations algebraically by factorising; find approximate solutions using a graph PRIOR KNOWLEDGE Students should be able to square negative numbers. Students should be able to substitute into formulae. Students should be able to plot points on a coordinate grid. Students should be able to expand single brackets and collect ‘like’ terms. KEYWORDS