Become a Maths Boss: 25 Problems with Solutions

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Become a Maths Boss: 25 Problems with Solutions

Become a Maths Boss: 25 Problems with Solutions

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A5a Rearranging formulas to change the subject N8b Surds A10a Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically slope standard N4c Prime numbers and prime factorisation, A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences Note: Even if Question-Level Analysis (QLA) spreadsheets could be populated in zero time, the use of QLAs ought to come with a health warning. While there are benefits that can arise from their use, QLAs can also result in unintended consequences if not used appropriately! If you do wish to use QLAs however, read on… A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences A25a - Finding the nth term of a linear sequence A25b - Finding the nth term of a quadratic sequence

G17a - Perimeter of polygons, G17b - Circumference of a circle, G16a - Area of rectangles, G17c - Area of a circle, N12a - Interpreting fractions and percentages as operators, R3a - Expressing one quantity as a fraction of another G10a R5a Dividing a ratio in a given quantity, G23a area of triangle using sine ratio, radius, shaded area, triangle, sine 1/2 ab sinC 1/2absinc Expanding, multiplying out, simplifying, collecting like terms, factorise, factorize, factorizing, solve, both sides, quadratics, ssdd additions, adding to, subtractions from, subtracting, take away, totals, sums, differences, wholes numbers, four operations, A9a A9c A10a Plotting straight-line graphs, Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line), gradient, Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically, slope, intercept, y=mx+c, adding and subtracting fractions and decimals, addition, subtractionG13a Plans and elevations of 3D shapes G12a Properties of 3D shapes with GeoGebra applets G1b 3D geometry terms R9a - Converting between fractions and percentages

G10a circle theorems Segment angles G22b G23a cosine rule area of triangle using sine 1/2 absinC probability fraction P2a Firstly, this helps draw attention to perpendicular distances. To find the perpendicular distance from a point to a circle, simply position your ruler so that it joins the point of interest to the centre of the circle. G10a circle theorems angle in a semicircle 90º degrees G20a Pythagoras' theorem Pythagorean G11a Solve geometrical problems on coordinate axes Surds positives, negatives, directed numbers, adding, additions to, subtracting, subtractions from, multiplying by, multiplications, dividing, divisionsA17a, A17b Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation,G3c The sum of angles in a triangle and the angle properties of polygons, polygons, exterior, sides, edges, writing setting up solve linear G13a Plans and elevations of 3D shapes, R11a - Using compound units, R1a - Changing between standard units and compound units in numerical and algebraic contexts transformations, scale factors, negative, fractional, fractions, enlarging, centre of, transforming Students should realise that equations can be seen like a balance. Whether seeing this as “doing the same thing to both sides” or a process of “breaking and repairing”, it is also important that students appreciate that it is mathematically valid to manipulate equations in many ways—and not just in ways that lead to simpler equations or even a solution. Of course, the skill is most often used in pursuit of a solution, but the skill is well worth practising in its own right.

A11b - Identifying turning points of quadratic functions by completing the square with GeoGebra applet Primes, Unique, factorizes, factorizations, factorising, factorizing,HCFs, LCMs, highest, lowest, common, multiples, factorises, factors, decompose, decomposition, decomposing, fundamental theorem of arithmetic constructions, equilateral, scalene, SSS,SAS,ASA, isosceles, right angled , using rulers and straight edges, compasses, without protractors G10a, N8a, G20a, A21b, A18a, Solving quadratic by factorising Deriving and solving an equation or simultaneous equations to describe a situation, Perimeter, circumference, circle theorems, obling, rectangles, diagonals, pi, exact values, cyclic quadrilateral, angles in a semicircle 90º degrees, factorize, factorise, factorization, factorisationRight angled triangles, Pythagoras's, Pythagorean, 90º, degrees, triple, a Greater, less, than, equal to, solves, unknowns, graphs, graphically, regions, shaded shades, shading by, inequality pi, radiuses, radii, diameters, lengths, areas, circumferences, finding, calculating, calculate, parts of N15a - Rounding and truncating N15b - Using inequality notation to specify simple error intervals A22a - Solving linear inequalities in one variable In the table below you find class and cohort versions of each QLA. The class QLAs (typically around 1 MB) can take data for up to 40 students while the cohort QLAs (typically around 5 MB) can take data for up to 300 students. The QLAs are otherwise identical. Because of the formulas in the spreadsheets, older computers may struggle to load or run the cohort QLAs, but should be fine with the class QLAs. Past papers, mark schemes, grade boundaries, and QLA links

FDP, of a number amount quantity, increase decrease, multipliers, reverse, percentages, reversing, undoing, compares, comparisons, ssddadditions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing improper, mixed numbers, vulgar, top-heavy, keep, kiss and flip, reciprocal discriminants, parabolas, parabolic, roots, solutions, solves, quadratics, algebraic fractions, graphs, completes, parabolas, parabolic, turning points, minimums, maximums, solves, minima, maxima, quadratics, algebraic fractions, vertex form completing the square completes,factorises, factorizse, factorizing, dynamic algebra tiles Use the grey <> tool to move the line horizontally, keeping it to the left of the semicircle. Once you’ve decided where you’d like the line, do not move it again. Keep it fixed. Estimating, approximating, rounding, calculators, calculating, technology, estimates, estimations, figures, significant N8b Surds simplifying. rationalising denominators, rationalizing, rationalise, rationalize, Statistics, S4a S4b S4c S4d



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