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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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… N2a - Adding and subtracting positive integers N2b - Multiplying positive integers N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference N2f - Applying the four operations to fractions N3a - Relationships between operations, including inverse operations N2e - Applying the four operations to negative numbers G13a Plans and elevations of 3D shapes, R11a - Using compound units, R1a - Changing between standard units and compound units in numerical and algebraic contexts

cubes, cuboids, prisms, cylinders, pyramids, cones, spheres, nets, vertices, faces, edges, corners, surfaces, sides, polyhedrons, polyhedra, curved, triangular, 3-d three dimensions dimensional A5a Rearranging formulas to change the subject N8b Surds A10a Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically slope standard

Question 6

Dividing, divisions, sharing, bus stops, chunking, methods, four operations, whole numbers remainders A3a - Understanding and using the concepts of expressions, equations, formulas, identities, inequalities, terms and factors additions, adding to, subtractions, subtracting from, multiplications, multiplying by, divisions, dividing improper, mixed numbers, vulgar, top-heavy, keep, kiss and flip, reciprocal 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 G1c - Reflection symmetry, probability, P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities, sample

Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, prove that, show, proving with intersections, intersects, intersecting, parabolas, parabolic, solutions, solves, graphs straight lines curves curved, quadratics inverse, including graphical and algebraic representations, imperial, metric, converting between to from miles kilometres centimetres cm km yards inches

Right angled triangles, Pythagoras's, Pythagorean, 90º, degrees, triple, a Gradients, y- intercepts, horizontal, vertical, slopes, lines, y=mx+c, y = mx + c, x = k, ax+by=c ax+by=k ax + by = c k - 0 N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference distributive law property distributivity 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

Then you can then go about solving the equation. You may like to decide what you could do to one side of the equation (e.g. add, subtract, multiply or divide by a quantity, which could be a constant or an expression involving \(x\)) to make that side of the equation simpler. If you only do this to one side of the equation, you break the equation, so you’ll need to do it to the other side to repair the equation. In other words, you need to do the same thing to both sides. Then simplify both sides where possible. Repeat the process until you have solved the equation. A14b - Plotting and interpreting graphs in real contexts to find approximate solutions to problems such as simple kinematic problems measure using a protractors rulers length size of lines, acute, right, obtuse, straight, reflex angles Powers, indices, base, rebasing rebase, substitute substituting A2a A11b A4i A17a A18a A18b Solving quadratic equations by factorising Solving quadratic equations by completing the square N7a Calculating with positive and negative integer indices transformations, scale factors, negative, fractional, fractions, enlarging, centre of, transforming

Question 3

N2f Applying the four operations to fraction A19a Solving two linear simultaneous equations algebraically by elimination G10a circle theorems Segment angles G20b G20c inverse trigonometric functions right-angled triangles A17b - Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation Arithmetic, linear, geometric, sequences, progression, quadratics, nth term, position to term, term to term -, ssdd Expanding, multiplying out, simplifying, collecting like terms, factorise, factorize, factorizing, solve, both sides, quadratics, ssdd



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