Question Mark Mathletics Project 15/11/96 Dr M Greenhow, Dept of Maths and Stats, Brunel University, Uxbridge UB8 3PH Email: martin.greenhow@brunel.ac.uk Tel:01895-274000 extn 2260 Fax:01895-203303 This Teaching Initiative and Strategic Development project has been funded by SPARC during 1995/96. The result is Mathlectics version 1.1 which provides a suite of BASIC mathematics questions, covering most of the A-level common core, together with some earlier material from GCSE level and some material commonly taught during the first year of an undergraduate course. Some parts of the project proved to be much bigger than originally envisioned and have gone well beyond the original proposal, while some parts of the original proposal (notably algebra) are still being written; they are identified in italics and some should be complete by end 1996 in time to help students with exam revision in Jan 1997. The questions themselves are all multi-choice with distracters (displayed in a random order at each run) chosen by common mal-rule application, with appropriate feedback. Thus a student will not only be know that he/she is wrong but will be told why. Multi-choice answers are also easily analysed by the lecturer and corrective action may then be taken. It is proposed to add other types of questions later. The questions exist in libraries with a .qdl extension. Navigation and revision screens is provided by various tests with a .qdt extension. These tests may easily be changed without re-writing the questions themselves, providing great flexibility. Thus a lecturer might want to ask all questions in a single library when covering that topic in class, while diagnostic or revision tests would ask only a few questions from each of many libraries. The first provision is possible for any library the test being in the same directory with the same name but with a .qdt extension replacing the .qdl extension. Existing tests for the second option have been detailed below (but other combinations are easily possible). The question choice made at each run is random making repeat tests useful for the student and making copying very difficult. This will encourage students to perfect and increase the speed of their basic mathematics by repeated practice with immediate marking and feedback which is almost completely absent from most first-level undergraduate modules, and appears less visible in schools than previously. A number of Maths and Stats students have been involved; final year projects; Shafraz Saju, Naizer Amlani, Henry Emmanuel work placements; Simon White, Adam Lawrence. Single events For each .qdl there is a .qdt test asking 10 randomly chosen questions from the .qdl in the subject directory. Pentathlons exist in each subject directory as specified below. Usually call 5 .qdls in same directory. Decathlons exist in the mathsub directory. Usually call 10 related .qdls eg in calculus. Marathons exist in the mathsub directory. Usually call 20 unrelated .qdls Trilathons exist in the mathsub directory. Usually call 30 unrelated .qdls Subjects covered [Notation: test subject (mathlet/directory) italics means not completed)] CALMAT Diagnostic tests 1 and 2 These tests are diagnostic and are explicitly linked to remedial help from the Calmat units written by Glasgow Caledonian University. calmat1.qdt - mostly algebra part of A-level core - calls 50 short libraries calmat2.qdt - mostly calculus part of A-level core - calls 50 short libraries. Decathlons Complex numbers (writes answers in mathlet/mathsub/answers) Differentiation (writes answers in mathlet/mathsub/answers) Foundations of Science Arithmetic test This is a different sytle of test, being more formal and allowing free navigation by student, with feedback given in review mode at the end. (Not turned on until test due date). Arithmetic arith5#1.qdt navigates through the following libraries: arithgen.qdl - number line, operations and their order, perfect squares, hcf, lcm arithpow.qdl - power manipulations, (-1)n, powers of fractions, powers of 10 decimal.qdl - decimal places and sig figs, %'s, scientific notation fraction.qdl - operations, ratios, powers, cancellation surds.qdl - operations and powers Complex comp5#1.qdt navigates through the following libraries: compgen.qdl - definitions of modulus,argument, conjugate, polar form comadd.qdl - addition/subtraction, z+c.c. forms commult.qdl - multiplication/division, mixed sums involving all 4 operations, interger powers argand.qdl - positions of various z and operations with z comp5#2.qdt navigates through the following libraries: compoly.qdl - roots of simple (mostly quadratic) complex polys comdemoi.qdl - multiple angle formulae, integer powers of z comroot.qdl - non-integer powers of z. comp5#3.qdt navigates through all of the above complex number libraries, asking 5 randomly chosen questions from each. It is designed for revision purposes. Vectors vect5#1.qdt navigates through the following libraries: vectgen.qdl - scalars and vectors, vector arithmetic dotcross.qdl - dot and cross, areas and normals triple.qdl - triple products, volumes of parallelopipeds, forms equivalent to 0 lineplan.qdl - lines and planes given combinations of points and directions Differentiation diff5#0.qdt navigates through the following libraries selecting easier questions manually: diffgen.qdl - mixture of basic polys, trig, products and quotients diffpow.qdl - polynomials, positive and negative integer and fractional powers logexp.qdl - logs (incl. manipulation) and log(fn(x)), exp and exp(fn(x)) basictri.qdl - all 6 trig fns, and with argument (ax) where a integer or rational diff5#1.qdt navigates through the following libraries: diffgen.qdl - mixture of basic polys, trig, products and quotients diffpow.qdl - polynomials, positive and negative integer and fractional powers logexp.qdl - logs (incl. manipulation) and log(fn(x)), exp and exp(fn(x)) basictri.qdl - all 6 trig fns, and with argument (ax) where a integer or rational hyptrig.qdl - all 6 hyp fns, and with argument (ax) where a integer or rational diff5#2.qdt navigates through the following libraries: product.qdl - products of polys, trig, ln, exp, hyp quotient.qdl - products of polys, trig, ln, exp, hyp chain.qdl - 2-deep chains of polys, trig, ln, exp, hyp diff5#3.qdt navigates through the following libraries: paramet.qdl - parametric fns logdiff.qdt - logarithmic differentiation implicit.qdl - implicit functions TO BE EXTENDED invtrig.qdl - inverse trig fns invhyp.qdl - inverse hyp fns Integration int5#1.qdt navigates through the following libraries: intpoly.qdl - definite integration of polynomials intalg.qdl - definite integration of algebraic fns intrat.qdl - definite integration of rationals inttrig.qdl - definite integration of sin(ax), cos(ax), tan(ax) and cot(ax) where a is an integer or simple fraction int5#2.qdt navigates through the following libraries: intsubs.qdl - definite integrals solved by substitution (incl. exps) intpart1.qdl - easy definite integrals of rational fns solved by partial fractions intpial1.qdl - easy definite integrals solved by integration by parts (incl. logs) int5#3.qdt navigates through the following libraries: inthyp.qdl - definite integrals of hyperbolics intpart2.qdl - hard definite integrals of rational fns solved by partial fractions intpial2.qdl - hard definite integrals solved by integration by parts (incl. inverse tri and hyp) intimpr.qdl - definite improper integrals intest.qdl - estimation of definite integrals by bounding functions and Taylor e xpansions. intnum.qdl - numerical methods. Algebra alg5#1.qdt navigates through the following libraries: algpower.qdl - integer and rational powers, Pascal's triangle, binomial theorem algquad.qdl - quadratics, roots/coeffs/factors, complete the square, max/min, general quadratic formula. alg5#2.qdt navigates through the following libraries: algpoly.qdl - roots/coeffs/factors, large x behaviour, poly long division. algpart.qdl - partial fractions of various types include. repeated roots. algser.qdl - general term, A.P's, G.P's, sum to Use of uninitialized value in concatenation (.) or string at E:\listplex\SYSTEM\SCRIPTS\filearea.cgi line 455, line 181. infinity. Matrices mat5#1.qdt navigates through the following libraries: matarith.qdl - basic matrix addition and multiplication matdet.qdl - determinants and linear dependence (vectors and sim eqns) mat5#2.qdt navigates through the following libraries: matnsq.qdl - under- and over-complete systems matinv.qdl - inverse matrices and solution of complete systems mateig.qdl - eigenvalues and eigenvectors Graphs fun5#1.qdt navigates through the following libraries: grpoly.qdl - graphs of polynomial graphs grrat.qdl - graphs of rational fns grtrig.qdl - graphs of trig fun5#2.qdt navigates through the following libraries: gralg.qdl - graphs of algebraic fns grgen.qdl - graphs of generalised fns grlogs.qdl - graphs of logs grexps.qdl - graphs of exps grhyp.qdl - graphs of hyperbolics Functions fun5#1.qdt navigates through the following libraries: funlogs.qdl - properties of logs funtrig.qdl - properties of trig fun5#2.qdt navigates through the following libraries: funlogs.qdl - properties of logs funexps.qdl - properties of exps funtrig.qdl - properties of trig funhyp.qdl - properties of hyperbolics