RandomTest.mws

---

A Randomized Algebra Test

by Otto Wilke
otto_wilke@hotmail.com

Randomized tests inhibit cheating and reduce the number of student-teacher confrontations. This application consists of four major sections.

SECTION ONE refers the reader to a file containing a large block of code that creates a table of procedures. In that file, procedures beginning with the letter d identify the kind of problem. Procedures beginning with the letter p create the problem. Problems are grouped by topic, NUMBER SYSTEMS, LINEAR EQUATIONS, CONICS, etc. Problems are not numbered consecutively. Space is reserved for 100 problems for each topic. Numbers p1 through p100 are reserved for number base problems. Numbers p101 through p200 are for algebraic operation problems, etc. When the block of code is executed, the table of procedures is created and stored in the binary file, algtest.m.

SECTION TWO consists of examples of problems currently in the test bank. Each problem is followed by the Maple 7 (I hope) code that could generate the answer(s) and by the answer(s).

SECTION THREE consists of code that generates a sample test and the output of that code. To generate a test without answers, set answers:=0: To generate the same version with answers, set answers:=1: It might be wise to set the seed for the random number generator, _seed, to some secret function of the version number. That would prevent students who read this from generating the test with answers. Desired problem numbers from the test bank in SECTION TWO, without the "p" prefix, are entered into list1 in the SECTION THREE code block. The same problem number can be entered in the list more that once to create variants of the same problem. For some versions, problem 104 will try to do something illegal. Just choose a different version number. Problem 501 doesn't exist. I accidentally skipped that number.

SECTION FOUR consists of code to generate a randomized final exam that contains one problem from each topic area. The code is followed by its output. Problem numbers can be removed from the problem lists for the topics to change the content of the exam. As before, to generate the test with answers set answers:=1:

I plan to add problems, especially application problems, and topic areas to the test bank. I hope some of you will generate additional problems and send them to me.

SECTION ONE
A TABLE OF PROCEDURES

To make the code in SECTION THREE and in SECTION FOUR functional, it is necessary to download and execute the file algtest.mws. Execution of that file will create a binary file named algtest.m. The code in SECTION THREE and SECTION FOUR will open the algtest.m file. Inspection of the code in algtest.mws will give the reader insight into the process of creating randomized problems.

SECTION TWO
THE TEST BANK

SECTION TWO consists of examples of problems currently in the test bank created by algtest.mws. Each problem is followed by the Maple 7 (I hope) code that could generate the answer(s) and by the answer(s).

NUMBER SYSTEMS

Test Bank Problem 1. Convert a decimal number to binary.

Convert 16 from decimal to binary.

> Answer=convert(16,binary);

Test Bank Problem 2. Convert a decimal number to hexadecimal.

Convert 100 from decimal to hexadecimal.

> Answer=convert(100,hex);

Test Bank Problem 3. Convert a binary number to decimal.

Convert 10000 from binary to decimal.

> Answer=convert(10000,decimal,binary);

>

Test Bank Problem 4. Convert a hexadecimal number to decimal.

Convert `38` from hexadecimal to decimal.

> Answer=convert("38",decimal,hex);

>

Test Bank Problem 5. Add, subtract, multiply, or divide numbers

in different bases.

Find the sum of 12 decimal and 100 binary. 

Give the answer in decimal form.

The answer is 16 decimal.

> Answer=12+convert(100,decimal,binary);

ALGEBRAIC OPERATIONS

Test Bank Problem 101. Evaluate an algebraic expression.

Evaluate.

> Answer=(8+(-24))/(6+(-1));evalf(%);

Test Bank Problem 102. Evaluate an algebraic expression.

Evaluate.

> Answer=(9+(-22))*(18+(-32));

Test Bank Problem 103. Evaluate an algebraic expression.

Evaluate.

Warning, the protected name Chi has been redefined and unprotected

when a = 3, b = 22, c = 26, d = 25,

e = 9, and f = 32.

> Answer=3+22/26-25*9*32;evalf(%);

Test Bank Problem 104. Evaluate an algebraic expression with exponents.

Evaluate.

when a = 2, b = 3, c = 3, d = 3,

e = 1, and f = 5.

> Answer=2*3+(3*3+1)^5;evalf(%);

RADICALS

Test Bank Problem 201. Simplify a radical.

Simplify the following radical.

> Answer=sqrt(25*x*y,symbolic);

Test Bank Problem 202. Multiply radicals.

Multiply the following radicals and simplify.

> Answer=sqrt((50*x^2*y^3)*(48*x*y^3),symbolic);

Test Bank Problem 203. Divide radicals.

Divide the following radicals and simplify.

> Answer=rationalize(sqrt((32*x^2*y)/(27*x*y^3),symbolic));

Test Bank Problem 204. Divide binomials with radicals.

Rationalize the following expressions and simplify. Assume x is real and positive.

> rationalize((2+sqrt(3*x,symbolic))/(5-3*sqrt(x,symbolic)));

> Answer=expand(numer(%))/denom(%);

SETS AND LISTS

Test Bank Problem 301. Find the union of two sets.

Find the union of sets A and B.

> Answer={3,9} union {2,4,6,7,8,10};

Test Bank Problem 302. Find the intersection of two sets.

Find the intersection of sets A and B.

> Answer={5, 8, 9} intersect {4, 6, 8, 9};

Test Bank Problem 303. Find the cardinality of a set.

Find the cardinality of set A.

> Answer=nops({5,7,8,9,11,14,16});

Test Bank Problem 304. Find the number of operands in a list.

Find the number of operands in list A.

> Answer=nops([17, 10, 3, 18, 6]);

Test Bank Problem 305. Find the value of an operand in a list.

Find the value of operand 2 in list A.

> Answer=op(2,[2, 16, 10, 8]);

SETS OF NUMBERS

Test Bank Problem 401. Express a rational number in decimal form.

Find the decimal value of following number.

> Answer=evalf(5/7,50);

Test Bank Problem 402. Express a decimal number in rational form.

Hint: Maple rounds the last digit.

Express the following decimal number in rational form.

> Answer=convert(.35294117647058823529411764705882352941176470588235,rational);

FACTORING

Test Bank Problem 502. Factor common factor.

Factor the following expression.

> Answer=factor(4*x^5+3*x);

Test Bank Problem 503. Factor trinomials with leading coefficient

equal to 1.

Factor the following expression.

> Answer=factor(x^2-9*x+18);

Test Bank Problem 504. Factor trinomials with leading coefficient

not equal to 1.

Factor the following expression.

> Answer=factor(10*x^2-24*x+8);

Test Bank Problem 505. Factor difference of squares.

Factor the following expression.

> Answer=factor(-8*x^8+18*y^6);

FRACTIONS

Test Bank Problem 601. Write a mixed number as a sum.

Write the mixed number 6 and 4/5 as a sum

of an interger and a rational fraction.

> Answer=" (6 + 4/5)";

Test Bank Problem 602. Multiply mixed numbers.

Multiply the mixed number 5 and 4/6 by

the mixed number 2 and 2/7.

> Answer=(5+4/6)*(3+2/5);evalf(%);

Test Bank Problem 603. Add mixed numbers.

Add the mixed number 3 and 2/5 and

the mixed number 3 and 2/5.

> Answer=(3+2/5)+(3+2/5);evalf(%);

COMPLEX NUMBERS

Test Bank Problem 701. Convert radicals with negative radicands to complex form.

Write the following in standard form for a complex number.

> Answer=-1+sqrt(-25);

Test Bank Problem 702. Operations with complex numbers.

Given the complex numbers z1 and z2 below, find z1 + z2,

z1 - z2, z1 * z2, z1 / z2, and z1 ^ z2.

> z1:=2+sqrt(-9);z2:=4+sqrt(-9);'z1'+'z2'=z1+z2;'z1'-'z2'=z1-z2;'z1'*'z2'=z1*z2;'z1'/'z2'=evalf(z1/z2);'z1'^'z2'=evalf(z1^z2);z1:='z1':z2:='z2':

CARTESIAN PLANE

Test Bank Problem 801. Graph a point in a plane.

Graph the point (-3, 8).

> plot([[-3,8]],style=point,symbol=circle,symbolsize=30,scaling=constrained,color=red,labels=[x,y],view=[-10..10,-10..10]);

>

Test Bank Problem 802. Graph a point in three dimensions.

Graph the point (-7, 2, -6).

Warning, the name changecoords has been redefined

> with(plots):plot3d({[-7,2,-6]},x=-10..10,y=-10..10,style=point,symbol=circle,symbolsize=30,view=[-10..10,-10..10,-10..10],axes=boxed,labels=[x,y,z],color=red);

>

Test Bank Problem 803. Graph a complex number.

Graph the number, -3 + 8 I, on the complex plane.

> plot([[-3,8]],symbol=circle,symbolsize=30, style=point,labels=[a,b],font=[TIMES,BOLD,12],scaling=constrained,view=[-10..10,-10..10]);

UNITS AND DIMENSIONS

Test Bank Problem 901. Length conversions.

Convert +3.71 meters to feet.

> with(Units);with(Units[Natural]):
Answer=convert(3.71*m,system,FPS);

Warning, the name Unit has been rebound

Warning, the name Unit has been rebound

Test Bank Problem 902. Mass conversions.

Convert  1.99 pounds_mass to kilograms.

> with(Units):with(Units[Natural]):GetUnits(dimension=mass);

Warning, the name Unit has been rebound

Warning, the assigned name polar now has a global binding

Warning, these protected names have been redefined and unprotected: *, +, -, /, <, <=, <>, =, Im, Re, ^, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, convert, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, factor, floor, frac, int, ln, log, log10, max, min, normal, root, round, sec, sech, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify

> Answer=convert(1.99*pound[avoirdupois],system,SI);

Test Bank Problem 903. Temperature conversions.

Convert  16.7 degree_Centigrade to Kelvin.

> with(Units):with(Units[Natural]):GetDimensions();

Warning, the name Unit has been rebound

Warning, the name Unit has been rebound

> GetUnits(dimension=thermodynamic_temperature);

> Answer=convert(16.7, temperature, centigrade, kelvin);

Test Bank Problem 904. Convert joules, newtons, volts or coulombs to SI.

Convert  82.0 joules to base_metric_units.

> with(Units):with(Units[Natural]):
Answer=convert(82.0*J,units,'kg*m^2/s^2');

Warning, the name Unit has been rebound

Warning, the name Unit has been rebound

Test Bank Problem 905. Application with units.

A pump pumps  75 gallons per minute against a pressure.

of  55 pounds per square inch.  What is its horsepower?

Convert flow and pressure to SI and then multiply.

> with(Units):with(Units[Natural]):
GetUnits(dimension=pressure);GetUnits(dimension=volume);GetUnits(dimension=power);

Warning, the name Unit has been rebound

Warning, the name Unit has been rebound

> evalf(55*pound_per_square_inch[standard])*75*gallon[US_liquid]/minute;

> Answer=convert(%,units,horsepower[UK]);

GEOMETRIC FORMULAE

Test Bank Problem 1001. Given two sides of a right triangle,

find its third side, perimeter, and area.

If a leg of a right triangle is  4.5 and the length of

the hypotenuse is  8.3 find the other leg, the perimeter of 

the triangle, and the area of the triangle.

> Leg=sqrt(8.3^2-4.5^2);

> Perimeter=4.5+8.3+6.974238310;

> Area=1/2*4.5*6.974238310;#one-half times base times height

Test Bank Problem 1002. Given three sides of a triangle,

find its area.

If the sides of a triangle are 14, 14,

and 2 find the area of the triangle.

> s:=(14+14+2)/2:Area=sqrt(s*(s-14)*(s-14)*(s-2));
evalf(%);s:='s':#Heron's formula

Test Bank Problem 1003. Given the radius or diameter of a circle,

find its circumference and area.

If the radius of a circle is  2.2, find the circumference

and the area of the circle.

> Circumference = 2*evalf(Pi)*2.2;Area =evalf(Pi)*2.2^2;

Test Bank Problem 1004. Find the volume of a cone or pyramid.

If a pyramid has a square base and each side of the base is  2.3,

and the height of the pyramid is  2.5, find the pyramid's volume.

> Volume =1/3*2.3^2*2.5;

Test Bank Problem 1005. Find the volume and area of a sphere.

If the radius of a sphere is   3.2, find its volume

and its surface area.

> Volume = 4/3*evalf(Pi)*3.2^3;Area = 4*evalf(Pi)*3.2^2;

>

LINEAR EQUATIONS

Test Bank Problem 1101. Solve a linear equation in one variable.

Solve.

> x=solve(-18*x-13 = -8,x);evalf(%);

Test Bank Problem 1102 Solve a linear equation in one variable with fractions.

Solve.

> x=solve(-1/3*x-7/4 = 1/3*x,x);evalf(%);

Test Bank Problem 1103 Solve a linear equation with x in the denominator.

Solve.

> x=solve(-5*1/(x+8)-4 = 7/3,x);evalf(%);

Test Bank Problem 1104. Solve a literal equation.

Solve for c.

> c=solve(a*b*c-d = e+f,c);

Test Bank Problem 1105. Distance, midpoint, slope, line.

Given the points (-2, -3) and (2, 2),

find the distance between the points, their midpoint, the slope

of the line through the points, and the equation of the line through

the points. Plot the points and the line.

> Distance=sqrt(''(x[2]-x[1])^2+(y[2]-y[1])^2''); Distance = sqrt((2-(-2))^2+(2-(-3))^2);evalf(%);

> x_midpoint=(x[1]+x[2])/[2];x_midpoint=(-2+2)/2;
y_midpoint=(y[1]+y[2])/[2];y_midpoint=(-3+2)/2;

> slope=(y[2]-y[1])/(x[2]-x[1]);slope=(2-(-3))/(2-(-2));

> y-y[1]=m*(x-x[1]);y=solve(y-(-3)=5/4*(x-(-2)),y);

> with(plots):p1:=plot([[-2,-3],[2,2]],style=point,symbol=box):
p2:=plot(-1/2+5/4*x,x=-5..5,y=-5..5,color=blue):
display({p1,p2});

LINEAR INEQUALITIES

Test Bank Problem 1201. Solve linear inequalities.

Solve.

> x=solve(0 < 8*x+11,x);

Test Bank Problem 1202. Solve double linear inequalities.

Solve.

> x=solve({2<=-4*x + (-9),-4*x + (-9)<=19},x);

Test Bank Problem 1204. Graph linear inequalities in two variables.

Solve.

> plots[inequal](y <= 5*x+5,x=-5..5,y=-5..5);
#Maple 6 bug: Use <= instead of < and >= instead of >

QUADRATIC EQUATIONS

Test Bank Problem 1301. Solve factorable quadratic equations with

leading coefficient of 1.

Solve.

> x=solve(x^2-4*x-60 = 0,x);

Test Bank Problem 1302. Solve factorable quadratic equations with

leading coefficient not 1.

Solve.

> x=solve(4*x^2+6*x = 0,x);

Test Bank Problem 1303. Solve quadratic equations with fractions.

Solve.

> x=solve(8*1/(x+2)-5/(x-9) = 2/5,x);evalf(%);

RADICAL EQUATIONS

Test Bank Problem 1401. Solve radical equations with one radical.

Solve.

> x={solve(sqrt(-7*x-5)-2 = 6,x)};evalf(%);

Test Bank Problem 1402. Solve radical equations with two radicals.

Solve.

> x={solve(sqrt(9*x-8)+sqrt(4*x+7) = 3,x)};evalf(%);

POLYNOMIAL EQUATIONS

Test Bank Problem 1501. Solve polynomial equations with real roots.

Solve.

> x=solve(-6*x^3-31*x^2+72*x-35 = 0,x);evalf(%);

Test Bank Problem 1502. Solve polynomial equations with complex roots.

Solve.

> x=solve(36*x^3+156*x^2-271*x+534 = 0,x);evalf(%);

FUNCTIONS

Test Bank Problem 1601. Find inverse functions.

Given the following function, F, find the inverse of F.

> F:=x->8*x+5;[F]^[-1]=solve(x=8*y+5,y);F:='F':
#Exchange x and y and solve for new y.

Test Bank Problem 1602. Find composite functions.

Given the following functions, F and G, find the F composite G.

> F:=x->-2*x+3;G:=x->2*x+3;F_comp_G=(F@G)(x);F:='F':G:='G':

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Test Bank Problem 1701. Solve exponential equation.

The accumulation in an annuity, A, is given by the following

equation in which P is the periodic contribution, r is the

rate of increase per period(expressed as a decimal),

and n is the number of periods.

Joan invested $110 each month into a tax-sheltered annuity

which earns  10.5 percent (APR) compounded annually.

How many years will it take for her to have a million dollars

in her annuity account?

> Answer = solve(1000000=110*((1+.105/12)^(12*x)-1)/(.105/12),x)*years;
#Interest rate as a decimal; with monthly contribution, use monthly
#rate and n is number of months.

Test Bank Problem 1702. Solve exponential equation.

The future value, A, (principle plus interest),  of principle, P

invested at compound interest rate, r for n periods

is given by the following equation.

Joan invested $6000 which earns  12.0 percent (APR) .

How many years will it take for her to double her money

if interest is compounded annually?

> Answer = solve(2*6000=6000*(1+.12)^n,n)*years;
#Interest rate as a decimal; with annual compounding, use yearly
#rate and n is number of years.

Test Bank Problem 1703. Solve logarithmic equation.

The pH of a solution having a hydronium ion concentration, H3O,

in moles per liter, is given by the following equation.

Find the hydronium ion concentration if the pH is  7.1.

> H3O =solve(7.1= -ln(H3O),H3O);

MATRICES

Test Bank Problem 1801. Add matrices.

Given the following matrices:

Find A + B.

> evalm([[-6,11],[6,-12]])+evalm([[5,-11],[3,-7]])=evalm([[-6,11],[6,-12]]+[[5,-11],[3,-7]]);

Test Bank Problem 1802. Multiply matrices.

Given the following matrices:

Find the product of A and B.

> evalm([[-9,-6],[-11,10]])*evalm([[-1,8],[4,5]])=evalm([[-9,-6],[-11,10]]&*[[-1,8],[4,5]]);

Test Bank Problem 1803. Multiply a constant by a matrix.

Multiply the following matrix by 3.

> 3*evalm([[-7,-7],[-4,-3]])=evalm(3*[[-7,-7],[-4,-3]]);

Test Bank Problem 1804. Find the inverse of a matrix.

Find the inverse of the following matrix.

Warning, the name fibonacci has been redefined

Warning, the protected names norm and trace have been redefined and unprotected

> with(linalg):A := array( [[-7,7],[-11,1]] ):[A]^[-1]=inverse(A);A:='A':

Test Bank Problem 1805. Find the determinant of a matrix.

Find the determinant of the following matrix.

> Answer=linalg[det](matrix([[-5, -10, 11], [-12, 9, 1], [10, 12, 12]]));

SIMULTANEOUS EQUATIONS

Test Bank Problem 1901. Solve two simultaneous equations.

Solve the following simultaneous equations.

> solve({7*x-y = 7,-7*x-8*y = 1},{x,y});

Test Bank Problem 1902. Solve three simultaneous equations.

Solve the following simultaneous equations.

> solve({-3*x+2*y-5*z = 6,9*x-7*y+7*z = 5,8*x-6*y+5*z = 2},{x,y,z});

Test Bank Problem 1903. Solve an underdetermined system.

Solve the following simultaneous equations.

> solve({4*x-3*y-6*z = -4,-9*x+4*y-7*z = 4},{x,y,z});

Test Bank Problem 1904. Reduced row echelon form.

Write the reduced row echelon from of the augmented matrix

for the following equations.

> with(linalg):rref([[1,-3,-3],[-3,1,4]]);

SIMULTANEOUS INEQUALITIES

Test Bank Problem 2001. Graph two simultaneous inequalities.

Graph the following inequalities.

> plots[inequal]({7*x+3*y <= -6,-9 <= x+y},x=-20..20,y=-20..20,thickness=8);
#Maple 6 bug: Use <= instead of < and >= instead of >

SEQUENCES

Test Bank Problem 2101. Common difference or ratio, general term, sums.

Arithmetic Sequence Formulae

Geometric Sequence Formulae

Is the following sequence arithmetic, geometric, or neither?

If arithmetic, what is the common difference, the general formula

for the nth term, and the sum of the first 7 terms?

If geometric, what is the common ratio, the general formula

for the nth term, and the sum of the first 7 terms?

If the geometric series converges, what is the sum of an infinite number of terms?

Test for common difference

> [-3-(-5),-9/5-(-3),-27/25-(-9/5),-81/125-(-27/25)];

Differences between successive terms not the same; therefore sequence is not arithmetic.

Test for common ratio.

> [-3/(-5),-9/5/(-3),-27/25/(-9/5),-81/125/(-27/25)];

Ratios of successive terms are the same, therefore sequence is geometric.

Geometric sequence

> a[n]=a[1]*r^(n-1); a[n]=-5*(3/5)^(n-1);

Use general formula in sum command

> Sum( -5*(3/5)^(n-1),n=1..7)=sum( -5*(3/5)^(n-1),n=1..7);

If the absolute value of the common ratio, r, is less than 1, find the sum of an infinite number of terms.

> Sum( -5*(3/5)^(n-1),n=1..infinity)=sum( -5*(3/5)^(n-1),n=1..infinity);

PROBABILITY

Test Bank Problem 2201. Factorial.

Calculate 9 factorial.

> Answer = 9!;

Test Bank Problem 2202. Combinations.

Calculate the number of combinations of 17 things taken 7 at a time.

Warning, the name fibonacci has been redefined

> with(combinat):Answer=numbcomb(17,7);

Test Bank Problem 2203. Permutations.

Calculate the number of permutations of 7 things taken 5 at a time.

> with(combinat):Answer=numbperm(7,5);

Test Bank Problem 2204. Probability of union.

A jar contains 2 red marbles, 4 blue marbles, and 7 yellow marbles.

If one marble is drawn from the jar, what is the probability it will

be red or yellow?

> Answer = (2+7)/(2+4+7);

Test Bank Problem 2205. Probability of independent events and complements.

The probability of rain today is  .20 and the probability

of rain tomorrow is  .45.  What is the probability of no

rain today?  What is the probability of rain both days?

What is the probability of no rain either day?

What is the probability of rain at least one day of the two?

> No_rain_today = 1-.2;

> Rain_both_days=.2*.45;

> No_rain_at_all = (1-.2)*(1-.45);

> Rain_one_day = 1-.440;

CONICS

Test Bank Problem 2301. Given equation, identify conic, locate centers, vertices, foci.

Does the following equation describe a line, a circle,

an ellipse, or a parabola?

If a circle, determine the radius and locate the center.

If an ellipse, locate the center and foci.

If a parabola, locate the vertex and focus.

In all cases, graph the equation and the determined points.

Graph the relationship.

> plots[implicitplot](4*x^2+40*x+108-4*y = 0,x=-20..20,y=-20..40);

Graph show a parabola. Also, because the coefficient of y^2 is zero, we know the graph is a parabola.
The standard from of the equation for a parabola opening in the y-direction is:

> k:='k':4*p*(y-k)=(x-h)^2;

> student[completesquare](4*x^2+40*x+108-4*y = 0,x);%/4;

Arrange in standard form for a parabola.

> 4*[1/4]*[y-2]=(x+5)^2;

Focus is distance p from the vertex in the y-direction (2+1/4).

> with(plots):p1:=implicitplot(4*x^2+40*x+108-4*y = 0,x=-10..-1,y=0..10):
p2:=plot([[-5,2],[-5,9/4]],style=point,symbol=circle):
display({p1,p2},scaling=constrained,axes=framed);

Test Bank Problem 2302. Given three points, find equation of parabola.

Given the following points, [x,y], find the equation of the parabola

passing through the points.  What are the coordinates of its vertex?

The standard form for the equation of a parabola is:

> solve({4*p*(6-k) = (2-h)^2,4*p*(-2-k) = (5-h)^2,4*p*(6-k) = (8-h)^2},{p,h,k});

> 4*(9/32)*(y-(-2))=(x-5)^2;

STATISTICS AND REGRESSION

Test Bank Problem 2401. Mean, median, standard deviation.

Calculate the mean, median, and standard deviation

of the following set of numbers.

> with(stats):Mean = describe[mean]([10, 7, 13, 9, 10, 11]);evalf(%);

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

> with(stats):Median = describe[median]([10, 7, 13, 9, 10, 11]);evalf(%);

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

> with(stats):Standard_deviation = describe[standarddeviation]([10, 7, 13, 9, 10, 11]);evalf(%);

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

Test Bank Problem 2402. Linear regression.

Calculate the the equation of the best-fit line

for the following set of points, [x,y].

Plot the points and the line.

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

> with(stats):fit[leastsquare[[x,y]]]([[4,9,11],[1,5,10]]);

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

> p1:=plot([[4,1],[9,5],[11,10]],style=point,symbol=cross):
p2:=plot(-164/39+31/26*x,x=0..15):
plots[display]({p1,p2});

LOGIC

Test Bank Problem 2501. Deductive reasoning.

Is the syllogism direct, indirect, or transitive reasoning and is the

argument a valid argument?

If John studies math two hours per day, then John passes math.

John studies math two hours per day,therefore John passes math.

The argument is DIRECT and VALID.

>

>

SECTION THREE
GENERATE A RANDOMIZED TEST

SECTION THREE consists of code that generates a sample test and the output of that code. To generate a test without answers, set answers:=0: To generate the same version with answers, set answers:=1: It might be wise to set the seed for the random number generator, _seed, to some secret function of the version number. That would prevent students who read this from generating the test with answers. Desired problem numbers from the test bank in SECTION TWO are entered into list1 in the SECTION THREE code block. The same problem number can be entered in the list more that once to create variants of the same problem. For some versions, problem 104 will try to do something illegal. Just choose a different version number. Problem 501 doesn't exist. I accidentally skipped that number.

> read `algtest.m`:with(combinat):
Version:=3:_seed:=Version:answers:=1:
printf("Randomized Test\n");
list1:=randperm([1,2,3,103,104,903]):
for j from 1 to nops(list1) do
printf("Problem% d, Version% d\n",j,Version);
s1:=``||op(j,list1):
algtest[`p`||s1](answers);printf("\n");od:

Warning, the protected name Chi has been redefined and unprotected

Randomized Test

Problem 1, Version 3

Evaluate.

when a =  4, b =  3, c =  5, d =  6

e =  4, and f =  4

Problem 2, Version 3

Convert  3 from decimal to hexadecimal.

Problem 3, Version 3

Convert  32 from decimal to binary.

Problem 4, Version 3

Convert 1011 from binary to decimal.

Problem 5, Version 3

Convert  63.50 degree_Centigrade to Kelvin.

Problem 6, Version 3

Evaluate.

when a =  25, b =  6, c =  18, d =  3

e =  21, and f =  31.

SECTION FOUR
GENERATE A RANDOMIZED FINAL EXAM

SECTION FOUR consists of code to generate a randomized final exam that contains one problem from each topic area. The code is followed by its output. Problem numbers can be removed from the problem lists for the topics to remove simplistic problems from the exam. As before, to generate the test with answers, set answers:=1:

> read `algtest.m`:with(combinat):
Version:=723011:_seed:=Version:answers:=1:j:=1:
printf("Problem % d, Version % d\n",j,Version);
list1:=[1,2,3,4,5]:
s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[101,102,103,104]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[201,202,203,204]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[301,302,303,304]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[401,402]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[502,503,504]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[601,602,603]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[701,702]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[801,802,803]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[901,902,903,904]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1001,1002,1003,1004]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1101,1102,1103,1104]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1201,1202,1204]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1301,1302,1303]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1401,1402]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1501,1502]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1601,1602]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1701,1702,1703]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1801,1802,1803,1804]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[1901,1902,1903]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[2001]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[2101]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[2301,2302]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[2401,2402]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);
j:=j+1:printf("\n");printf("\n");
printf("Problem % d, Version % d\n",j,Version);
list1:=[2501]:s1:=``||op(1,randcomb(list1,1)):
algtest[`p`||s1](answers);

Warning, the protected name Chi has been redefined and unprotected

Problem  1, Version  723011

Convert  5 from decimal to binary.

Problem  2, Version  723011

Evaluate.

Problem  3, Version  723011

Divide the following radicals and simplify.

Problem  4, Version  723011

Find the cardinality of set A.

Problem  5, Version  723011

Find the decimal value of following number.

Problem  6, Version  723011

Factor the following expression.

Problem  7, Version  723011

Write the mixed number  6 and  2/ 6 as a sum

of an interger and a rational fraction.

Problem  8, Version  723011

Given the complex numbers z1 and z2 below, find z1 + z2,

z1 - z2, z1 * z2, z1 / z2, and z1 ^ z2.

Problem  9, Version  723011

Graph the point ( 0,  7).

Problem  10, Version  723011

Convert  88.20 newtons to base_metric_units.

Problem  11, Version  723011

If the radius of a cone is  6.40 and its height

is  5.70, find its volume.

Problem  12, Version  723011

Solve.

Problem  13, Version  723011

Solve.

Problem  14, Version  723011

Solve.

Problem  15, Version  723011

Solve.

Problem  16, Version  723011

Solve.

Problem  17, Version  723011

Given the following function, F, find the inverse of F.

Problem  18, Version  723011

The pH of a solution having a hydronium ion concentration, H3O,

in moles per liter, is given by the following equation.

Find the hydronium ion concentration if the pH is 6.2.

Problem  19, Version  723011

Given the following matrices:

Find the product of A and B.

Problem  20, Version  723011

Solve the following simultaneous equations.

Problem  21, Version  723011

Graph the following inequalities.

Problem  22, Version  723011

Arithmetic Sequence Formulae

Geometric Sequence Formulae

Is the following sequence arithmetic, geometric, or neither?

If arithmetic, what is the common difference, the general formula

for the nth term, and the sum of the first  8 terms?

If geometric, what is the common ratio, the general formula

for the nth term, and the sum of the first  8 terms?

If the geometric series converges, what is the sum of an infinite number of terms?

Arithmetic sequence

Problem  23, Version  723011

Does the following equation describe a line, a circle,

an ellipse, or a parabola?

If a circle, determine the radius and locate the center.

If an ellipse, locate the center and foci.

If a parabola, locate the vertex and focus.

In all cases, graph the equation and the determined points.

Problem  24, Version  723011

Calculate the the equation of the best-fit line

for the following set of points, [x,y].

Plot the points and the line.

Warning, the name changecoords has been redefined

Problem  25, Version  723011

Is the syllogism direct, indirect, or transitive reasoning and is the

argument a valid argument?

If John studies math two hours per day, then John passes math.

John studies math two hours per day,therefore John passes math.

The argument is DIRECT and VALID.

>