Intermediate Objectives Please note that there are 400 ALEKS topics total. Some of the objective topics overlap with each and that is why there are more topics listed in this chart. Please use this chart and record the page number from your notebook when you take notes. This will make it easier to find your work at the end of the semester when you need it. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Intermediate Objective 1 (52 topics, due on September 14) Computing a percentage from a table of values Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction to a percentage: Denominator of 20, 25, or 50 Converting a fraction to a terminating decimal: Advanced Converting a fraction to a terminating decimal: Basic Converting a percentage to a fraction in simplest form Converting between percentages and decimals Decimal place value: Tenths and hundredths Division of a decimal by a power of ten Equivalent fractions Evaluating an expression with a negative exponent: Negative integer base Evaluating an expression with a negative exponent: Positive fraction base Evaluating expressions with exponents of zero Exponents and integers: Problem type 1 Exponents and integers: Problem type 2 Exponents and signed fractions Fractional part of a circle Fractional position on a number line Identifying numbers as integers or non‐integers Identifying numbers as rational or irrational Introduction to exponents Introduction to the power of a power rule of exponents Introduction to the power of a product rule of exponents Introduction to the product rule of exponents Introduction to the quotient rule of exponents Multiplication of a decimal by a power of ten Multi‐step word problem involving fractions and multiplication Ordering integers Ordering numbers with negative exponents Ordering numbers with positive exponents Plotting integers on a number line Plotting rational numbers on a number line Power of a power rule with negative exponents Power rules with positive exponents: Multivariate products Power rules with positive exponents: Multivariate quotients Product rule with negative exponents Product rule with positive exponents: Multivariate Quotient of expressions involving exponents Page # 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Quotient rule with negative exponents: Problem type 1 Rewriting an algebraic expression without a negative exponent Rounding decimals Scientific notation with negative exponent Scientific notation with positive exponent Simplifying a fraction Understanding the power rules of exponents Understanding the product rule of exponents Using a common denominator to order fractions Writing a mixed number as an improper fraction Writing a ratio as a percentage without a calculator Writing a signed number for a real‐world situation Writing an improper fraction as a mixed number Writing expressions using exponents Intermediate Objective 2 (47 topics, due on September 21) Equivalent fractions Absolute value of a number Addition or subtraction of fractions with different denominators Addition or subtraction of fractions with the same denominator Area of a square or a rectangle Area of a triangle Circumference and area of a circle Combining like terms in a quadratic expression Combining like terms: Integer coefficients Combining like terms: Whole number coefficients Converting between radical form and exponent form Cube root of an integer Decimal multiplication: Problem type 1 Degree and leading coefficient of a univariate polynomial Degree of a multivariate polynomial Domain and range from ordered pairs Estimating a square root Evaluating a linear expression: Integer multiplication with addition or subtraction Evaluating a quadratic expression: Integers Evaluating functions: Linear and quadratic or cubic Finding a percentage of a whole number without a calculator: Basic Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction: Problem type 1 Integer subtraction: Problem type 2 Integer subtraction: Problem type 3 Multiplication of 3 or 4 integers Multiplication of a decimal by a power of ten 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 Multiplication of a decimal by a whole number Perimeter of a square or a rectangle Properties of addition Properties of real numbers Signed decimal addition and subtraction with 3 numbers Simplifying a fraction Square root of a perfect square Square root of a rational perfect square Translating a phrase into a two‐step expression Translating a sentence by using an inequality symbol Translating a sentence into a one‐step equation Using a common denominator to order fractions Using distribution and combining like terms to simplify: Univariate Using distribution with double negation and combining like terms to simplify: Multivariate Variable expressions as inputs of functions Volume of a rectangular prism Writing a multi‐step inequality for a real‐world situation Writing a one‐step expression for a real‐world situation Writing an inequality for a real‐world situation Intermediate Objective 3 (48 topics, due on October 5) Factors Prime numbers Prime factorization Greatest common factor of 2 numbers Least common multiple of 2 numbers Word problem with common multiples Solving a word problem on proportions using a unit rate Addition or subtraction of fractions with different denominators Product of a unit fraction and a whole number Product of a fraction and a whole number: Problem type 1 Introduction to fraction multiplication Fraction multiplication Multi‐step word problem involving fractions and multiplication Order of operations with fractions: Problem type 1 Order of operations with fractions: Problem type 2 Writing an improper fraction as a mixed number Writing a mixed number as an improper fraction Addition of mixed numbers with the same denominator and carry Subtraction of mixed numbers with the same denominator and borrowing Addition of mixed numbers with different denominators and carry Subtraction of mixed numbers with different denominators and borrowing Mixed number multiplication Area of a piecewise rectangular figure 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 Area involving rectangles and circles Integer multiplication and division Multiplication of 3 or 4 integers Signed fraction multiplication: Basic Signed fraction multiplication: Advanced Signed decimal addition and subtraction with 3 numbers Distributive property: Integer coefficients Writing a multi‐step equation for a real‐world situation Simplifying a sum or difference of two univariate polynomials Simplifying a sum or difference of three univariate polynomials Multiplying a univariate polynomial by a monomial with a positive coefficient Multiplying a multivariate polynomial by a monomial Multiplying binomials with leading coefficients of 1 Multiplying binomials in two variables Multiplying conjugate binomials: Univariate Squaring a binomial: Univariate Multiplication involving binomials and trinomials in two variables Introduction to the GCF of two monomials Greatest common factor of two multivariate monomials Factoring out a monomial from a polynomial: Univariate Factoring out a monomial from a polynomial: Multivariate Adding rational expressions with common denominators and binomial numerators Adding or subtracting complex numbers Multiplying complex numbers Sum, difference, and product of two functions Intermediate Objective 4 (71 topics, due on October 19) Addition or subtraction of fractions with different denominators Adding rational expressions involving different quadratic denominators Adding rational expressions with denominators ax and bx: Advanced Adding rational expressions with denominators ax and bx: Basic Adding rational expressions with linear denominators without common factors: Advanced Adding rational expressions with linear denominators without common factors: Basic Adding rational expressions with multivariate monomial denominators: Advanced Addition of mixed numbers with different denominators and carry Converting a decimal to a proper fraction in simplest form: Advanced Converting a fraction to a repeating decimal: Advanced Converting a fraction to a repeating decimal: Basic Converting a fraction to a terminating decimal: Advanced Converting a fraction to a terminating decimal: Basic Converting a mixed number to a terminating decimal: Advanced 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 Converting a mixed number to a terminating decimal: Basic Dividing a polynomial by a monomial: Multivariate Dividing a polynomial by a monomial: Univariate Dividing numbers written in scientific notation: Basic Dividing rational expressions involving multivariate monomials Division involving a whole number and a fraction Division of a decimal by a 2‐digit decimal Division of a decimal by a whole number Factoring a difference of squares in one variable: Advanced Factoring a difference of squares in one variable: Basic Factoring a multivariate polynomial by grouping: Problem type 1 Factoring a multivariate polynomial by grouping: Problem type 2 Factoring a perfect square trinomial with leading coefficient 1 Factoring a product of a quadratic trinomial and a monomial Factoring a quadratic in two variables with leading coefficient greater than 1 Factoring a quadratic with leading coefficient 1 Factoring a quadratic with leading coefficient greater than 1: Problem type 1 Factoring a quadratic with leading coefficient greater than 1: Problem type 2 Factoring a sum or difference of two cubes Factoring a univariate polynomial by grouping: Problem type 1 Factoring a univariate polynomial by grouping: Problem type 2 Factoring out a monomial from a polynomial: Multivariate Factoring out a monomial from a polynomial: Univariate Factoring with repeated use of the difference of squares formula Fraction division Fraction multiplication Greatest common factor of two multivariate monomials Introduction to fraction multiplication Introduction to the GCF of two monomials Introduction to the LCM of two monomials Least common multiple of two monomials Mixed number division Mixed number multiplication Multiplying numbers written in scientific notation: Basic Multiplying rational expressions involving multivariate monomials Multiplying rational expressions involving quadratics with leading coefficients of 1 Order of operations with fractions: Problem type 1 Order of operations with fractions: Problem type 2 Polynomial long division: Problem type 1 Polynomial long division: Problem type 2 Polynomial long division: Problem type 3 Power and product rules with positive exponents Power of a power rule with negative exponents 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 Power rules with negative exponents Power rules with positive exponents: Multivariate products Power rules with positive exponents: Multivariate quotients Power, product, and quotient rules with negative exponents Product of a fraction and a whole number: Problem type 1 Product of a unit fraction and a whole number Product rule with negative exponents Product rule with positive exponents: Multivariate Signed fraction addition or subtraction: Advanced Signed fraction addition or subtraction: Basic Simplifying a ratio of multivariate polynomials Simplifying a ratio of polynomials: Problem type 1 Simplifying a ratio of polynomials: Problem type 2 Subtraction of mixed numbers with different denominators and borrowing Intermediate Objective 5 (52 topics, due on November 2) Order of operations with whole numbers Average of two numbers Complex fraction involving multivariate monomials Complex fraction involving univariate monomials Complex fraction without variables: Problem type 1 Complex fraction without variables: Problem type 2 Complex fraction: GCF factoring Complex fraction: Quadratic factoring Division involving a whole number and a fraction Finding the percentage increase or decrease: Advanced Finding the sale price without a calculator given the original price and percent discount Fraction division Mean of a data set Mixed number division Operations with absolute value: Problem type 2 Order of operations with fractions: Problem type 1 Order of operations with fractions: Problem type 2 Order of operations with integers Order of operations with integers and exponents Order of operations with whole numbers and exponents: Basic Order of operations with whole numbers and grouping symbols Product rule with negative exponents Product rule with positive exponents: Multivariate Rational exponents: Negative exponents and fractional bases Rational exponents: Non‐unit fraction exponent with a whole number base Rational exponents: Powers of powers with negative exponents Rational exponents: Products and quotients with negative exponents Rationalizing a denominator using conjugates: Integer numerator 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 Rationalizing a denominator using conjugates: Square root in numerator Rationalizing a denominator: Quotient involving higher radicals and monomials Rationalizing a denominator: Quotient involving square roots Rationalizing a denominator: Square root of a fraction Simplifying a higher radical expression: Multivariate Simplifying a higher root of a whole number Simplifying a product involving square roots using the distributive property: Advanced Simplifying a product of radical expressions: Multivariate Simplifying a product of radical expressions: Multivariate, fractional expressions Simplifying a radical expression with an even exponent Simplifying a radical expression with two variables Simplifying a sum or difference of radical expressions: Multivariate Simplifying the square root of a whole number less than 100 Special products of radical expressions: Conjugates and squaring Square root addition or subtraction Square root multiplication: Advanced Square root of a perfect square monomial The reciprocal of a number Using i to rewrite square roots of negative numbers Word problem on proportions: Problem type 1 Word problem on proportions: Problem type 2 Word problem on unit rates associated with ratios of whole numbers: Decimal answers Word problem with addition of 3 or 4 decimals and whole numbers Word problem with subtraction of a whole number and a decimal: Regrouping with zeros Intermediate Objective 6 (90 topics, due on November 16) Additive property of equality with fractions and mixed numbers Additive property of equality with a negative coefficient Additive property of equality with decimals Additive property of equality with integers Additive property of inequality with whole numbers Applying the percent equation: Problem type 1 Applying the percent equation: Problem type 2 Applying the quadratic formula: Exact answers Completing the square Computations from a circle graph Finding the original price given the sale price and percent discount Finding the perimeter or area of a rectangle given one of these values Finding the roots of a quadratic equation with leading coefficient 1 Finding the roots of a quadratic equation with leading coefficient greater than 1 Finding the side length of a rectangle given its perimeter or area Finding the value for a new score that will yield a given mean 287 288 289 290 291 292 293 294 295 296 297 298 299 Graphing a compound inequality on the number line Graphing a linear inequality on the number line Introduction to solving an absolute value equation Multiplicative property of equality with decimals Multiplicative property of equality with fractions Multiplicative property of equality with integers Multiplicative property of equality with signed fractions Multiplicative property of inequality with integers Roots of a product of polynomials Similar polygons Solving a compound linear inequality: Interval notation Solving a compound linear inequality: Problem type 1 Solving a decimal word problem using a linear equation of the form Ax + B = C Solving a decimal word problem using a linear equation with the variable on both sides Solving a decimal word problem using a two‐step linear inequality Solving a fraction word problem using a linear equation of the form Ax = B Solving a fraction word problem using a linear equation with the variable on both sides Solving a linear equation with several occurrences of the variable: Fractional forms with binomial numerators Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution Solving a linear equation with several occurrences of the variable: Variables on both sides and fractional coefficients Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear inequality with multiple occurrences of the variable: Problem type 3 Solving a proportion of the form a/(x+b) = c/x Solving a quadratic equation by completing the square: Exact answers Solving a quadratic equation needing simplification Solving a quadratic equation using the square root property: Exact answers, advanced Solving a quadratic equation using the square root property: Exact answers, basic Solving a quadratic equation with complex roots 316 Solving a radical equation that simplifies to a linear equation: One radical, basic 317 Solving a radical equation that simplifies to a linear equation: Two radicals Solving a radical equation that simplifies to a quadratic equation: One radical, 318 advanced 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 Solving a radical equation that simplifies to a quadratic equation: One radical, basic Solving a radical equation with two radicals that simplifies to sqrt(x) = a Solving a rational equation that simplifies to linear: Denominator x Solving a rational equation that simplifies to linear: Denominator x+a Solving a rational equation that simplifies to linear: Denominators a, x, or ax Solving a rational equation that simplifies to linear: Unlike binomial denominators Solving a rational equation that simplifies to quadratic: Binomial denominators and numerators Solving a rational equation that simplifies to quadratic: Binomial denominators, constant numerators Solving a rational equation that simplifies to quadratic: Proportional form, advanced Solving a two‐step equation with integers Solving a two‐step equation with signed decimals Solving a two‐step equation with signed fractions Solving a two‐step linear inequality: Problem type 1 Solving a two‐step linear inequality: Problem type 2 Solving a word problem using a quadratic equation with irrational roots Solving a word problem with three unknowns using a linear equation Solving an absolute value equation: Problem type 1 Solving an absolute value equation: Problem type 2 Solving an absolute value inequality: Problem type 3 Solving an equation to find the value of an expression Solving an equation using the odd‐root property: Problem type 1 Solving an equation using the odd‐root property: Problem type 2 Solving an equation with a root index greater than 2: Problem type 1 Solving an equation with a root index greater than 2: Problem type 2 Solving an equation with exponent 1/a: Problem type 1 Solving an equation with positive rational exponent Solving an equation written in factored form Solving equations with zero, one, or infinitely many solutions Solving for a variable in terms of other variables in a linear equation with fractions Solving for a variable in terms of other variables in a rational equation: Problem type 1 Solving for a variable in terms of other variables using addition or subtraction with division Solving for a variable in terms of other variables using addition or subtraction: Basic Solving for a variable in terms of other variables using multiplication or division: Basic Solving for a variable inside parentheses in terms of other variables Translating a sentence into a compound inequality 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 Using two steps to solve an equation with whole numbers Word problem on combined variation Word problem on direct variation Word problem on inverse variation Word problem on proportions: Problem type 1 Writing an equation that models variation Writing an inequality given a graph on the number line Intermediate Objective 7 (46 topics, due on November 30) Solving a word problem with two unknowns using a linear equation Application problem with a linear function: Finding a coordinate given the slope and a point Application problem with a linear function: Finding a coordinate given two points Choosing a graph to fit a narrative : Advanced Classifying systems of linear equations from graphs Finding a solution to a linear equation in two variables Finding inputs and outputs of a function from its graph Finding intercepts of a nonlinear function given its graph Finding slope given the graph of a line on a grid Finding slope given two points on the line Finding slopes of lines parallel and perpendicular to a line given in the form Ax + By = C Finding the slope and y‐intercept of a line given its equation in the form Ax + By = C Finding the slope and y‐intercept of a line given its equation in the form y = mx + b Finding x‐ and y‐intercepts of a line given the equation: Advanced Graphically solving a system of linear equations Graphing a line by first finding its slope and y‐intercept Graphing a line by first finding its x‐ and y‐intercepts Graphing a line given its equation in slope‐intercept form: Fractional slope Graphing a line given its equation in slope‐intercept form: Integer slope Graphing a line given its equation in standard form Graphing a line given its x‐ and y‐intercepts Graphing a line through a given point with a given slope Graphing a linear equation of the form y = mx Graphing a linear inequality in the plane: Slope‐intercept form Graphing a linear inequality in the plane: Standard form Graphing a linear inequality in the plane: Vertical or horizontal line Graphing a system of two linear inequalities: Basic Graphing a vertical or horizontal line Identifying solutions to a linear equation in two variables Identifying solutions to a system of linear equations Interpreting the graphs of two functions Plotting a point in the coordinate plane 393 Pythagorean Theorem 394 Reading a point in the coordinate plane 395 Scatter plots and correlation Solving a decimal word problem using a linear inequality with the variable on 396 both sides 397 Solving a system of linear equations that is inconsistent or consistent dependent Solving a system of linear equations using elimination with multiplication and 398 addition 399 Solving a system of linear equations using substitution 400 Table for a linear equation Writing an equation and drawing its graph to model a real‐world situation: 401 Advanced 402 Writing an equation in slope‐intercept form given the slope and a point 403 Writing an equation of a line given the y‐intercept and another point Writing equations of lines parallel and perpendicular to a given line through a 404 point 405 Writing the equation of the line through two given points 406 Writing the equations of vertical and horizontal lines through a given point Intermediate Objective 8 (64 topics, due on December 7) 407 Solving a word problem on proportions using a unit rate 408 Adding or subtracting complex numbers 409 Adding rational expressions involving different quadratic denominators Application problem with a linear function: Finding a coordinate given the slope 410 and a point 411 Computing a percent mixture 412 Computing unit prices to find the better buy 413 Converting between percentages and decimals in a real‐world situation 414 Converting between temperatures in Fahrenheit and Celsius Dividing rational expressions involving quadratics with leading coefficients 415 greater than 1 416 Estimating a tip without a calculator 417 Factoring a difference of squares in one variable: Advanced 418 Factoring a quadratic with leading coefficient greater than 1: Problem type 3 419 Finding the roots of a quadratic equation of the form ax^+bx=0 Finding the sale price without a calculator given the original price and percent 420 discount 421 Multiplying binomials in two variables 422 Polynomial long division: Problem type 2 423 Power and quotient rules with negative exponents: Problem type 2 424 Power rules with positive exponents: Multivariate quotients 425 Power, product, and quotient rules with negative exponents 426 Quotient of expressions involving exponents 427 Rational exponents: Products and quotients with negative exponents 428 Rationalizing a denominator using conjugates: Variable in denominator Simplifying a product involving square roots using the distributive property: 429 Advanced 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 Simplifying a radical expression with two variables Simplifying a ratio of polynomials: Problem type 2 Simplifying a sum or difference of radical expressions: Multivariate Solving a distance, rate, time problem using a linear equation Solving a distance, rate, time problem using a rational equation Solving a distance, rate, time problem using a system of linear equations Solving a fraction word problem using a linear equation with the variable on both sides Solving a one‐step word problem using the formula d = rt Solving a percent mixture problem using a linear equation Solving a percent mixture problem using a system of linear equations Solving a quadratic equation with complex roots Solving a radical equation with two radicals that simplifies to sqrt(x) = a Solving a rational equation that simplifies to quadratic: Factorable quadratic denominator Solving a tax rate or interest rate problem using a system of linear equations Solving a value mixture problem using a linear equation Solving a value mixture problem using a system of linear equations Solving a word problem involving rates and time conversion Solving a word problem using a quadratic equation with rational roots Solving a word problem using a system of linear inequalities Solving a word problem with two unknowns using a linear equation Solving a work problem using a rational equation Square roots of integers raised to even exponents Translating a phrase into a one‐step expression Translating a phrase into a two‐step expression Translating a sentence into a multi‐step equation Translating a sentence into a one‐step equation Word problem involving addition or subtraction of fractions with different denominators Word problem involving fractions and multiplication Word problem involving multiple rates Word problem on combined variation Word problem on direct variation Word problem on inverse proportions Word problem on inverse variation Word problem on proportions: Problem type 1 Word problem with decimal addition and multiplication Writing a one‐step expression for a real‐world situation Writing a signed number for a real‐world situation Writing an equation that models variation Writing equations of lines parallel and perpendicular to a given line through a point Writing ratios for real‐world situations Writing ratios using different notations