MA119 Learning Goals

There are in total learning goals. Check the goals you have mastered and click the following button to see your level of mastery.

Preliminaries

P1. Arithmetic

• I can add, subtract, multiply, divide and simplify fractions.

  • Sample 1 (117177)
  • Sample 2 (117182)
  • Sample 3 (613823)
  • Sample 4 (614175)
  • Sample 5 (614176)

• I can evaluate and simplify arithmetic expressions without the use of a calculator.

  • Sample 1 (140352)

P2. Integral Exponents

• I can demonstrate understanding of integral exponents of whole numbers.

  • Sample 1 (625190)

• I can use the properties of integral exponents to simplify and evaluate expressions with integral exponents.

  • Sample 1 (420859)
  • Sample 2 (123512)

P3. Polynomial Essentials

• I can identify the degree of a polynomial and describe coefficients.

  • Sample 1 (14066)

• I can differentiate between a “term” and a “factor”.

  • Sample 1 (1220894)

• I can evaluate algebraic expressions with given variable values.

  • Sample 1 (296)
  • Sample 2 (293)
  • Sample 3 (71057)

• I can simplify polynomials using the order of operations, associative, commutative, and distributive properties, and combining like terms.

  • Sample 1 (104810)
  • Sample 2 (150965)
  • Sample 3 (14087)
  • Sample 4 (134415)

P4. Geometry Essentials

• I can use the Pythagorean Theorem.

  • Sample 1 (2758)
  • Sample 2 (2759)
  • Sample 3 (2760)

• I know and can apply geometry formulas (perimeter/circumference/area/volume) related to squares, triangles, circles, and boxes.

  • Sample 1 (534317)
  • Sample 2 (743691)
  • Sample 3 (1033347)

Expressions

A1. Integer Exponents

• I can use the properties of integer exponents to simplify and evaluate expressions with integer exponents.

  • Sample 1 (212096)
  • Sample 2 (123505)
  • Sample 3 (3599)
  • Sample 4 (286981)
  • Sample 5 (287081)

A2. Factoring Essentials

• I can identify a greatest common factor (GCF) and use it to factor polynomials.

  • Sample 1 (124509)
  • Sample 2 (188408)
  • Sample 3 (189016)

• I can apply grouping method to factor a polynomial with four terms.

  • Sample 1 (188446)
  • Sample 2 (682796)

• I can apply the trial and error method to factor a trinomial.

  • Sample 1 (832089)
  • Sample 2 (189359)
  • Sample 3 (189360)
  • Sample 4 (189361)
  • Sample 5 (189363)

• I can factor a binomial using formulas (difference of squares, difference or sum of cubes).

  • Sample 1 (189373)
  • Sample 2 (191352)
  • Sample 3 (134492)
  • Sample 4 (189720)

• I can factor a polynomial completely using various methods.

  • Sample 1 (176138)
  • Sample 2 (194178)
  • Sample 3 (192356)
  • Sample 4 (281595)
  • Sample 5 (1446191)

• I can use substitution idea to factor a polynomial whose terms contain powers of another polynomial.

  • Sample 1 (957290)
  • Sample 2 (957226)
  • Sample 3 (998106)

A3. Rational Expressions

• I can determine the domain of a rational expression by identifying values that make the denominator zero.

  • Sample 1 (45296)
  • Sample 2 (1587158)

• I can use the equivalence property of rational expressions to simplify rational expressions.

  • Sample 1 (659817)
  • Sample 2 (758063)
  • Sample 3 (1083558)

• I can add, subtract, multiply, and divide rational expressions and express the result in reduced form.

  • Sample 1 (1456397)
  • Sample 2 (758133)
  • Sample 3 (1987)
  • Sample 4 (758137)
  • Sample 5 (217151)

• I can simplify complex rational expressions.

  • Sample 1 (40311)
  • Sample 2 (3079)
  • Sample 3 (657805)

A4. Radicals and Rational Exponents

• I can evaluate and simplify a radical without using a calculator.

  • Sample 1 (378674)
  • Sample 2 (436428)
  • Sample 3 (491951)
  • Sample 4 (966314)

• I can perform arithmetic operations on radical expressions.

  • Sample 1 (220360)
  • Sample 2 (287343)
  • Sample 3 (134495)
  • Sample 4 (756265)
  • Sample 4 (663014)

• I can express a radical using rational exponents and backward.

  • Sample 1 (269329)
  • Sample 2 (19891)
  • Sample 3 (280744)

• I can evaluate expressions with rational exponents.

  • Sample 1 (3973)
  • Sample 2 (134505)

• I can simplify rational exponents and radicals using the properties of (rational) exponents and radicals.

  • Sample 1 (674328)
  • Sample 2 (3986)
  • Sample 3 (782641)
  • Sample 3 (161602)

• I can rationalize the denominator or numerator of a given (radical) expression.

  • Sample 1 (756330)
  • Sample 2 (959969)
  • Sample 3 (910311)

A5. Complex Numbers

• I can perform arithmetic operations with complex numbers.

  • Sample 1 (3144)
  • Sample 2 (3145)
  • Sample 3 (3149)
  • Sample 4 (401478)
  • Sample 5 (129682)

• I can simply an expression involving powers of the imaginary unit (i) using $i^4=1$.

  • Sample 1 (71448)
  • Sample 2 (3551)

• I can evaluate polynomials and other functions at complex numbers.

  • Sample 1 (212126)
  • Sample 2 (1587687)

Equations

E1. Quadratic Equations

• I can simplify and solve quadratic equations by factoring.

  • Sample 1 (191434)
  • Sample 2 (191437)
  • Sample 3 (191439)
  • Sample 4 (191440)
  • Sample 5 (260939)

• I can solve a cubic equation by factoring.

  • Sample 1 (191446)
  • Sample 2 (29169)
  • Sample 3 (188366)

• I can complete the square for a quadratic expression, and use it to solve a quadratic equation.

  • Sample 1 (131849)
  • Sample 2 (2538)
  • Sample 3 (32705)
  • Sample 4 (79591)
  • Sample 5 (181145)

• I can simplify and solve quadratic equations by using the quadratic formula.

  • Sample 1 (2228)
  • Sample 2 (165353)
  • Sample 3 (2232)

• I can solve equations that can be written in quadratic form by substitution.

  • Sample 1 (254360)
  • Sample 2 (442835)

• I can build quadratic equations for word problems, solve the equations, and interpret the solutions in context.

  • Sample 1 (949915)
  • Sample 2 (511032)
  • Sample 3 (262159)
  • Sample 4 (1462990)
  • Sample 5 (1463105)
  • Sample 6 (1461407)

E2. Rational Equations

• I can solve rational equations.

  • Sample 1 (18633)
  • Sample 2 (311504)
  • Sample 3 (51502)
  • Sample 4 (51503)
  • Sample 5 (657791)

• I can identify and check for extraneous solutions.

  • Sample 1 (51506)
  • Sample 2 (18991)
  • Sample 3 (38400)
  • Sample 4 (44861)

• I can solve word problems involving rational equations.

  • Sample 1 (895901)
  • Sample 2 (61345)

• I can solve a literal equation for a specified variable.

  • Sample 1 (29561)
  • Sample 2 (29564)

E3. Radical Equations

• I can solve radical equations involving only one radical.

  • Sample 1 (19110)
  • Sample 2 (152748)
  • Sample 3 (1587849)
  • Sample 4 (287496)
  • Sample 5 (687537)

• I can identify and check for extraneous solutions.

  • Sample 1 (175995)
  • Sample 2 (175961)

• I can solve equations involving two radical terms.

  • Sample 1 (175994)
  • Sample 2 (175990)

• I can solve radical equations involving rational expressions.

  • Sample 1 (38406)
  • Sample 2 (442834)

• I can solve quadratic-like equations involving radicals.

  • Sample 1 (442833)
  • Sample 2 (1400099)

• I can solve word problems involving radical equations.

  • Sample 1 (97041)
  • Sample 2 (865033)
  • Sample 3 (895941)

E4. Absolute Value Equations

• I can evaluate absolute values and use properties to simplify expressions.

  • Sample 1 (327)
  • Sample 2 (1422045)

• I can solve simple absolute value equations involving one absolute value expression.

  • Sample 1 (7659)
  • Sample 2 (7666)
  • Sample 3 (7663)
  • Sample 4 (152608)
  • Sample 5 (687539)
  • Sample 6 (190456)

• I can solve absolute value equations involving two absolute value expressions.

  • Sample 1 (7667)
  • Sample 2 (7668)

E5. Solving Inequalities

• I can convert between set builder notation, interval notation, inequality notation, and graphical notation for subsets of real numbers.

  • Sample 1 (211373)
  • Sample 2 (7745)
  • Sample 3 (52539)
  • Sample 4 (52535)
  • Sample 5 (70096)
  • Sample 6 (57846)

• I can use properties of inequalities to solve linear inequalities and write the solution set in interval notation.

  • Sample 1 (38186)
  • Sample 2 (65462)
  • Sample 3 (352291)
  • Sample 4 (352303)

• I can solve compound linear inequalities and write the solution set in interval notation.

  • Sample 1 (7753)
  • Sample 2 (7751)
  • Sample 3 (7755)

E6. Systems of Linear Equations

• I can solve systems of linear equations in two variables.

  • Sample 1 (213951)
  • Sample 2 (59306)
  • Sample 3 (150824)

• I can identify inconsistent systems of linear equations in two variables.

  • Sample 1 (1151237)
  • Sample 2 (191459)

• I can identify dependent system of linear equations in two variables and express the solution in terms of one variable.

  • Sample 1 (115188)
  • Sample 2 (142417)

• I can solve a word problem involving a system of equations in two variables.

  • Sample 1 (332763)
  • Sample 2 (558399)
  • Sample 3 (53595)

Functions

F1. Function Essentials

• I can determine when relations are functions given a graph, table, or real-world situation.

  • Sample 1 (183310)
  • Sample 2 (647740)
  • Sample 3 (740315)
  • Sample 4 (742633)
  • Sample 5 (314074)

• I can define a function and use function notations correctly.

  • Sample 1 (194692)
  • Sample 2 (221904)
  • Sample 3 (647741)
  • Sample 4 (740316)
  • Sample 5 (490593)

• I can evaluate a function for a given input and find inputs for a given output.

  • Sample 1 (23809)
  • Sample 2 (38986)
  • Sample 3 (14302)
  • Sample 4 (1648)
  • Sample 5 (549003)

• I can evaluate and simplify expressions involving function notation, e.g. difference quotient.

  • Sample 1 (73979)
  • Sample 2 (74635)
  • Sample 3 (348429)
  • Sample 4 (1003530)

• I can find the domain and range of a function defined by a graph.

  • Sample 1 (1413244)
  • Sample 2 (53557)
  • Sample 3 (267727)
  • Sample 3 (40067)

• I can estimate and interpret intercepts, locate extremum, and determine intervals of increase/decrease and where a function is positive or negative using its graph.

  • Sample 1 (160177)
  • Sample 2 (20070)
  • Sample 3 (354480)

F2. Linear Functions

• I can find the slope and identify the type of slope (negative, positive, zero, undefined) of a line passing through two points.

  • Sample 1 (39022)

• I can find the slope and intercepts of a line from its equation or graph.

  • Sample 1 (39024)
  • Sample 2 (107019)
  • Sample 3 (39026)
  • Sample 4 (357483)

• I can write the equation of a linear function or a line (including vertical line) in the slope-intercept, the point-slope form, or the general form.

  • Sample 1 (685669)
  • Sample 2 (831101)
  • Sample 3 (357126)
  • Sample 4 (298149)
  • Sample 5 (19703)

• I can find equations of parallel or perpendicular lines.

  • Sample 1 (343370)
  • Sample 2 (173606)
  • Sample 3 (173612)
  • Sample 4 (173613)
  • Sample 5 (97494)

• I can construct a linear function model a real-world scenario and interpret values and results in context.

  • Sample 1 (274342)
  • Sample 2 (73756)
  • Sample 3 (53591)
  • Sample 4 (285167)

F3. Quadratic Functions

• I can find the vertex, axis of symmetry, intercepts, extremum of a quadratic function using its equation or graph.

  • Sample 1 (516195)
  • Sample 2 (965094)
  • Sample 3 (24021)
  • Sample 4 (32571)
  • Sample 5 (134514)
  • Sample 6 (134515)

• I can convert an equation of a quadratic function from standard form to vertex form.

  • Sample 1 (173318)
  • Sample 2 (933754)

• I can graph a quadratic function using its axis of symmetry, the vertex and intercepts.

  • Sample 1 (19227)
  • Sample 2 (19228)
  • Sample 2 (34267)

• I can write an equation for a quadratic function based its graph.

  • Sample 1 (15812)
  • Sample 2 (15950)

• I can model real-world scenarios using quadratic functions and interpret values and results in context.

  • Sample 1 (32649)
  • Sample 2 (677391)
  • Sample 3 (362527)
  • Sample 4 (362422)
  • Sample 5 (1184185)
  • Sample 6 (362527)

F4. Rational and Radical Functions

• I can find the domain of a rational function or a radical function.

  • Sample 1 (1587158)
  • Sample 2 (173634)
  • Sample 3 (24078)
  • Sample 4 (24079)
  • Sample 5 (287400)
  • Sample 6 (360900)

• I can solve word problems involving rational or radical functions and interpret values and results in context.

  • Sample 1 (647934)
  • Sample 2 (685709)
  • Sample 3 (390621)
  • Sample 4 (176332)
  • Sample 4 (1394474)

F5. Exponential Functions

• I can determine if a function is exponential or not.

  • Sample 1 (683611)

• I can find the domain and range of an exponential function.

  • Sample 1 (805589)
  • Sample 2 (805744)
  • Sample 3 (805756)

• I can determine whether an exponential function is growth or decay.

  • Sample 1 (1443302)

• I can evaluate exponential functions in the form (y=ab^x) and relate the meaning to real-world contexts.

  • Sample 1 (125769)
  • Sample 2 (125770)
  • Sample 3 (684417)
  • Sample 4 (790777)
  • Sample 5 (790789)

• I can set up exponential functions for compounding investments (with finite periods or continuously) and determine outcomes.

  • Sample 1 (1317138)
  • Sample 2 (126956)
  • Sample 3 (130624)
  • Sample 4 (14378)

F6. Logarithmic Functions

• I can convert between exponential and logarithmic forms.

  • Sample 1 (477435)
  • Sample 2 (355805)
  • Sample 3 (73194)
  • Sample 4 (23994)

• I can determine the value of a logarithmic function.

  • Sample 1 (984721)
  • Sample 2 (1356292)
  • Sample 3 (974975)

• I can find the domain of a logarithmic function.

  • Sample 1 (152158)
  • Sample 2 (748478)

• I can use basic properties of logarithms to evaluate logarithms.

  • Sample 1 (77595)
  • Sample 2 (134525)
  • Sample 3 (666698)

• I can use properties of logarithms to expand a logarithm and write a logarithmic expression as a single logarithm.

  • Sample 1 (129766)
  • Sample 2 (203356)
  • Sample 3 (392224)
  • Sample 4 (1451112)
  • Sample 5 (63323)
  • Sample 6 (35440)
  • Sample 7 (271539)

• I can evaluate a logarithm using a calculator and the base change property.

  • Sample 1 (13569)
  • Sample 2 (1499118)

F7. Exponential Equations

• I can solve a simple exponential equation (in linear form or with no constant terms).

  • Sample 1 (35076)
  • Sample 2 (100564)
  • Sample 3 (374702)

• I can solve a quadratic-like equation involving exponential expressions.

  • Sample 1 (1070076)
  • Sample 2 (537572)

• I can solve applied problems involving exponential equations or functions and interpret parameters and solutions in context.

  • Sample 1 (1563)
  • Sample 2 (1546294)
  • Sample 3 (100755)
  • Sample 4 (15919)
  • Sample 5 (51682)

F8. Logarithmic Equations

• I can solve a logarithmic equation and identify extraneous solutions.

  • Sample 1 (100545)
  • Sample 2 (14407)
  • Sample 3 (173872)
  • Sample 4 (173913)
  • Sample 5 (393168)
  • Sample 6 (393170)

• I can solve applied problems involving logarithmic equations or functions and interpret parameters and solutions in context.

  • Sample 1 (51673)