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Test Assessing Secondary Completion (TASC) Mathematics Syllabus

The Mathematics syllabus for Test Assessing Secondary Completion (TASC) in full: 6 chapters, 27 topics and 53 sub-topics, every one listed below, plus 59 Mathematics flashcards with answers.

6Chapters
27Topics
53Sub-topics
59Flashcards

Mathematics syllabus: all 6 chapters

Expand any chapter to see its topics and sub-topics.

  1. Number and Quantity

     5 topics
    • Operations with Rational Numbers
      • Integers, fractions, and decimals
      • Order of operations (PEMDAS)
    • Ratios, Rates, and Proportions
      • Setting up and solving proportions
      • Unit rates and scaling
    • Percentages and Applications
      • Percent increase and decrease
      • Interest, discount, tax, and tip problems
    • Exponents and Roots
      • Laws of exponents
      • Square and cube roots
      • Scientific notation
    • Units and Measurement
      • Unit conversions within and across systems
      • Dimensional analysis

  2. Algebra and Expressions

     5 topics
    • Algebraic Expressions
      • Evaluating and simplifying expressions
      • Combining like terms and distributive property
    • Linear Equations and Inequalities
      • Solving one- and two-step equations
      • Multi-step equations with variables on both sides
      • Solving and graphing inequalities
    • Systems of Linear Equations
      • Solving by substitution
      • Solving by elimination
      • Graphical interpretation of solutions
    • Polynomials and Factoring
      • Adding, subtracting, and multiplying polynomials
      • Factoring quadratics and common factors
    • Quadratic Equations
      • Solving by factoring
      • Using the quadratic formula

  3. Functions

     4 topics
    • Function Concepts and Notation
      • Domain and range
      • Evaluating functions and function notation
    • Linear Functions
      • Slope and rate of change
      • Slope-intercept and point-slope forms
      • Interpreting intercepts in context
    • Nonlinear and Quadratic Functions
      • Parabolas, vertex, and axis of symmetry
      • Comparing linear, quadratic, and exponential growth
    • Interpreting and Building Functions from Context
      • Modeling real-world situations with functions
      • Reading function behavior from graphs and tables

  4. Geometry

     5 topics
    • Lines, Angles, and Triangles
      • Angle relationships and parallel lines
      • Triangle properties and congruence
    • Perimeter, Area, and Circumference
      • Polygons and composite figures
      • Circles: area and circumference
    • Surface Area and Volume
      • Prisms, cylinders, and pyramids
      • Cones and spheres
    • The Pythagorean Theorem
      • Finding missing side lengths
      • Applications and distance on the plane
    • Coordinate Geometry
      • Distance and midpoint formulas
      • Slope between two points

  5. Statistics and Probability

     4 topics
    • Measures of Center and Spread
      • Mean, median, mode, and range
      • Effect of outliers on measures
    • Data Displays and Interpretation
      • Bar graphs, histograms, and line plots
      • Box plots and scatter plots
    • Probability of Events
      • Simple and compound probability
      • Independent and dependent events
    • Interpreting Two-Way Tables and Trends

  6. Test Strategy and the Calculator

     4 topics
    • Calculator and Non-Calculator Sections
      • Using the on-screen TI-30XS or handheld calculator
      • Estimation for the non-calculator portion
    • Using the TASC Mathematics Reference Sheet
      • Locating area, volume, and algebra formulas
    • Word Problem Strategies
      • Translating words into equations
      • Multi-step problem planning
    • Gridded-Response and Constructed-Response Items

Test Assessing Secondary Completion (TASC) Mathematics flashcards — 59 questions with answers

  1. What is the rule for the sign of a product or quotient of two nonzero rational numbers?

    Same signs give a positive result; different signs give a negative result. For example, $(-)\times(-)=+$ and $(+)\times(-)=-$.

  2. How do you add two fractions with unlike denominators, such as $\frac{2}{3}+\frac{1}{4}$?

    Rewrite each fraction with the least common denominator, then add the numerators: $\frac{2}{3}+\frac{1}{4}=\frac{8}{12}+\frac{3}{12}=\frac{11}{12}$.

  3. How do you divide by a fraction?

    Multiply by its reciprocal: $\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$.

  4. What is the order of operations used to evaluate a numerical expression?

    PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).

  5. What is a ratio, and how does it differ from a rate?

    A ratio compares two quantities of the same kind (e.g. $3:2$). A rate compares two quantities with different units, such as miles per hour ($\frac{60\text{ mi}}{1\text{ h}}$).

  6. What is a unit rate, and how do you find it?

    A unit rate is a rate with a denominator of 1. Find it by dividing the numerator by the denominator, e.g. $\frac{150\text{ mi}}{3\text{ h}}=50$ mi/h.

  7. What is a proportion, and how do you solve one?

    A proportion states two ratios are equal, $\frac{a}{b}=\frac{c}{d}$. Solve by cross-multiplying: $a\,d=b\,c$.

  8. Solve the proportion $\frac{x}{8}=\frac{3}{4}$.

    Cross-multiply: $4x=24$, so $x=6$.

  9. How do you convert a percent to a decimal and to a fraction? Use $45\%$ as an example.

    Divide by 100. As a decimal: $45\%=0.45$. As a fraction: $\frac{45}{100}=\frac{9}{20}$.

  10. What is the basic percent formula relating part, whole, and percent?

    $\text{part}=\text{percent}\times\text{whole}$, often written $\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}$.

  11. How do you compute percent change from an old value to a new value?

    $\text{percent change}=\frac{\text{new}-\text{old}}{\text{old}}\times 100\%$. A positive result is an increase; a negative result is a decrease.

  12. A $\$80$ item is discounted $25\%$. What is the sale price?

    Discount $=0.25\times 80=\$20$, so the sale price is $80-20=\$60$ (equivalently $0.75\times 80$).

  13. State the product and quotient rules for exponents with the same base.

    $a^{m}\cdot a^{n}=a^{m+n}$ and $\frac{a^{m}}{a^{n}}=a^{m-n}$.

  14. What do the rules $a^{0}$, $a^{-n}$, and $(a^{m})^{n}$ equal?

    $a^{0}=1$ (for $a\neq 0$), $a^{-n}=\frac{1}{a^{n}}$, and $(a^{m})^{n}=a^{mn}$.

  15. How is a fractional exponent related to a root?

    $a^{1/n}=\sqrt[n]{a}$ and $a^{m/n}=\sqrt[n]{a^{m}}=\left(\sqrt[n]{a}\right)^{m}$.

  16. Simplify $\sqrt{50}$ to simplest radical form.

    $\sqrt{50}=\sqrt{25\cdot 2}=5\sqrt{2}$.

  17. How many inches are in a foot, feet in a yard, and how do you convert units using a conversion factor?

    $12$ in $=1$ ft and $3$ ft $=1$ yd. Multiply by a fraction equal to 1 that cancels the unwanted unit, e.g. $5\text{ ft}\times\frac{12\text{ in}}{1\text{ ft}}=60$ in.

  18. List the metric prefixes kilo-, centi-, and milli- as powers of the base unit.

    kilo- $=10^{3}$, centi- $=10^{-2}$, milli- $=10^{-3}$ of the base unit. So $1$ km $=1000$ m and $1$ cm $=0.01$ m.

  19. What is the difference between a term, a coefficient, and a constant in an algebraic expression?

    A term is a single number or product of numbers and variables; a coefficient is the numerical factor of a term; a constant is a term with no variable. In $3x+5$, $3x$ and $5$ are terms, $3$ is a coefficient, and $5$ is a constant.

  20. What does the distributive property state, and how do you apply it to $3(x+4)$?

    $a(b+c)=ab+ac$. So $3(x+4)=3x+12$.

Show the other 39 Mathematics flashcards

  1. What are like terms, and how do you combine $5x+2-3x+7$?

    Like terms have the same variable raised to the same power. Combine them: $5x-3x=2x$ and $2+7=9$, giving $2x+9$.

  2. How do you solve a one-variable linear equation such as $2x+5=13$?

    Isolate the variable using inverse operations: subtract 5 to get $2x=8$, then divide by 2 to get $x=4$.

  3. What is the key rule when solving an inequality that involves multiplying or dividing by a negative number?

    Reverse the direction of the inequality sign. For example, $-2x<6$ becomes $x>-3$.

  4. Solve the inequality $3x-4\geq 11$.

    Add 4: $3x\geq 15$; divide by 3: $x\geq 5$.

  5. What are the three possible numbers of solutions for a system of two linear equations, and what does each mean graphically?

    One solution (lines intersect at one point), no solution (parallel lines), or infinitely many solutions (same line).

  6. Describe the substitution method for solving a system of linear equations.

    Solve one equation for one variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute to find the first.

  7. Solve the system $y=2x$ and $x+y=9$.

    Substitute: $x+2x=9$, so $3x=9$, $x=3$, and $y=2(3)=6$. Solution: $(3,6)$.

  8. Describe the elimination method for solving a system of linear equations.

    Add or subtract the equations (after scaling if needed) so that one variable cancels, solve for the remaining variable, then substitute back to find the other.

  9. What is a polynomial, and what is the degree of $4x^{3}-2x+7$?

    A polynomial is a sum of terms of the form $a x^{n}$ with whole-number exponents. The degree is the highest exponent, here $3$.

  10. How do you multiply two binomials using FOIL? Apply it to $(x+3)(x+2)$.

    Multiply First, Outer, Inner, Last terms and combine: $(x+3)(x+2)=x^{2}+2x+3x+6=x^{2}+5x+6$.

  11. Factor the trinomial $x^{2}+7x+12$.

    Find two numbers multiplying to $12$ and adding to $7$: $3$ and $4$. So $x^{2}+7x+12=(x+3)(x+4)$.

  12. What is the difference of squares factoring pattern?

    $a^{2}-b^{2}=(a+b)(a-b)$. For example, $x^{2}-9=(x+3)(x-3)$.

  13. What is the standard form of a quadratic equation, and what does the zero product property let you do?

    Standard form is $ax^{2}+bx+c=0$ with $a\neq 0$. The zero product property states that if a product equals zero, at least one factor is zero, so you can set each factor to 0 to solve.

  14. State the quadratic formula.

    $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ for $ax^{2}+bx+c=0$.

  15. What is the discriminant, and what does its sign tell you about the roots?

    The discriminant is $b^{2}-4ac$. If positive, there are two real roots; if zero, one real (repeated) root; if negative, no real roots.

  16. Solve $x^{2}-5x+6=0$ by factoring.

    $(x-2)(x-3)=0$, so $x=2$ or $x=3$.

  17. What is a function, and what does function notation $f(x)$ represent?

    A function assigns exactly one output to each input. $f(x)$ denotes the output value of the function $f$ for the input $x$.

  18. What are the domain and range of a function?

    The domain is the set of all allowed input values ($x$); the range is the set of all resulting output values ($y$ or $f(x)$).

  19. What is the vertical line test, and what does it determine?

    If any vertical line crosses a graph more than once, the graph is not a function. It tests whether each input has exactly one output.

  20. Evaluate $f(x)=2x^{2}-3$ at $x=4$.

    $f(4)=2(4)^{2}-3=2(16)-3=32-3=29$.

  21. What is the slope-intercept form of a linear function, and what does each part mean?

    $y=mx+b$, where $m$ is the slope (rate of change) and $b$ is the $y$-intercept (value of $y$ when $x=0$).

  22. How do you compute the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$?

    $m=\dfrac{y_2-y_1}{x_2-x_1}$, the change in $y$ over the change in $x$.

  23. What is the slope of a line that goes through $(1,2)$ and $(5,10)$?

    $m=\dfrac{10-2}{5-1}=\dfrac{8}{4}=2$.

  24. How can you tell if a function is linear or nonlinear from a table of values?

    A function is linear if it has a constant rate of change (equal $\Delta y$ for equal $\Delta x$); otherwise it is nonlinear.

  25. What is the shape of the graph of a quadratic function, and what is its turning point called?

    The graph of $y=ax^{2}+bx+c$ is a parabola; its turning point is the vertex. It opens upward if $a>0$ and downward if $a<0$.

  26. How do you find the $x$-coordinate of the vertex of $y=ax^{2}+bx+c$?

    $x=-\dfrac{b}{2a}$; substitute it back into the function to get the $y$-coordinate.

  27. When building a linear function from a real-world context, what do the slope and $y$-intercept typically represent?

    The slope represents the constant rate of change (per-unit amount), and the $y$-intercept represents the starting or fixed initial value.

  28. A taxi charges a $\$3$ flat fee plus $\$2$ per mile. Write a function for the cost $C$ of riding $m$ miles.

    $C(m)=2m+3$, where $3$ is the fixed fee and $2$ is the rate per mile.

  29. What are complementary angles and supplementary angles?

    Complementary angles sum to $90^{\circ}$; supplementary angles sum to $180^{\circ}$.

  30. What is the sum of the interior angles of any triangle, and how are triangles classified by their angles?

    The interior angles sum to $180^{\circ}$. By angle: acute (all $<90^{\circ}$), right (one $=90^{\circ}$), obtuse (one $>90^{\circ}$).

  31. What does it mean for two triangles to be similar, and what is true about their sides?

    Similar triangles have equal corresponding angles and proportional corresponding sides (the same shape, possibly different size).

  32. Give the formulas for the perimeter and area of a rectangle with length $l$ and width $w$.

    Perimeter $P=2l+2w$; area $A=lw$.

  33. What are the formulas for the area of a triangle and the circumference and area of a circle?

    Triangle area $A=\frac{1}{2}bh$. Circle circumference $C=2\pi r$; circle area $A=\pi r^{2}$.

  34. What is the area of a circle with radius $5$? Leave your answer in terms of $\pi$.

    $A=\pi r^{2}=\pi(5)^{2}=25\pi$.

  35. Give the volume formulas for a rectangular prism and a cylinder.

    Rectangular prism: $V=lwh$. Cylinder: $V=\pi r^{2}h$.

  36. What is the formula for the surface area of a rectangular prism with dimensions $l$, $w$, and $h$?

    $SA=2lw+2lh+2wh$, the sum of the areas of all six faces.

  37. What is the volume of a sphere of radius $r$?

    $V=\frac{4}{3}\pi r^{3}$.

  38. State the Pythagorean theorem and what each variable represents.

    $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of a right triangle and $c$ is the hypotenuse (the side opposite the right angle).

  39. A right triangle has legs of length $3$ and $4$. Find the hypotenuse.

    $c=\sqrt{3^{2}+4^{2}}=\sqrt{9+16}=\sqrt{25}=5$.

Test Assessing Secondary Completion (TASC) Mathematics FAQ

What is in the Test Assessing Secondary Completion (TASC) Mathematics syllabus?

Test Assessing Secondary Completion (TASC) Mathematics is split into 6 chapters: Number and Quantity, Algebra and Expressions, Functions, Geometry, Statistics and Probability and Test Strategy and the Calculator. Together they contain 27 topics and 53 sub-topics.

How many chapters are in Test Assessing Secondary Completion (TASC) Mathematics?

6 chapters, containing 27 topics and 53 sub-topics. The largest chapter is Number and Quantity, with 5 topics.

Are there flashcards for Test Assessing Secondary Completion (TASC) Mathematics?

Yes — a 59-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.