Test Assessing Secondary Completion (TASC) Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in Test Assessing Secondary Completion (TASC), not a summary of it.

1. 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. 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. 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. 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. 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. 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

Mathematics flashcards for Test Assessing Secondary Completion (TASC)

21 of 59 cards from the Mathematics deck — real questions with worked 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 $3(x+4)=3x+12$.

21. 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 $2x+9$.

See more Mathematics flashcards →

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