Equivalent forms of exponential expressions
- Description
- Determine whether pairs of exponential expressions are equivalent.
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Determine whether pairs of exponential expressions are equivalent. |
Timed Test
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Solve triangles using the law of cosines
- Description
- Solve missing triangle measures using the law of cosines.
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Solve missing triangle measures using the law of cosines. |
Timed Test
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Expand binomials
- Description
- Use the binomial theorem in order to expand integer powers of binomial expressions.
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Use the binomial theorem in order to expand integer powers of binomial expressions. |
Timed Test
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Divide polynomials with remainders: monomial divisors
- Description
- Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> is a polynomial <em><strong>b</strong></em> is a monomial, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>.
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Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> is a polynomial <em><strong>b</strong></em> is a monomial, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>. |
Timed Test
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Graph quadratics in standard form
- Description
- Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15.
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Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15. |
Timed Test
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Quadratic word problems (standard form)
- Description
- Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form.
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Solve real-world word problems that involve quadratic models. In this exercise, that models are given in standard form. |
Timed Test
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General triangle word problems
- Description
- Solve word problems that involve general triangles using trigonometry.
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Solve word problems that involve general triangles using trigonometry. |
Timed Test
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Rewrite exponential expressions
- Description
- Rewrite a given exponential expression in a specific desired form.
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Rewrite a given exponential expression in a specific desired form. |
Timed Test
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Divide polynomials with remainders: binomial divisors
- Description
- Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> is a polynomial <em><strong>b</strong></em> is a linear binomial, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>.
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Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> is a polynomial <em><strong>b</strong></em> is a linear binomial, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>. |
Timed Test
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Evaluate composite functions
- Description
- Given the formulas of two functions, evaluate the composition of the two functions at a given input.
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Given the formulas of two functions, evaluate the composition of the two functions at a given input. |
Timed Test
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Graph quadratics in factored form
- Description
- Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2).
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Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2). |
Timed Test
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Prove polynomial identities
- Description
- Determine whether given polynomial identities are true, and whether given proofs of such identities are valid.
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Determine whether given polynomial identities are true, and whether given proofs of such identities are valid. |
Timed Test
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Solve exponential equations using exponent properties
- Description
- Example: Solve 2^(3x+5) = 64^(x-7).
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Example: Solve 2^(3x+5) = 64^(x-7). |
Timed Test
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Use the Pythagorean identity
- Description
- Given the sine (or cosine) of an angle, find its cosine (or sine) using the Pythagorean identity.
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Given the sine (or cosine) of an angle, find its cosine (or sine) using the Pythagorean identity. |
Timed Test
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Divide polynomials with remainders
- Description
- Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> and <em><strong>b</strong></em> are polynomials, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>.
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Rewrite expressions of the form <em><strong>a(x)/b(x)</strong></em>, where <em><strong>a</strong></em> and <em><strong>b</strong></em> are polynomials, in the form <em><strong>q(x)+r(x)/b(x)</strong></em>, where <em><strong>q</strong></em> and <em><strong>r</strong></em> are polynomials and the degree of <em><strong>r</strong></em> is less than the degree of <em><strong>b</strong></em>. |
Timed Test
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Factor polynomials: complex numbers
- Description
- Identify correctly factored forms of given polynomials. Factorizations may use complex numbers.
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Identify correctly factored forms of given polynomials. Factorizations may use complex numbers. |
Timed Test
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Evaluate composite functions: graphs & tables
- Description
- Given the graphs, or some tables of values, of two functions, evaluate the composition of those functions at a given input.
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Given the graphs, or some tables of values, of two functions, evaluate the composition of those functions at a given input. |
Timed Test
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Graph quadratics in vertex form
- Description
- Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5.
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Graph quadratic functions that are given in the vertex form a(x+b)²+c. For example, graph y=-2(x-2)²+5. |
Timed Test
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Solve exponential equations using exponent properties (advanced)
- Description
- Example: Solve 32^(x/3) = 8^(x-12).
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Example: Solve 32^(x/3) = 8^(x-12). |
Timed Test
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Trig values of special angles
- Description
- Find the sine and cosine of special angles, which are angles whose trig values we can determine without the use of a calculator.
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Find the sine and cosine of special angles, which are angles whose trig values we can determine without the use of a calculator. |
Timed Test
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