Gr12 Mathematics: Term test 1

<p>The average of the two numbers</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>The sequence increases</p> Signup and view all the answers

<p>They form a linear pattern</p> Signup and view all the answers

<p>Use the formula Tn = a + (n - 1)d</p> Signup and view all the answers

<p>The ratio between consecutive terms</p> Signup and view all the answers

<p>Tn = ar^(n-1)</p> Signup and view all the answers

<p>The square root of ab</p> Signup and view all the answers

<p>An exponential curve</p> Signup and view all the answers

<p>By checking if the ratio between consecutive terms is constant</p> Signup and view all the answers

<p>The sum of the terms of a sequence</p> Signup and view all the answers

<p>Sn</p> Signup and view all the answers

<p>S∞ = T1 + T2 + ...</p> Signup and view all the answers

<p>To represent the sum of terms in a sequence</p> Signup and view all the answers

<p>The starting index of the sequence</p> Signup and view all the answers

<p>Sn = a(1 - r^n) / (1 - r)</p> Signup and view all the answers

<p>-1 &lt; r &lt; 1</p> Signup and view all the answers

<p>S∞ = a / (1 - r)</p> Signup and view all the answers

<p>A sequence of numbers where each term is added by a constant value.</p> Signup and view all the answers

<p>Tn = a + (n - 1) d</p> Signup and view all the answers

<p>Writing the numbers in ascending and descending order and adding corresponding pairs of terms.</p> Signup and view all the answers

<p>5050</p> Signup and view all the answers

<p>A series where a known number of terms in a geometric sequence are summed.</p> Signup and view all the answers

<p>A series where an infinite number of terms in a geometric sequence are summed.</p> Signup and view all the answers

<p>When -1 &lt; r &lt; 1.</p> Signup and view all the answers

<p>y = ±√(x/a)</p> Signup and view all the answers

<p>Domain: ℝ+, Range: ℝ</p> Signup and view all the answers

<p>x ≥ 0 if a &gt; 0, x ≤ 0 if a &lt; 0</p> Signup and view all the answers

<p>Falls rapidly</p> Signup and view all the answers

<p>y = logb(x)</p> Signup and view all the answers

<p>$S_n = \frac{n}{2} (a + l)$</p> Signup and view all the answers

<p>The exponent to which a base must be raised to yield a number</p> Signup and view all the answers

<p>The function must be one-to-one.</p> Signup and view all the answers

<p>Increasing</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>Every vertical line intersects the graph at most once.</p> Signup and view all the answers

<p>A rule that associates each element of one set with at least one element of another set.</p> Signup and view all the answers

<p>loga(x/y) = loga(x) - loga(y)</p> Signup and view all the answers

<p>$S_n = \frac{n}{2} (2a + (n - 1) d)$</p> Signup and view all the answers

<p>loga(x^b) = b loga(x)</p> Signup and view all the answers

<p>It reverses the operation of a given function.</p> Signup and view all the answers

<p>$f^{-1}(x)$</p> Signup and view all the answers

<p>The graph of the inverse function is the reflection of the original function's graph across the line y = x.</p> Signup and view all the answers

<p>Multiple elements of the domain map to the same element of the range.</p> Signup and view all the answers

<p>Interchange x and y, then solve for y.</p> Signup and view all the answers

<p>( \log_a x = \frac{\log_b x}{\log_b a} )</p> Signup and view all the answers

<p>The line y = x</p> Signup and view all the answers

<p>x &gt; 0</p> Signup and view all the answers

<p>pH = -log10[H+]</p> Signup and view all the answers

<p>cos( - ) = cos cos + sin sin</p> Signup and view all the answers

<p>Using the distance formula and cosine rule</p> Signup and view all the answers

<p>Calculating loan repayments and interest rates</p> Signup and view all the answers

<p>A = P(1 + i)^n</p> Signup and view all the answers

<p>θ = sin⁻¹x + k × 360°</p> Signup and view all the answers

<p>$\sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>When no perpendicular height is given</p> Signup and view all the answers

<p>$\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>$\sin(2\alpha) = 2 \sin \alpha \cos \alpha$</p> Signup and view all the answers

<p>When three sides are given</p> Signup and view all the answers

<p>$\cos(2\alpha) = \cos^2 \alpha - \sin^2 \alpha$</p> Signup and view all the answers

<p>h = (d sin α) / (sin β)</p> Signup and view all the answers

<p>Infinitely many</p> Signup and view all the answers

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>Simplify the equation using algebraic methods and trigonometric identities</p> Signup and view all the answers

<p>When two angles and a side are given</p> Signup and view all the answers

<p>To determine where the function is positive or negative</p> Signup and view all the answers

<p>All of the above</p> Signup and view all the answers

<p>$\cos(\alpha - \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>h = (b sin α sin θ) / (sin(β + θ))</p> Signup and view all the answers

<p>$\cos(2\alpha) = 1 - 2 \sin^2 \alpha$</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>38</p> Signup and view all the answers

<p>2, 4, 8, 16, 32</p> Signup and view all the answers

<p>9</p> Signup and view all the answers

<p>7.5</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>The terms form a linear pattern</p> Signup and view all the answers

<p>Decreasing</p> Signup and view all the answers

<p>$T_n = ar^{n-1}$</p> Signup and view all the answers

<p>To denote the sum of a finite sequence</p> Signup and view all the answers

<p>The ratio between consecutive terms is constant</p> Signup and view all the answers

<p>$\sqrt{ab}$</p> Signup and view all the answers

<p>An exponential graph</p> Signup and view all the answers

<p>$S_n$</p> Signup and view all the answers

<p>$i$</p> Signup and view all the answers

<p>A finite series has a specific number of terms, while an infinite series has infinitely many terms</p> Signup and view all the answers

<p>To find the nth term of the sequence</p> Signup and view all the answers

<p>The sequence alternates in sign</p> Signup and view all the answers

<p>$S_n = \frac{a(1 - r^n)}{1 - r}$</p> Signup and view all the answers

<p>$-1 &lt; r &lt; 1$</p> Signup and view all the answers

<p>$S_\infty = \frac{a}{1 - r}$</p> Signup and view all the answers

<p>$T_n = a + (n - 1)d$</p> Signup and view all the answers

<p>Writing the numbers in ascending and descending order and adding corresponding pairs of terms</p> Signup and view all the answers

<p>$\frac{n(a + l)}{2}$</p> Signup and view all the answers

<p>A finite geometric series has a fixed number of terms, whereas an infinite geometric series has an infinite number of terms</p> Signup and view all the answers

<p>$T_n = a \cdot r^{n-1}$</p> Signup and view all the answers

<p>When $-1 &lt; r &lt; 1$</p> Signup and view all the answers

<p>$\frac{n(a + l)}{2}$</p> Signup and view all the answers

<p>$S_n = \frac{n}{2} [2a + (n - 1) d]$</p> Signup and view all the answers

<p>A rule that associates each element of one set with at least one element of another set.</p> Signup and view all the answers

<p>The function must be one-to-one.</p> Signup and view all the answers

<p>The graph of the inverse function is the reflection of the original function's graph across the line y = x.</p> Signup and view all the answers

<p>f^{-1}(x) = \frac{x - q}{a}</p> Signup and view all the answers

<p>An inverse function reverses the operation of a given function.</p> Signup and view all the answers

<p>f^{-1}(x)</p> Signup and view all the answers

<p>The common ratio must be less than 1.</p> Signup and view all the answers

<p>Every horizontal line intersects the graph at most once.</p> Signup and view all the answers

<p>S_n = \frac{n}{2} (a + l)</p> Signup and view all the answers

<p>f^(-1)(x) = log(x)</p> Signup and view all the answers

<p>y = 0</p> Signup and view all the answers

<p>cos(α - β) = cos α cos β + sin α sin β</p> Signup and view all the answers

<p>A = P(1 + i)^n</p> Signup and view all the answers

<p>y = ±√(x/a)</p> Signup and view all the answers

<p>sin(α + β) = sin α cos β + cos α sin β</p> Signup and view all the answers

<p>log_a(x) = log_b(x) / log_b(a)</p> Signup and view all the answers

<p>x ≥ 0</p> Signup and view all the answers

<p>y = b^x</p> Signup and view all the answers

<p>pH = -log10[H+]</p> Signup and view all the answers

<p>y = logb(x)</p> Signup and view all the answers

<p>The graph of the logarithmic function</p> Signup and view all the answers

<p>The exponent to which a base must be raised to yield a given value.</p> Signup and view all the answers

<p>Increasing</p> Signup and view all the answers

<p>loga(xy) = loga(x) + loga(y)</p> Signup and view all the answers

<p>loga(x^b) = b × loga(x)</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>loga(x/y) = loga(x) - loga(y)</p> Signup and view all the answers

<p>sin(α - β) = sin α cos β - cos α sin β</p> Signup and view all the answers

<p>cos(α + β) = cos α cos β - sin α sin β</p> Signup and view all the answers

<p>sin(2α) = 2 sin α cos α</p> Signup and view all the answers

<p>cos(2α) = cos^2 α - sin^2 α</p> Signup and view all the answers

<ol> <li>Simplify the equation, 2. Find the reference angle, 3. Use the CAST diagram, 4. Find angles within a specified interval</li> </ol> Signup and view all the answers

<p>To determine where the function is positive or negative</p> Signup and view all the answers

<p>sin(2α) = 2 sin α cos α</p> Signup and view all the answers

<p>cos(2α) = cos^2 α - sin^2 α</p> Signup and view all the answers

<p>Simplify, find the reference angle, use the CAST diagram, and find angles within a specified interval</p> Signup and view all the answers

<p>It helps to find all possible solutions to the equation</p> Signup and view all the answers

<p>h = FB tan β</p> Signup and view all the answers

<p>Area = (1/2)ab sin C</p> Signup and view all the answers

<p>When no right angle is given, and two sides and the included angle are given</p> Signup and view all the answers

<p>a = b sin A / sin B</p> Signup and view all the answers

<p>Draw a sketch of the problem</p> Signup and view all the answers

<p>a^2 = b^2 + c^2 - 2bc cos A</p> Signup and view all the answers

<p>When no perpendicular height is given</p> Signup and view all the answers

<p>Area = (1/2)ab sin C</p> Signup and view all the answers

<p>tan A = opposite side / adjacent side</p> Signup and view all the answers

<p>To find the area of a triangle</p> Signup and view all the answers

<p>31</p> Signup and view all the answers

<p>No, because the common difference is not constant</p> Signup and view all the answers

<p>y = dx + a</p> Signup and view all the answers

<p>-7</p> Signup and view all the answers

<p>150</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>8</p> Signup and view all the answers

<p>10</p> Signup and view all the answers

<p>2366</p> Signup and view all the answers

<p>4</p> Signup and view all the answers

<p>6</p> Signup and view all the answers

<p>195</p> Signup and view all the answers

<p>5</p> Signup and view all the answers

<p>2</p> Signup and view all the answers

<p>177147</p> Signup and view all the answers

<p>4</p> Signup and view all the answers

<p>4</p> Signup and view all the answers

<p>2, $-\sqrt{6}$, $-3\sqrt{6}$, ...</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>84</p> Signup and view all the answers

<p>T_n = ar^(n-1)</p> Signup and view all the answers

<p>S_n</p> Signup and view all the answers

<p>Sigma notation</p> Signup and view all the answers

<p>\sum_{i=m}^{n} T_i = T_m + T_{m+1} + ... + T_n</p> Signup and view all the answers

<p>The sequence alternates in sign</p> Signup and view all the answers

<p>An exponential curve</p> Signup and view all the answers

<p>Calculate the ratio between consecutive terms</p> Signup and view all the answers

<p>\frac{4}{3}</p> Signup and view all the answers

<p>S_n = (n/2)(2a + (n - 1)d)</p> Signup and view all the answers

<p>The function must be one-to-one.</p> Signup and view all the answers

<p>The graph of the inverse function is the reflection of the original function's graph about the line y = x.</p> Signup and view all the answers

<p>S_n = (n/2)(2a + (n - 1)d)</p> Signup and view all the answers

<p>f^{-1}(f(x)) = x</p> Signup and view all the answers

<p>A relation is a rule that associates each element of one set with at least one element of another set.</p> Signup and view all the answers

<p>Every vertical line intersects the graph at most once.</p> Signup and view all the answers

<p>f^{-1}(x)</p> Signup and view all the answers

<p>f^{-1}(x) = (y - q)/a</p> Signup and view all the answers

<p>Multiple elements of the domain map to the same element of the range.</p> Signup and view all the answers

<p>f^{-1}(x) = \sqrt{\frac{x}{a}} if x \geq 0</p> Signup and view all the answers

<p>y = log_2 x</p> Signup and view all the answers

<p>x \geq 0</p> Signup and view all the answers

<p>Increasing</p> Signup and view all the answers

<p>1</p> Signup and view all the answers

<p>It is always one-to-one</p> Signup and view all the answers

<p>It must be one-to-one</p> Signup and view all the answers

<p>f^{-1}(x)</p> Signup and view all the answers

<p>A logarithmic function</p> Signup and view all the answers

<p>a(1 - r^n) / (1 - r)</p> Signup and view all the answers

<p>y = x</p> Signup and view all the answers

<p>log_a x = (log_b x) / (log_b a)</p> Signup and view all the answers

<p>1/x</p> Signup and view all the answers

<p>A = P(1 + i)^n</p> Signup and view all the answers

<p>cos(alpha + beta) = cos alpha cos beta - sin alpha sin beta</p> Signup and view all the answers

<p>sin(alpha - beta) = sin alpha cos beta - cos alpha sin beta</p> Signup and view all the answers

<p>pH = -log[H+]</p> Signup and view all the answers

<p>A logarithmic curve</p> Signup and view all the answers

<p>Draw a sketch, consider the given information, apply trigonometric identities, and calculate the desired quantities</p> Signup and view all the answers

<p>h = d sin α tan β / sin β</p> Signup and view all the answers

<p>When no right angle is given, and either two sides and the included angle or three sides are given</p> Signup and view all the answers

<p>Area = (1/2)ac sin B</p> Signup and view all the answers

<p>h = b sin α sin θ / sin(β + θ)</p> Signup and view all the answers

<p>When no right angle is given, and either two sides and an angle (not the included angle) or two angles and a side are given</p> Signup and view all the answers

<p>Area = √(s(s-a)(s-b)(s-c))</p> Signup and view all the answers

<p>Find angles in the interval [0°, 360°] that satisfy the equation and add multiples of the period</p> Signup and view all the answers

<p>tan θ = h / d</p> Signup and view all the answers

<p>$\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>$\sin(2\alpha) = 2 \sin \alpha \cos \alpha$</p> Signup and view all the answers

<p>|r| &lt; 1</p> Signup and view all the answers

<p>$\cos(2\alpha) = \cos^2 \alpha - \sin^2 \alpha$</p> Signup and view all the answers

<p>$\sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>Using the sum and difference formulas</p> Signup and view all the answers

<p>To determine where a trigonometric function is positive or negative</p> Signup and view all the answers

<p>Find angles within a specified interval by adding or subtracting multiples of the period</p> Signup and view all the answers

<p>$\cos(\alpha - \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>To expand the trigonometric functions of sums and differences of angles</p> Signup and view all the answers

<p>35</p> Signup and view all the answers

<p>2</p> Signup and view all the answers

<p>10</p> Signup and view all the answers

<p>8</p> Signup and view all the answers

<p>The sequence is decreasing</p> Signup and view all the answers

<p>A straight line</p> Signup and view all the answers

<p>The sequence is linear</p> Signup and view all the answers

<p>To find the common difference</p> Signup and view all the answers

<p>4375</p> Signup and view all the answers

<p>4</p> Signup and view all the answers

<p>40</p> Signup and view all the answers

<p>-1 &lt; r &lt; 1</p> Signup and view all the answers

<p>a(r^n - 1) / (1 - r)</p> Signup and view all the answers

<p>6536</p> Signup and view all the answers

<p>3</p> Signup and view all the answers

<p>a / (1 - r)</p> Signup and view all the answers

<p>78</p> Signup and view all the answers

<p>a + (n - 1)d</p> Signup and view all the answers

<p>$T_n = ar^{n-1}$</p> Signup and view all the answers

<p>$\sqrt{ab}$</p> Signup and view all the answers

<p>An exponential curve</p> Signup and view all the answers

<p>Check if the ratio between consecutive terms is constant</p> Signup and view all the answers

<p>$S_n = T_1 + T_2 + ... + T_n$</p> Signup and view all the answers

<p>$S_\infty = T_1 + T_2 + T_3 + ...$</p> Signup and view all the answers

<p>To find the sum of a sequence</p> Signup and view all the answers

<p>The index of the term being summed</p> Signup and view all the answers

<p>$S_n = a(r^n - 1) / (r - 1)$</p> Signup and view all the answers

<p>$r &lt; 1$</p> Signup and view all the answers

<p>$\log_a x = \frac{\log_b x}{\log_b a}$</p> Signup and view all the answers

<p>y = x</p> Signup and view all the answers

<p>$\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$</p> Signup and view all the answers

<p>To calculate the monthly repayment</p> Signup and view all the answers

<p>A curve that opens upwards</p> Signup and view all the answers

<p>$S_n = rac{n}{2} (2a + (n - 1) d)$</p> Signup and view all the answers

<p>A = P(1 + i)^n</p> Signup and view all the answers

<p>The function must be one-to-one.</p> Signup and view all the answers

<p>pH = -log10[H+]</p> Signup and view all the answers

<p>$\sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$</p> Signup and view all the answers

<p>Every vertical line intersects the graph at most once.</p> Signup and view all the answers

<p>Interchange x and y, then solve for y.</p> Signup and view all the answers

<p>It undoes the operation of the original function.</p> Signup and view all the answers

<p>f^-1(x)</p> Signup and view all the answers

<p>The graph is reflected about the line y = x.</p> Signup and view all the answers

<p>y = √(x/a) if x ≥ 0</p> Signup and view all the answers

<p>A reflection about the line y = x</p> Signup and view all the answers

<p>Every horizontal line intersects the graph more than once.</p> Signup and view all the answers

<p>|r| &lt; 1</p> Signup and view all the answers

<p>A rule that associates each element of one set with at least one element of another set.</p> Signup and view all the answers

<p>$S = rac{a}{1 - r}$</p> Signup and view all the answers

<p>y = log(x)/log(2)</p> Signup and view all the answers

<p>f(x) = x^2</p> Signup and view all the answers

<p>The function must be one-to-one</p> Signup and view all the answers

<p>logₐ(x) = logᵦ(x) / logᵦ(a)</p> Signup and view all the answers

<p>Increasing and concave up</p> Signup and view all the answers

<p>The logarithmic function is the inverse of the exponential function</p> Signup and view all the answers

<p>x ≥ 0 if a &gt; 0</p> Signup and view all the answers

<p>sin(α - β) = sin(α)cos(β) - cos(α)sin(β)</p> Signup and view all the answers

<p>cos(α + β) = cos(α)cos(β) + sin(α)sin(β)</p> Signup and view all the answers

<p>sin(2α) = 2sin(α)cos(α)</p> Signup and view all the answers

<p>cos(2α) = cos^2(α) - sin^2(α)</p> Signup and view all the answers

<p>By using algebraic methods and trigonometric identities.</p> Signup and view all the answers

<p>To determine where the function is positive or negative.</p> Signup and view all the answers

<p>sin(α + β) = sin(α)cos(β) + cos(α)sin(β)</p> Signup and view all the answers

<p>cos(α - β) = cos(α)cos(β) + sin(α)sin(β)</p> Signup and view all the answers

<p>To determine the restricted values within a specified interval.</p> Signup and view all the answers

<p>θ = cos^-1 x + k ⋅ 360°</p> Signup and view all the answers

<p>It implies that there are infinitely many angles that satisfy a given trigonometric equation.</p> Signup and view all the answers

<p>Area = (1/2)ac sin B</p> Signup and view all the answers

<p>h = (d sin α) / (sin β) tan β</p> Signup and view all the answers

<p>h = (b sin α sin θ) / (sin(β + θ))</p> Signup and view all the answers

<p>|r| &lt; 1</p> Signup and view all the answers

<p>S = a / (1 - r)</p> Signup and view all the answers

<p>θ = tan^-1 x + k ⋅ 90°</p> Signup and view all the answers

<p>sin A / a = sin B / b = sin C / c</p> Signup and view all the answers

<p>a^2 = b^2 + c^2 - 2bc cos A</p> Signup and view all the answers

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate desired quantities</p> Signup and view all the answers