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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1851. |
State whether the given measurements determine zero, one, or two triangles. B = 84°, b = 28, c = 25? |
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Answer» State whether the given measurements determine zero, one, or two triangles. B = 84°, b = 28, c = 25? Solution: |
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| 1852. |
Identify the surface with the given vector equation. r(s, t) = s sin(4t), s2, s cos(4t) |
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Answer» Identify the surface with the given vector equation. r(s, t) = s sin(4t), s2, s cos(4t) Solution: |
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| 1853. |
Express the series in summation notation, 2 + 4 + 6 + 8 + 10 + 12 |
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Answer» Express the series in summation notation, 2 + 4 + 6 + 8 + 10 + 12 Solution: |
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| 1854. |
What divisor is represented by the synthetic division below? -5,5,x + 5,x - 5. |
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Answer» What divisor is represented by the synthetic division below?
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| 1855. |
Find dy/dx and d2y/dx2? x = 5 sint, y = 6 cost, 0 < t < 2π |
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Answer» Find dy/dx and d2y/dx2? x = 5 sint, y = 6 cost, 0 < t < 2π Solution: |
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| 1856. |
Graph the function. How is the graph a translation of f(x) = x2? y = (x -1)2 + 3 f(x) translated down 3 unit(s) and translated to the right 1 unit(s) f(x) translated down 3 unit(s) and translated to the left 1 unit(s) f(x) translated up 3 unit(s) and translated to the left 1 unit(s) f(x) translated up 3 unit(s) and translated to the right 1 unit(s) |
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Answer» Graph the function. How is the graph a translation of f(x) = x2? y = (x -1)2+ 3 Solution: |
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| 1857. |
How do you graph the inequality 6x + 3y > 12? |
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Answer» How do you graph the inequality 6x + 3y > 12? Solution: |
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| 1858. |
Find the volume of the solid formed by revolving the region bounded by the graphs of y = x3, x = 2, and y = 1 about the y-axis. |
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Answer» Find the volume of the solid formed by revolving the region bounded by the graphs of y = x3, x = 2, and y = 1 about the y-axis. Solution: |
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| 1859. |
Use summation notation to write the series 2+4+6+8 for 10 terms |
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Answer» The sum of the series2+4+6+8 for 10 terms is 110. The sum of the series can be easily calculated by using a summation formula for the nthterm of the series. |
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| 1860. |
Solve the following system by any method. 8x + 9y = -5 and -8x - 9y = 5 |
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Answer» Solve the following system by any method. 8x + 9y = -5 and -8x - 9y = 5 Solution: |
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| 1861. |
Find the linear approximation of the following function at (x, y, z) = (3, 2, 6).f(x, y) = √(x2+ y2 + z2) |
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Answer» Find the linear approximation of the following function at (x, y, z) = (3, 2, 6). f(x, y) = √(x2 + y2 + z2) Solution: |
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| 1862. |
Find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 2π |
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Answer» Find the exact length of the polar curve. r =θ2, 0 ≤ θ ≤ 2π Solution: |
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| 1863. |
What function is represented below? f(x) = (1/4)x + 2 f(x) = (1/4)x + 2 f(x) = (1/4)x - 2 f(x) = (1/4)x - 2 |
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Answer» What function is represented below? f(x) = (1/4)x + 2f(x) = (1/4)x+ 2 f(x) = (1/4)x - 2f(x) = (1/4)x- 2
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| 1864. |
Solve the given differential equation by undetermined coefficients. y(4) + 2y'' + y = (x -5)2 |
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Answer» Solve the given differential equation by undetermined coefficients. y(4) + 2y'' + y = (x - 5)2 Solution: |
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| 1865. |
If the quadratic formula is used to solve 2x(x + 5) = 4, what are the solutions? |
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Answer» If the quadratic formula is used to solve 2x(x + 5) = 4, what are the solutions? Solution: |
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| 1866. |
Suppose c and d vary inversely, and d = 2 when c = 17. Write an equation that models the variation? Find d when c = 68 |
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Answer» Suppose c and d vary inversely, and d = 2 when c = 17. Write an equation that models the variation? Find d when c = 68 Solution: |
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| 1867. |
Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1 |
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Answer» Find the exact length of the curve. y = 3 + 2x3/2, 0 ≤ x ≤ 1 Solution: |
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| 1868. |
What is the slope of a line passing through the points (2, 5) and (0, -4)? |
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Answer» What is the slope of a line passing through the points (2, 5) and (0, -4)? Solution: |
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| 1869. |
The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon? |
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Answer» The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon? Solution: |
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| 1870. |
The function f(x) is given by the set of ordered pairs. {(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)}.Which equation is true? f of negative 10 = 1 f of 2 = negative 10 f of 0 = 6 f of 1 = negative 10 |
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Answer» The function f(x) is given by the set of ordered pairs. {(1, 0), (-10, 2), (0, 6), (3, 17), (-2, -1)}. Which equation is true? Solution: |
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| 1871. |
What are the possible rational zeros of f(x) = 2x3 - 15x2 + 9x + 22? |
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Answer» What are the possible rational zeros of f(x) = 2x3- 15x2 + 9x + 22? Solution: |
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| 1872. |
Simplify m - {n + [p - (m + n - p)]}. |
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Answer» Simplify m - {n + [p - (m + n - p)]}. Solution: |
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| 1873. |
Find the volume of the solid in the first octant bounded by the cylinder z = 16 - x2 and the plane y = 5? |
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Answer» Find the volume of the solid in the first octant bounded by the cylinder z = 16 - x2 and the plane y = 5? Solution: |
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| 1874. |
Find dy/dx by implicit differentiation. x2 - 6xy + y2 = 6 |
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Answer» Find dy/dx by implicit differentiation. x2- 6xy + y2= 6 Solution: |
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| 1875. |
72 is what percent of 480? write and solve an equation to solve the problem. |
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Answer» 72 is what percent of 480? write and solve an equation to solve the problem. Solution: |
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| 1876. |
A student was asked to find the equation of the tangent plane to the surface determined by z = x3- y4 at the point (x, y) = (1, 3). |
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Answer» A student was asked to find the equation of the tangent plane to the surface determined by z = x3- y4at the point (x, y) = (1, 3). Solution: |
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| 1877. |
What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26, … |
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Answer» What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26, … Solution: |
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| 1878. |
Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. |
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Answer» Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. Solution: |
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| 1879. |
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) Find the local minimum and maximum values of f. local minimum value local maximum value. Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.) |
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Answer» Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4ln(x) Solution: |
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| 1880. |
Find the arc length function for the curve y = 2x3/2 with starting point p0(25, 250). |
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Answer» Find the arc length function for the curve y = 2x3/2 with starting point p0(25, 250). Solution: |
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| 1881. |
The function f(x) = (x - 4)(x - 2) is shown. What is the range of the function? |
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Answer» The function f(x) = (x - 4)(x - 2) is shown. What is the range of the function? Solution: |
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| 1882. |
In right triangle ABC, ∠C is a right angle and sin A = sin B. What is m∠a? |
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Answer» In right triangle ABC, ∠C is a right angle and sin A = sin B. What is m∠a? Solution: |
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| 1883. |
Which is one way to check out the answer to 120 ÷ 4 = 30? 120 × 4 = 30 30 × 120 = 4 30 ÷ 4 = 120 30 × 4 = 120 |
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Answer» Which is one way to check out the answer to 120 ÷ 4 = 30? Solution: |
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| 1884. |
Points J and K are midpoints of the sides of triangle FGH. What is the value of y? J and K are the midpoints of the sides ΔFGH. Line segments GJ and JH are congruent. Line segments HK and KF are congruent. The Length of JK is 2y + 5 and the length of GF is 5y + 3. What is the value of y? |
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Answer» Points J and K are midpoints of the sides of triangle FGH. What is the value of y? Solution: |
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| 1885. |
Use the equations to find ∂z/∂x and ∂z/∂y. x2+ 4y2 + 3z2 = 1 |
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Answer» Use the equations to find ∂z/∂x and ∂z/∂y. x2+ 4y2+ 3z2= 1 Solution: |
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| 1886. |
If h(x) = x - 7 and g(x) = x2, which expression is equivalent to g(h(5))? (5 - 7)2 (5)2 - 7 (5)2(5 - 7) (5 - 7)x2 |
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Answer» If h(x) = x - 7 and g(x) = x2, which expression is equivalent to g(h(5))? Solution: |
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| 1887. |
Circle O is shown. Line segments AC and BD are diameters. The measure of arc AB is (3x minus 70) degrees and the measure of arc DC is (x + 10) degrees. What is mArc BC? |
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Answer» Circle O is shown. Line segments AC and BD are diameters. The measure of arc AB is (3x minus 70) degrees and the measure of arc DC is (x + 10) degrees. What is mArc BC?
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| 1888. |
What is the result of the following expression? 10 + 5 * 3 - 20 |
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Answer» What is the result of the following expression? 10 + 5 * 3 - 20 Solution: |
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| 1889. |
Find an equation for the nth term of the sequence. -4, -16, -64, -256, … |
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Answer» Find an equation for the nth term of the sequence. -4, -16, -64, -256, … Solution: |
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| 1890. |
In triangle ABC, a = 9, c = 5, and B = 120°. Find b2. |
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Answer» In triangle ABC, a = 9, c = 5, and B = 120°. Find b2. Solution: |
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| 1891. |
Find the derivative of the function using the definition of derivative. g(x) = 1 - x |
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Answer» Find the derivative of the function using the definition of derivative. g(x) = 1 - x Solution: |
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| 1892. |
Solve this quadratic equation using the quadratic formula. 3x2+ 5x + 1 = 0 |
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Answer» Solve this quadratic equation using the quadratic formula. 3x2+ 5x + 1 = 0 Solution: |
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| 1893. |
Find the perimeter of triangle ABC, with coordinates A(-3, 0), B(0, 4), and C(3, 0). |
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Answer» Find the perimeter of triangle ABC, with coordinates A(-3, 0), B(0, 4), and C(3, 0). Solution: |
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| 1894. |
The equation of a graph is 4x - 3y = 5. What is the x-intercept? |
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Answer» The equation of a graph is 4x - 3y = 5. What is the x-intercept? Solution: |
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| 1895. |
What is the slope of the line passing through the points (-3, 4) and (2, -1)? |
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Answer» What is the slope of the line passing through the points (-3, 4) and (2, -1)? Solution: |
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| 1896. |
Prove that the sum of the measures of the interior angles of a triangle is 180° |
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Answer» Prove that the sum of the measures of the interior angles of a triangle is 180° Solution: |
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| 1897. |
Solve the system using elimination. 2x - 2y = -8 and x + 2y = -1 |
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Answer» Solve the system using elimination. 2x - 2y = -8 and x + 2y = -1 Solution: |
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| 1898. |
Find the slope and the y-intercept of the equation y - 3(x - 1) = 0. |
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Answer» Find the slope and the y-intercept of the equation y - 3(x - 1) = 0. Solution: |
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| 1899. |
Find an equation for the nth term of the arithmetic sequence. 9, 11, 13, 15, … |
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Answer» Find an equation for the nth term of the arithmetic sequence. 9, 11, 13, 15, … Solution: |
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| 1900. |
The equation of the circle whose center is at (2, 1) and radius is 3 is |
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Answer» The equation of the circle whose center is at (2, 1) and radius is 3 is Solution: |
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