1. The correct answer is B. The y-intercept at x = 0 has the value f(x) = +3. For an x-intercept, the value of f(x) must be 0 for some real value of x, but f(x) in this case never has a value less than +3.
2. The correct answer is C. The set C corresponds to the values of x for which the area above the curve defined by f(x) is coincident with the area below the curve defined by g(x). This area contains all values bounded by the condition that f(x) = g(x), which in this case is true only at x = −√3 and x = +√3.
3. The correct answer is B. The total surface area of the cylinder is the sum of the two circular ends plus the outer surface of the body. The outer body can be represented as a plane rectangle of which two opposite sides meet at the same line, with the dimensions of the length and the circumference of the cylinder. The circumference is 2pr and the length is h. The area of each end of the cylinder is the area of a circle, pr2, and there are two ends, so the total area of the ends is 2pr2. The total surface area of the cylinder is therefore 2prh + 2pr2, or 2pr(h + r).
4. The correct answer is D. The cross-section of the prism is a right triangle with orthogonal sides of 2 cm. The hypotenuse side is, by Pythagorean Theorem, √8 or 2√2 cm. The surface area of the two ends is calculated as 2(1/2 bh), or 4 cm2. The surface area of the two orthogonal sides of the prism is 2(2 × 10) cm, or 40 cm2. The surface of the angle face of the prism is 2√2 × 10, or 20√2 cm2. Altogether the total surface area of the prism is therefore (44 + 20√2) cm2, or 2(22 + 10√2) cm2. The volume is calculated as (1/2 bh) l = 20 cm3.
5. The correct answer is B. For the stated values of a and b, the only set element common to all three sets is 1.
6. The correct answer is D. The first and third or the second and third branches of the circuit are represented as active in the second, fourth and eighth columns. But in the fourth column the first and second branches are indicated as active, negating the ‘Light on’ signal.
7. The correct answer is A. A maximum or minimum value of a function coincides with a point at which the slope of the tangent to the function is zero; that is, at the points at which the value of the derivative of the function is zero. For this function. dy/dx = 6x − 6, and dy/dx = 0 at x = 1. The value of the function y at x = 1 is 15.
8. The correct answer is B. Using the general formula for finding the roots of a quadratic equation: x = (−b ± √(b2 − 4ac)) / 2a, where a = 1, b = −2 and c = 3, substitute the values of a, b and c and complete the calculation.
9. The correct answer is C. The vector ‘dot product’ A●B is calculated as A●B = |A||B|cosθ, where |A| and |B| are the magnitudes or absolute values of the vectors A and B, and cosθ is the cosine of the angle between the two vectors A and B. The vectors both begin at the origin (0, 0). Their magnitudes are then calculated using the Pythagorean Theorem, and are found to be equivalent values of 17.09. The ratio of the y-coordinate to the respective calculated values of |A| and |B| determine the sin of the angle formed by the vectors and the x-axis. The difference between these two angles is the angle θ separating the two vectors. Substitution of the appropriate values into the formula A●B = |A||B|cosθ produces the value of the dot product A●B.
10. The correct answer is A. The mean range is calculated as the proportional average of the lowest value of each range and of the highest value of each range. The median range is the range in which there are an equal number of test scores in ranges greater than and less than that particular range. The mode range is the range containing the greatest number of test scores.