Welcome to your Grade 12 2005 maths
1.
If {an} is a sequence such that a1 = 2, and an+1= an + 4 for all n ≥ 1, then 
is equal to :
3.
If f(x) =e2x + x - 3 cosx, then what is f''(x)?
4.
Which one of the following intervals does f(x) = x4 + 4x increase?
5.
Which one of the following is the simplest form of
Which one of the following is the simplest form of 
6.
If Z = cos (π /10) + isin (π/10), then what is the value of Z5?
7.
What is the value of ∣ x ∣ + 2x if x ≤0 ?
9.
Suppose that A and B are 3 x 3 matrices, I is the identity matrix of order 3 such that AB=2I. If det B= ∣ B ∣= 6. What is det (AT)?
10.
What is the 50th term of the sequence 3, 10, 17, 24, 31,�?
11.
For real members x and y, which one of the following statements is true?
12.
Which one of the following functions has NO vertical asymptote?
13.
Let p, q and r be propositions such that p⇒(r ∨ ¬q) is false. Then, which one of the following propositions is true?
15.
If x2 - 6x + y2 + k = 0 is equation of a circle with radius 2, then what is the value of k?
16.
If a line with angle of inclination of 3 π/4 passes through (0, 1), which one of the following is the equation of the line?
20.
Among students who took a quiz, 15 students scored 6, 20 students scored 7, 10 students scored 8 and 5 students scored 10. What is the average score of the students?
21.
A parabola with focus (3, -1) has directrix y = 3. Which one of the following is the equation of the parabola?
22.
How many four digit even numbers can be formed from 1, 2, 3, 4 and 5 if the numbers start with 3?
23.
A satellite moves along a hyperbolic curve whose horizontal transverse axis is 24 km and an asymptote y = 5/12 x + 2. Then, what is the eccentricity of the hyperbola?
25.
At which valeu(s) of x does f(x) = 0.25 x4 -2x2 have a local maximum?
26.
In the set of complex numbers, which one of the following is the solution set of Z3 - iZ2 + 2Z = 0?
27.
The population of certain country is currently 80 million with growth rate of 2% per year.
28.
The volume V of a melting ice cube after t seconds is V= 2000 - 40t + 0.2t2 (in cm3). How fast is the volume changing when t=40 seconds?
32.
Which one of the following is equal to ∫(1+ x)3x dx?
33.
A committee consisting of 3 students is to be selected from 10 candidates among which 4 are girls. What is the probability that at least one girl is selected?
34.
A group of six students take their seats at random in a round table for a discussion. What is the probability that two specific students do NOT sit together?
36.
The mark that students scored in an examination is grouped in class intervals as shown in the following table.
37.
A box seen below is to have a square base, an open top and volume of 32 cubic units. If x is the length of each side of its base and y is its height, how many units should x and y be in order to make the box with the smallest amount of material?
39.
Consider the following argument:
41.
A box contains 5 white, 6 red and 4 black balls of all identical size. If 3 balls are randomly taken out of the box after the other, what is the probability that the first ball is white and both the second and third balls are red?
42.
Which one of the following is the equation of the line tangent to the graph of f(x) = 1/(x+1) + cosx at (0,f(0))?
47.
Suppose f is differentiable on (-∞,∞) and the graph of its derivative is as shown below. Which one of the following is true about f ?
48.
Which one of the following is true about the derivative of f(x) = x∣x∣?
49.
What is the area of the region between the graphs of y = x2 and y = -x + 2, where 0 ≤ x ≤ 2 ?
50.
For what value of b does the parabola p(x) = ax2 + x + b pass through the points (-1, 5) and (2, -1)?
52.
Which one of the following is equal to sec(π/2 -x) sin3 x + cos2x?
54.
What is the solution of cos2 x + 0.5 sin2x=1 in the interval [0, 2π)?
56.
one of the following points is closer to the sphere x2 + y2 + z2 - 2x + 6z + 9 = 0 ?
57.
Which one of the following describes the principle of Mathematical Induction on a set of natural numbers?
58.
What is the cot(arc sinx) if 0 < x< 1?
60.
A line given by a vector equation r(t)=(0, 3) + t(1, 1) is tangent to a circle at point (0,3). If the radius of the circle is ?2 which one of the following is the center of the circle?
61.
Suppose the following statements are the premises of an argument.
62.
What is the image of the ellipse whose equation is 2(x + 2)2 + (y - 1)2 = 2 under a translation that takes (2, 1) to (4, 0) followed by a rotation of 900?
65.
Which one of the following is necessarily true?
