Test 2 Sample Questions
Math160
Algebra (12 mins)
X (2, 5, –1)
1.
The vector XY is (?, ?, ?)
2.
Solve 4x + (1, –1, 3) = (1, 3, –5) for x.
3.
If v = (11, 10, –2), then | v | = ?
4.
Which of the following vectors is not parallel to the others?
a = (6, 4, –8), b = (–3, –2, 4), c = (9, 6, –12), d = (3, –2, –4)
5.
If d = (6, –3, 2) then the unit vector d is (?, ?, ?).
6.
The mid-point of the line joining (3, 6, 1) to (9, –2, –7) is (?, ?, ?).
7.
The position vector of the point X on the line from P to Q such that
PX : XQ = 3 : 8 is: x = (? p + ? q) / ?
8.
If a = (2, –1, 3) and b = (4, 1, –2) then a . b = ? Are these vectors perpendicular?
9.
The points P, Q, X and Y have position vectors p, q, x and y.
If PXQY is a parallelogram, then (in terms of p, q and x) y = ?
10.
If u, v and w are vectors, then (u . v) w is: a) a scalar, b) a vector, c) not defined.
and (u . v) . w is: a) a scalar, b) a vector, c) not defined.
Y (0, 8, 4)
Calculus (12 mins)
1. 2. 3. The first three questions will require you to find the equation of a line in the form
y = ?x + ? given for example [gradient and y-intercept], or [two points on the line], or
[gradient and one point on the line].
4.
Given a straight-line graph, identify its equation from a choice of four.
5.
Find the difference quotient
f (a + h) − f (x)
for a given quadratic and value a.
h
0.5
Note for Q6 and Q7: to enter an answer of the form 3x – 13x
3x^0.5 – 13x^(-4)
–4
you need to type:
6.
Find
dy
1.5
−3
for y = 5x + 6x + 1 .
dx
7.
Find
dy
x7 − 5 .
for y =
dx
x3
8.
Find the equation of the tangent line to the graph of y = 4x3 at the point (2, 32).
9.
An object travels a distance 3t + 4t + 1 in time t. What is its speed when t = 2?
10.
Given values of f (7) and f ′ (7) , find the equation of the tangent line to y = f (x) at x = 7.
3
2