Macquarie University
Your mark:
STAT171 – 2011
_____ 41
Maths QUIZ This quiz is designed to allow students to “self-assess” their choice of 100-level statistics unit at Macquarie University. The quiz consists of mathematical questions representative of the required prerequisite knowledge for STAT171.
In previous years, students were required to submit their attempt at these questions, however, the work is not being collected in 2011. The set-out of the questions has not been altered, and as such there is no need to put the “final” answers in the answer boxes. You need to: • Complete the questions below. • Mark your attempt from the check answers available on the web, putting the mark at the top of the sheet as indicated. Please note that if you have difficulty completing the questions in the quiz, you should discuss your choice of 100-level Statistics unit with a Statistics Academic Adviser. Students are able to transfer from STAT171 to STAT170 until the end of the second week of teaching. However, it is preferable if all transfers are complete by the end of the first week of teaching.
1.
Suppose a, b, c and d are numbers. We want to express
a c e as a ratio of the form + b d f
. Write out e and f as expressions in terms of some or all of a, b, c and d.
e=
f=
2.
Evaluate -2(2-6)/(4-7)
3.
Simplify the expression:
4.
Expand in increasing powers of y-1: (1+3y-1)3
(y2-9) / [ -(y-3)(y+2) / (3y3) ]
1
5.
Which of the following are correct?
Correct
6.
(a)
|y-3| = y+3,
(b)
|y-3| = y-3,
(c)
|y-3| = the greater of 3-y and y+3
(d)
|y-3| = the greater of –y+3 and -3+y
(e)
|y-3| = the lesser of 3-y and y+3
(f)
|y-3| = the lesser of –y+3 and -3+y
Incorrect
Consider the following product: 2a2×3b3. To which of the following expressions is it equivalent (there may be more than one):
Equivalent Not
7.
2 3
(a)
6a b
(b)
5a2b3
(c)
5(ab)3/a
(d)
6(a2b2)2/(a2b)
Consider the following expression: (3a-1)2/(6ab-3/2)2. To which of the following expressions is it equivalent:
Equivalent Not 2
3/2 2
a)
(-3a) /(-6ab )
b)
b3/4
c)
4b3
d)
1/(4b3)
e)
b3/(4a4)
f)
4a-4b-3
2
8.
Which of the following statements about square roots is true or false?
True 2
False
2
(a) √(a +b ) = a+b (b) √(4a+12b) = 4√(a+3b)
9.
In scientific notation, the expression: 3.24E-02 means
(a) (b) (c) (d) (e) (f)
10.
11.
324, 3.24 0.0324 1/(32.4)2 1/(64.8) 1.24
Find the roots of each of the following equations (i.e. find the values of x for which the equality holds):
(a)
2x + 3 = 5
(b)
x2 - 5x + 6 = 0
Solve the pair of equations below (in other words, find the point (x,y) that is common to the two lines)
y=x+4 2y = 3x – 12
x=
3
y=
12.
The following functions are graphed below (for x>0). Which graph (A-H) corresponds to which function (i – viii)?
Graph (i)
y = loge(x)
(ii)
y = 2loge(x)
(iii)
y = loge(2x)
(iv)
y = loge(x+2)
(v)
y = loge(x) + 2
(vi)
xy = 1
(vii)
4xy = 1
(viii)
(x + 2)y = 4
B
C 2
2
• 0
1.5
2 0
6
8
0
2
6
8
0
2
F
6
8
0
2
4
6
8
6
8
H
5
•
30
4
0
2
20 10
0
2
4
6
8
2 0
2
4
6
8
•
0
-10
•
0
-4
-5
4
0 -2
6
•
4
G
40
E
4
10
4
8
2
-4
.5
.5
-2
1
•
-2
•
1
•
0
D
1.5
2
4
2.5
A
0
2
4
6
8
0
2
4
Note: remember that loge(1)=0. To assist you, the point (1,1) is indicated with a dot.
4
13.
Which of the following functions are straight lines with a gradient of 2?
True (a)
2y = 6x + 4
(b)
y = 2x + 3√x + 2
(c)
3y = 5x – 6
(d)
1.5y = 3x + 3
(e)
5y = 10x – tan(x) + 20
False
for x ≥ 0
14.
Which of the functions in the previous question are straight lines with an intercept of 2?
15.
Roughly sketch the function y = (x-1)2 + 1 for -3 ≤ x ≤ 3.
5
16.
What is the value of (4!) ?
17.
What is the equation of the family of straight lines that pass through the point (1, 4)?
18.
Simplify (withOUT use of your calculator):
(a) 8(-2/3)
(b) 41.5
(c) log216
(d) ln(√e)
19.
Solve (a) log10(1+x) = 3
20.
Evaluate
4
∑i i =0
2
21.
Evaluate
∫
22.
Find x in:
∫
2
(b) ln4x – 3ln(x2) = ln2
1 +1
x 2 dx
1
x
1
t dt = 0.78
6