Diagnostic Quiz 1: Some precalculus

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Question 1

Evaluate the following expression: 1 2 -1 3 + 1 4 -2 5
a)
1 30
  b)
1 120
c)
1 60
  d)
- 1 60
e)
- 1 30

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 2

Simplify the following expression: 5 + 1 5 - 1
a)
3 + 5 2
  b)
3 -5 2
c)
5 - 3 2
  d)
6 + 5 2
e)
6 -5 2

 

Your answer is correct.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 3

The equation of the line passing through the points (1,2) and (2,7) in the xy-plane is
a)
y = 3x - 1
  b)
y = 5x - 3
c)
y = 3x + 1
  d)
y = 4x - 1
e)
y = 4x - 2

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 4

The quadratic 2x2 + 7x - 15 factorises as
a)
(2x + 3)(x - 5)
  b)
(2x - 5)(x + 3)
c)
(2x - 5)(x - 3)
  d)
(2x + 5)(x - 3)
e)
(2x - 3)(x + 5)

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Your answer is correct.

Question 5

Find the number of radians that are represented by the following angle: 300
a)
3π 2
  b)
2π 3
c)
5π 3
  d)
5π 6
e)
4π 3

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 6

PIC Which of the following functions describes the above graph?
a)
y = -(x - 1)2 + 2
  b)
y = 2x(2 - x)
c)
y = -2(x + 1)2 + 2
  d)
y = 2(x - 1)2 + 2
e)
y = x(2 - x)

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 7

Find an equivalent expression to the following: e2xe5x2
a)
e7x2
  b)
e10x3
c)
ex(2+5x)
  d)
e2x + e5x2
e)
e10x(1+x)

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 8

Find an equivalent expression to the following:ln ab3 c2
a)
lna + ln3b - ln2c
  b)
lna + 3lnb - 2lnc
c)
3lnab - 2lnc
  d)
3lnab - ln2c
e)
lna - 3lnb + 2lnc

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 9

Evaluate the following expression: tan(5π6)
a)
3
  b)
-3
c)
- 1 3
  d)
1 3
e)
- 1

 

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Your answer is correct.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

Question 10

Solve for x for the following equation: 1 x - 1 + 1 x + 3 = 2
a)
x = 1 ±17 2
  b)
x = - 1 ±17 2
c)
x = ±5
  d)
x = ±2
e)
x = 2

 

Not correct. Choice (a) is false.
Your answer is correct.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.
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