MCD 2130-Functions & Their Applications
Diagnostic Test
The test consists of short answer problems (Please show all working).
The result of this test does NOT contribute to the subject assessment.
Working time: 75 minutes
Instructions to Candidates:
Quadratic Formula
x=
−b ± b 2 − 4ac
2a
Calculators are not permitted.
Write your working into space provided in this test paper.
You must hand in this entire test paper at the end of the test.
Do not open this test until instructed to do so.
When instructed please enter your name and student ID number below.
Name:
Student ID:
Tutor’s Name:
Class Time &
Day:
Test Result:
Teacher’s Recommendation:
MCD2130 Diagnostic Test
Page 1 out of 13
1. Find the value of:
4
2
f ( x ) = + 5, when x =
x −3
(1 mark)
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2. Solve the following linear equations for x :
(a)
4 − x 3x − 2
5
+
=
3
4
(2 marks)
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(b)
d −x a−x
=
a
d
(3 marks)
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3. Transpose the following equations to make y the subject:
(a) 3 x + 2 y − 17 =
0
(2 marks)
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MCD2130 Diagnostic Test
Page 2 out of 13
(b) 2 x − 3 y 2 =
(2 marks)
10
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4. Solve the following in-equations for x :
(a) 7 −
3x
≤ −2
8
(2 marks)
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(b) 4 ( 2 + 3 x ) > 8 − 3 ( 2 x + 1)
(3 marks)
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5. Solve the following simultaneous equations and find the values of x and y :
(a)
2x − y =
7
7x − 5y =
42
(2 marks)
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MCD2130 Diagnostic Test
Page 3 out of 13
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(b)
ax − by =
a
Where a and b are constants
bx + ay =
b
(2 marks)
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(c) The length of a rectangle is 12 cm greater than twice its width. If the perimeter of
the rectangle is 48cm , calculate its length and width. (Hint: form a linear equation for
the perimeter and then solve it)
(2 marks)
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6. Expand each of the following expressions:
(a) ( 5 x + 1)( 2 x − 3)
(2 marks)
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MCD2130 Diagnostic Test
Page 4 out of 13
(b) ( 7 y + 3 x )
2
(2 marks)
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(c) ( 3 x + 1)
3
(2 marks)
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(
)(
(d) x + 2 3 x − 2 3
)
(2 marks)
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7. Simplify
x4 −1 1 + x2
(a)
÷
x −3 3− x
(3 marks)
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(b)
x2 + 4x
x2 + 2x − 8
(3 marks)
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MCD2130 Diagnostic Test
Page 5 out of 13
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8. Simplify:
x
(a) ( xy ) ×  
 y
2
3 2
(2 marks)
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 2

(b) a 7 x  5 x + a 2 x 
a

(2 marks)
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9. Factorise the following expressions:
(a) x 2 − 5 x − 36
(2 marks)
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(b) 4 x + 12 x 2 − 5
(2 marks)
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(c) x 2 − 5
(2 marks)
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(d) a 2 − 2ab + b 2 − c 2
(2 marks)
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MCD2130 Diagnostic Test
Page 6 out of 13
10. Expand and simplify
(a) 3 2 4 2 − 5 8
(
)
(2 marks)
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11. The line passing through the point ( 4, −8 ) with gradient (slope) −2 intersects the
line =
y 3 x + 5 at the point Q . Find the coordinates of Q .
(3 marks)
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12. Solve the following equations
(a) e 2 x +1 = 3
(1 mark)
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(b) log 2 ( x + 1) =
3
(1 mark)
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MCD2130 Diagnostic Test
Page 7 out of 13
13. Write the following expressions in the form a ( x − h ) + k :
2
(a) x 2 + 10 x + 8
(2 marks)
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(b) 2 x 2 − 8 x + 20
(2 marks)
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14. Solve the following quadratic equations:
0
(a) ( 5 x − 2 )( 2 x + 3) =
(2 marks)
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(b) x 2 + 16 x − 36 =
0
(2 marks)
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(c) x 2 + 5 x + 1 =
0
(2 marks)
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(d) ( 5 x − 1) − 16 =
0
2
(2 marks)
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MCD2130 Diagnostic Test
Page 8 out of 13
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15. Consider the following triangle to answer question 15.
(a) Use the above triangle to find the value of x :
(1 mark)
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(b) Hence find the value of cos α
(1 mark)
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(c) Hence find the value of tan α
(1 mark)
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MCD2130 Diagnostic Test
Page 9 out of 13
16. Sketch the following functions, clearly indicating any intercepts and other
important points:
(a) 2 x − 4 y + 10 =
0
(3 marks)
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(b) =
y 10 x + 2
(3 marks)
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MCD2130 Diagnostic Test
Page 10 out of 13
(c) y = x 2 − 4 x + 3
(3 marks)
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(d) y =
1
x
(2 marks)
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MCD2130 Diagnostic Test
Page 11 out of 13
(e) y = log10 x
(2 marks)
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17. Evaluate the following limits:
(a) lim ( 2 x − 7 )
(1 mark)
x →12
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x2 −1
(b) lim
x →1 x − 1
(1 mark)
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18. Find the derivative,
(a) y = x 3
dy
of each of the following:
dx
(1 mark)
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MCD2130 Diagnostic Test
Page 12 out of 13
(b) y =
1 − 3x3
x
(2 marks)
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19. Find the integral ∫ ( x + 6 ) dx
(1 mark)
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Please select the best option
When did you last study mathematics?
1. Between 0 – 1 year ago
2. Between 1 – 2 years ago
3. More than 2 years ago
MCD2130 Diagnostic Test
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