MATH141: Mathematics 1C Part 1

Index of worked solutions for fundamentals, differentiation, polar coordinates and integration

Many students have asked for additional worked solutions to be made available. Worked solutions to previous exam papers can be found via the MATH141 home page. On this page I have catalogued these questions according to their topic.

Fundamentals (listed in alphabetical oder)

Algebraic Fractions

1. 2000 Question 1(a)(i).
2. 2002 Question 2(a)(i)
3. 2006 Question 2(b)

Factorial notation n!

1. 2007 Question 2(e).

Function notation

1. 2005 Question 2(b).

Geometry (Non-trig, includes simple curve sketching)

1. 2000 Question 1(a)(iii).
2. 2001 Question 2(d)(i).
3. 2002 Question 2(a)(ii)
4. 2003 Question 2(b)(i)
5. 2003 Question 2(d)(iii)
6. 2007 Question 2(c)

Indices

1. 2002 Question 2(a)(iv)
2. 2007 Question 2(d)

Logarithms

1. 2000 Question 1(a)(ii).
2. 2002 Question 2(a)(iii)
3. 2003 Question 2(a)(iii)
4. 2005 Question 2(a).

Miscellaneous

1. 2006 Question 2(a) [average speed].

Polynomials

1. 2000 Question 1(a)(iv).
2. 2001 Question 2(b)(i-ii).
3. 2003 Question 2(a)(vi)
4. 2005 Question 2(d).

Quadratic Equations

1. 2003 Question 2(a)(ii&iv)
2. 2007 Question 2(b)

Surds

1. 2003 Question 2(a)(i)
2. 2004 Question 2(a).
3. 2007 Question 2(a).

Trigonometry

1. 2001 Question 2(a).
2. 2001 Question 2(c).
3. 2003 Question 2(a)(vii)
4. 2004 Question 2(b).
5. 2004 Question 2(c).
6. 2005 Question 2(c).
7. 2006 Question 2(c)(i)&(iii).

Zeroes of functions

1. 2006 Question 2(d).
2. 2007 Question 2(f).

Differentiation (listed in the order that they are taught)

Functions

1. 2000 Question 1(b)(i&ii).
2. 2000 Question 1(c)(i).
3. 2001 Question 2(d)(ii).
4. 2002 Question 2(c).
5. 2003 Question 2(a)(v)
6. 2003 Question 2(b)(ii)
7. 2004 Question 2(d).
8. 2004 Question 2(e).
9. 2006 Question 2(g)(i).
10. 2007 Question 2(h)(ii).

Limits

1. 2000 Question 2(a).
2. 2001 Question 2(f).
3. 2002 Question 4(a).
4. 2003 Question 4(a)
5. 2004 Question 2(f).
6. 2005 Question 2(f).
7. 2006 Question 2(f).
8. 2007 Question 2(g).

Elementary differentiation

1. 2000 Question 2(b)(i-iii).
2. 2001 Question 4(b)(i-iii).
3. 2002 Question 2(d)(i-ii).
4. 2003 Question 4(b)(i-iv).
5. 2004 Question 4(a).
6. 2005 Question 4(a)(i-iv).
7. 2006 Question 4(a)(i-iii).
8. 2007 Question 4(a)(i-iv).

Hyperbolic functions

1. 2000 Question 1(c)(ii).
2. 2001 Question 2(e).
3. 2003 Question 2(c)(i&ii).
4. 2005 Question 2(e).
5. 2006 Question 2(e)(ii).
6. 2007 Question 2(h)(i).

One-to-one and inverse functions

1. 2000 Question 1(b)(iii).
2. 2001 Question 2(d)(iii).
3. 2003 Question 2(b)(iii).
4. 2004 Question 2(g).
5. 2005 Question 2(g)(ii).

Inverse Trigonometric Functions

1. 2000 Question 1(c)(iii&v).
2. 2001 Question 4(a)(i).
3. 2002 Question 2(b).
4. 2006 Question 2(c)(ii).
5. 2007 Question 2(h)(iii).

Inverse Hyperbolic Functions

1. 2003 Question 2(c)(iii)
2. 2005 Question 2(g)(i).
3. 2006 Question 2(e)(i)&(ii).

The Derivative of an Inverse Function

1. 2000 Question 1(c)(iv).
2. 2001 Question 4(a)(ii).
3. 2002 Question 2(e)(iv).
4. 2003 Question 4(b)(v).
5. 2005 Question 2(g)(iii).
6. 2006 Question 2(g)(ii).
7. 2007 Question 2h(iii).

Logarithmic Differentiation

1. 2000 Question 2(b)(iv).
2. 2001 Question 4(b)(iv).
3. 2002 Question 2(e)(iii).
4. 2005 Question 4(a)(v).
5. 2007 Question 4(a)(v).

Implicit Differentiation

1. 2000 Question 2(c).
2. 2001 Question 4(c).
3. 2002 Question 2(e).
4. 2003 Question 4(c).
5. 2004 Question 4(b).
6. 2005 Question 4(b).
7. 2006 Question 4(b).
8. 2007 Question 4(b).

Parametric Equations and Curves

1. 2000 Question 2(d).
2. 2001 Question 4(d).
3. 2002 Question 4(c).
4. 2003 Question 4(d).
5. 2004 Question 4(c).
6. 2005 Question 4(c).
7. 2006 Question 4(c).
8. 2007 Question 4(c).

Polar coordinates and polar curves (listed in the order that they are taught)

Polar coordinates

• Finding the cartesian coordinates of a polar point.
  1. 2001 Question 4(e)(iB)
  2. 2005 Question 4(d)(i).
• Finding the polar coordinates of a cartesian point.
  1. 2002 Question 4(a)(i2).
  2. 2003 Question 2(d)(i)
  3. 2005 Question 4(d)(ii).
• Finding more than one polar representation of a point
  1. 2001 Question 4(e)(iA)
  2. 2002 Question 4(a)(i2).
• Plotting polar points
  1. 2004 Question 4(d)(i).
• Miscellaneous
  1. 2006 Question 4d(i) [finding the value of r from r=f(theta), given theta]
  2. 2007 Question 4d(i) [finding the value of r from r=f(theta), given theta]

Polar curves

• Converting a cartesian equation into a polar equation.
  1. 2001 Question 4(e)(ii)
  2. 2003 Question 2(d)(iii)
• Converting a polar equation into a cartesian equation.
  1. 2002 Question 4(e)(ii).
  2. 2003 Question 2(d)(ii),
  3. 2004 Question 4(d)(ii).
  4. 2005 Question 4(d)(iii).
• Sketching a polar equation
  1. 2003 Question 2(d)(ii).
  2. 2006 Question 4(d)(ii).
  3. 2007 Question 4(d)(ii).

Integration (listed in the order that they are taught)

Differentiating definite integrals

1. 2000 Question 2(b)(v).
2. 2001 Question 4(b)(v).
3. 2002 Question 2(d)(v).
4. 2007 Question 4(e)(v).

Methods of integration

1. 2000 Question 2(e).
2. 2001 Question 4(f).
3. 2002 Question 4(d).
4. 2003 Question 4(e).
5. 2004 Question 4(e).
6. 2005 Question 4(e).
7. 2006 Question 4(e).
8. 2007 Question 4(e).