My former colleague, who was Head of Mathematics at the international school where we used to teach, would like to solicit responses to the following 50 questions...He is the BEST Maths teacher that I know ...and teaches Maths innovatively with so much energy, passion and dedication!!
If you feel bored enough or would like some intellectual stimulation, please post your answers in the comment page...Thanks!
P.S. I feel quite illiterate because I could only answer less than ten questions and I don't even know if my answers are correct!!!! haha! Have fun! Have a nice day....
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How much do you know about your basic O'level Maths? try out these 50 questions and assess yourself!
Prepared by Mr. P. Tan
Theory Assessment Test for O’levels:
If you can answer these 50 correctly, then you have a sound knowledge of your O’level course. Answer each question fully.
1) Draw a chart to show the REAL Number System. Define each type of numbers in the chart accompanied by an example.
2) Define the following and give an example to illustrate it.
Highest Common Factor (HCF);
Lowest Common Multiple (LCM);
Palindromic Number;
Orders of Operation for working out an arithmetic problem.
3) In Set Theory, what is meant by:
A Universal set;
A complement of a set;
A subset;
Intersection and union of two given sets?
4) How many types of fractions are there? List it out and give an example for each type of fractions.
5) How many units are there in the Metric System of Measurements for Length? Write down all the units and show how each units differ from the next.
6) What is the equivalent unit for:
Cubic decimeters, (b) milliliters, (c) hectares?
7) What is the relationship between miles per hour (mph) and kilometer per hour (km/h)?
8) Define a JULIAN year and a LEAP year? How can we tell a certain year is a leap year?
9) Write down the equation of a straight line for each of the followings:
(a) General form, (b) gradient-intercept form, (c) intercept form.
10. How many types of angles are there altogether? List out ALL the angles accompanied by an example.
11. What is a four-sided figure called? How many types of figures fall under this category?
12. What is meant by rotational symmetry? State the number of rotational symmetry (if any) for each of the figures in question 11?
13. What is a polygon? What is meant by a regular and an irregular polygon? List all the names of the polygons up to 10 sides. How can we find the sum of all the interior angles of a polygon and how do we test for regularity?
14. How are percentages related to decimals, fractions and ratios? Illustrate your answer with a chart and an example.
15. What is a Matrix? When can we add or subtract two or more matrices together?
16. When can we multiply two matrices together?
17. Can we divide one matrix by another of the same order? Why?
18. What is a Singular matrix? Give an example. What is the significance of a singular matrix?
19. How many types of triangles are there? List out all the names of the triangles and illustrate each case with an example.
20. What is a locus? Give an example.
21. The quadratic function y = ax2 + bx + c where a, b, and c are constants. What are the significance of the coefficients a, b and c with respect to the function? Explain thoroughly with examples and illustrations.
22. The solution of the equation ax2 + bx + c = 0 can be obtained by the Formula:
x = (-b±√(b^2-4ac))/2a where a, b and c are constants.
What is the significance of the term: x = - b/2a ? (b) b2 – 4ac ?
Describe fully the implications attached to (b) with respect to the type of answers we expect to get as well as whether the equation can be factorized or not.
23. What is meant by inconsistent equations? Give an example.
24. In Probability, state the lowest and highest range of values it can have. What is the significance of the probability being zero, one or more than 1?
25. State Pythagoras’ theorem and illustrate it with an example. Why is this theorem so important? How can we use this theorem to show whether a triangle is right-angled, acute-angled or obtuse-angled triangle?
26. In Geometry, explain what is meant by:
a) Centroid, (b) orthocenter, (c) median, (d) similar triangles e) congruent triangles?
27. Given a triangle, how do we circumscribe or inscribe a circle?
28. In Statistics, what is meant by mean, mode and median of a set of a set of scores?
29. In Statistics, what is meant by putting a set of scores in Rank order?
column in your table?
33. What is an OGIVE graph? What is the importance of an Ogive curve?
34. What is the Interquartile range (IQR)? What is the significance of IQR?
35. When the Mean, Mode and Median coincide in a frequency distribution, what is the significance of this occurrence?
36. What is trigonometry? Explain.
37. When do we use the Sine and Cosine Rules? State the conditions for each of the rules.
38. In Transformations, what is the relationship between the enlargement factor and the resulting area obtained?
39. What is the relationship between speed, distance and time?
40. In each of the following graphs:
(a) distance vs time,
(b) speed vs time,
(c) acceleration vs time; state the quantity represented by the gradient and area in each graphs (if there is a relationship).
41. Which Mathematician’s equation is used to find out whether a figure is a Solid or not given the numbers of edges, faces and vertices? Write down the equation connecting these three quantities.
42. What is a Unicursal or Transversible network? Give an example.
43. What is the difference between a Relation and a Function?
What is the relationship between them. How do we test whether a given graph is a relation or a function? Give an example.
44. What is the difference between “x > 1” and “x 1”?
45. If set A is a subset of set B, write down in Set notation, the probability of selecting an element in set A with respect to set B.
46. What is meant by two events are independent and two events are mutually exclusive? Give an example.
47. Draw out the net for each of the following solids:
(a) cylinder,
(b) rectangular pyramid,
(c) cuboid,
(d) an equilateral prism.
48. Write down the formulae for the volume of each of the figures in Question 47.
49. What is a Hemi-sphere? Write down the formula for its surface area (solid) and its volume.
50. State the conditions for which two triangles are
(a) similar,
(b) congruent.
Illustrate each case with an example.
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