Lady Cadet Course Academic Test - Mathematics Syllabus

Academic Test - Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Academic Test - Mathematics in Lady Cadet Course, not a summary of it.

1. 1

   Arithmetic

   8 topics

   • Number System
   • Fractions and Decimals
   • Ratio and Proportion
   • Percentage
   • Profit and Loss
   • Simple and Compound Interest
   • Time, Speed and Distance
   • Time and Work
2. 2

   Algebra

   5 topics

   • Algebraic Expressions
   • Linear Equations
   • Quadratic Equations
   • Factorization
   • Exponents and Logarithms
3. 3

   Geometry and Mensuration

   5 topics

   • Lines and Angles
   • Triangles and Polygons
   • Circles
   • Area and Perimeter
   • Surface Area and Volume
4. 4

   Data Interpretation

   4 topics

   • Tables and Charts
   • Bar and Pie Graphs
   • Averages
   • Basic Probability

Academic Test - Mathematics flashcards for Lady Cadet Course

24 of 51 cards from the Academic Test - Mathematics deck — real questions with worked answers.

1. What are natural numbers?

   The counting numbers starting from 1: {1, 2, 3, 4, ...}. They do not include zero, fractions, or negatives.

2. What are whole numbers and how do they differ from natural numbers?

   Whole numbers are {0, 1, 2, 3, ...}. They are the natural numbers plus zero.

3. What are integers?

   The set of whole numbers and their negatives: {..., -3, -2, -1, 0, 1, 2, 3, ...}. They include no fractions.

4. What is a rational number?

   A number expressible as p/q where p and q are integers and q is not 0. Its decimal form either terminates or repeats.

5. What is an irrational number? Give an example.

   A number that cannot be written as p/q; its decimal is non-terminating and non-repeating. Examples: pi, square root of 2.

6. What is a prime number? Give the smallest one.

   A natural number greater than 1 with exactly two factors, 1 and itself. The smallest prime is 2 (the only even prime).

7. What is a composite number?

   A natural number greater than 1 that has more than two factors. Example: 6 has factors 1, 2, 3, 6.

8. How do you find the LCM and HCF relationship for two numbers?

   Product of the two numbers = LCM x HCF. So LCM x HCF = a x b.

9. What is the test of divisibility by 3?

   A number is divisible by 3 if the sum of its digits is divisible by 3.

10. What is the test of divisibility by 9 and by 11?

    By 9: digit sum divisible by 9. By 11: the difference between the sum of digits in odd positions and even positions is 0 or divisible by 11.

11. How do you add two fractions with different denominators?

    Find the LCM of the denominators, convert each fraction to equivalent fractions with that common denominator, then add the numerators.

12. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal (invert) of the second. For example, a/b divided by c/d = a/b x d/c.

13. What is a proper fraction versus an improper fraction?

    Proper: numerator less than denominator (value less than 1). Improper: numerator greater than or equal to denominator (value 1 or more).

14. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator using long division. For example, 3/4 = 0.75.

15. How do you convert a terminating decimal to a fraction?

    Write the decimal over a power of 10 equal to the number of decimal places, then simplify. For example, 0.25 = 25/100 = 1/4.

16. What is a ratio?

    A comparison of two quantities of the same kind by division, written a:b or a/b, where b is not 0.

17. What is a proportion?

    A statement that two ratios are equal, written a:b = c:d or a/b = c/d. Here a and d are extremes, b and c are means.

18. State the cross-multiplication rule for a proportion a:b = c:d.

    Product of extremes equals product of means: a x d = b x c.

19. What is the mean proportional (geometric mean) between a and b?

    It is the square root of (a x b). If a:x = x:b, then x squared = ab, so x = sqrt(ab).

20. What is the difference between direct and inverse proportion?

    Direct: both quantities increase/decrease together (a/b constant). Inverse: as one increases the other decreases (a x b constant).

21. How do you convert a fraction to a percentage?

    Multiply the fraction by 100 and add the percent sign. For example, 3/5 = (3/5) x 100 = 60 percent.

22. How do you find x percent of a number N?

    Compute (x/100) x N. For example, 20 percent of 50 = (20/100) x 50 = 10.

23. How do you calculate percentage increase?

    Percentage increase = (Increase / Original value) x 100.

24. If a value increases by x percent and then decreases by x percent, what is the net change?

    There is a net decrease of (x squared / 100) percent. For example, +10 percent then -10 percent gives a net 1 percent decrease.

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