Cadet College Entry Test Mathematics Syllabus

Is zero positive, negative, even, or odd?

Zero is neither positive nor negative, but it IS an even number and it is an integer and a whole number.

How do you compare two integers on the number line?

On the number line, any number to the right is greater and any number to the left is smaller. So a positive number is always greater than a negative number, and among negatives the one closer to zero (e.g. −2) is greater than one farther from zero (e.g. −7).

What are directed (signed) numbers?

Directed or signed numbers are numbers that carry a positive (+) or negative (−) sign to indicate direction or opposite quantities, such as +5 (gain, above zero) and −5 (loss, below zero).

State the rules for adding two signed numbers.

If the signs are the same, add the absolute values and keep the common sign. If the signs are different, subtract the smaller absolute value from the larger and take the sign of the number with the larger absolute value.

State the rules for multiplying or dividing two signed numbers.

Like signs give a positive result: (+)(+) = + and (−)(−) = +. Unlike signs give a negative result: (+)(−) = − and (−)(+) = −. The same rule applies to division.

What is the additive inverse and the absolute value of a number?

The additive inverse of a number a is −a (the number that adds to it to give 0). The absolute value |a| is the distance of a from zero on the number line and is always non-negative, e.g. |−7| = 7.

What is a factor of a number?

A factor (or divisor) of a number is a whole number that divides it exactly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.

What is a multiple of a number?

A multiple of a number is the product of that number with any whole number. For example, multiples of 4 are 4, 8, 12, 16, 20, ... Every number is a multiple of itself and of 1.

What is a prime number and what is a composite number?

A prime number has exactly two distinct factors: 1 and itself (e.g. 2, 3, 5, 7, 11). A composite number has more than two factors (e.g. 4, 6, 8, 9). Note: 1 is neither prime nor composite.

What is the only even prime number?

2 is the only even prime number; every other even number has 2 as a factor, making it composite.

What is the HCF (GCD) of two numbers and how is it found by prime factorization?

The Highest Common Factor (HCF), also called GCD, is the largest number that divides both numbers exactly. By prime factorization, write each number as a product of primes and multiply the common prime factors taken with the lowest power.

What is the LCM of two numbers and how is it found by prime factorization?

The Lowest Common Multiple (LCM) is the smallest number that is a multiple of both numbers. By prime factorization, take all prime factors that appear, each with its highest power, and multiply them.

State the relationship between HCF and LCM of two numbers.

For any two numbers a and b: HCF × LCM = a × b. So the product of the two numbers equals the product of their HCF and LCM.

State the divisibility rules for 2, 3, and 5.

A number is divisible by 2 if its last digit is even (0,2,4,6,8); by 3 if the sum of its digits is divisible by 3; and by 5 if its last digit is 0 or 5.

State the divisibility rules for 9 and 10.

A number is divisible by 9 if the sum of its digits is divisible by 9, and divisible by 10 if its last digit is 0.

What is a rational number?

A rational number is any number that can be written in the form p/q, where p and q are integers and q is not equal to 0. This includes integers, fractions, terminating decimals, and recurring decimals.

How do you add or subtract two rational numbers (fractions) with different denominators?

Find the LCM of the denominators to get a common denominator, convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators while keeping the common denominator.

How do you multiply and divide rational numbers?

To multiply, multiply numerator by numerator and denominator by denominator: (a/b) × (c/d) = ac/bd. To divide, multiply by the reciprocal of the divisor: (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc.

What are proper, improper, and mixed fractions?

A proper fraction has numerator smaller than denominator (e.g. 3/5). An improper fraction has numerator greater than or equal to denominator (e.g. 7/4). A mixed fraction (mixed number) combines a whole number and a proper fraction (e.g. 1 3/4).

What are equivalent fractions and how do you simplify a fraction to its lowest terms?

Equivalent fractions represent the same value, obtained by multiplying or dividing numerator and denominator by the same non-zero number. To reduce to lowest terms, divide both numerator and denominator by their HCF.

How do you convert an improper fraction to a mixed number, and a mixed number to an improper fraction?

Improper to mixed: divide numerator by denominator; the quotient is the whole part, the remainder over the denominator is the fraction. Mixed to improper: multiply the whole number by the denominator, add the numerator, and place the result over the denominator.

How do you convert a fraction to a decimal and a decimal to a fraction?

Fraction to decimal: divide the numerator by the denominator. Decimal to fraction: write the decimal over a power of 10 (10, 100, 1000 ...) matching the number of decimal places, then simplify, e.g. 0.75 = 75/100 = 3/4.

What is the rule for placing the decimal point when multiplying two decimals?

Multiply the numbers ignoring the decimal points, then count the total number of decimal places in both factors and place the decimal point that many places from the right in the product.

How do you divide a number by a decimal?

Move the decimal point in the divisor to the right to make it a whole number, move the decimal point in the dividend the same number of places, then divide normally.

What is the square of a number, and what is a perfect square?

The square of a number is the number multiplied by itself (n × n = n²). A perfect square is a number that is the square of an integer, e.g. 1, 4, 9, 16, 25, 36.

What digits can a perfect square never end in?

A perfect square can never end in the digits 2, 3, 7, or 8. Perfect squares end only in 0, 1, 4, 5, 6, or 9.

What is the square root of a number, and what symbol represents it?

The square root of a number is a value that, when multiplied by itself, gives that number. It is represented by the radical symbol √. For example, √49 = 7 because 7 × 7 = 49.

How do you find the square root of a number by prime factorization?

Express the number as a product of prime factors, group the identical primes into pairs, then take one factor from each pair and multiply them. For example, √144 = √(2×2 × 2×2 × 3×3) = 2 × 2 × 3 = 12.

What is the cube of a number, and what is a perfect cube?

The cube of a number is the number multiplied by itself three times (n × n × n = n³). A perfect cube is the cube of an integer, e.g. 1, 8, 27, 64, 125.

What is the cube root of a number, and how is it found by prime factorization?

The cube root (∛) of a number is a value that, when cubed, gives that number, e.g. ∛64 = 4. By prime factorization, group the prime factors into triples and take one factor from each triple, e.g. ∛216 = ∛(2³ × 3³) = 2 × 3 = 6.