Tips

Question 1

For a given annual % of interest & initial principal

Answer 1

Increasing the frequency of compounding, increases the interest amount accumulated

Question 2

If multiply/divide both sides of an inequality with a -ve number

Answer 2

DIRECTION of the inequality changes (reverses)

Question 3

Listing down factors of a number

Answer 3

Use the T method (stop when pairs start repeating)

Question 4

Multiple of every +ve integer

Answer 4

0

Question 5

Standard form for a Quadratic equation

Answer 5

y=ax²+bx+c; if |a| > 1 skinny, if |a| < 1 wide; if a>0, graph opens upwards, if a<0, graph opens downwards

Question 6

Impact of outliers on Median

Answer 6

Changing highest/lowest no on a list, DOESN’T change median

Question 7

When there is a distinct outlier or a set of outliers in one direction

Answer 7

That pulls the mean away from the median

Question 8

Exponents of prime factors of a square

Answer 8

Must all be EVEN

Question 9

Numbers with exactly 3 divisors

Answer 9

Squares of prime numbers (1, p, p²)

Question 10

Numbers with 5 factors can be

Answer 10

Square of a prime’s square (1, p, p², p³, p⁴)

Question 11

Some mathematical exceptions (x, x²)

Answer 11

For most +ve nos, x² > x; For x=0 & x=1, x²=x; For fractions b/w 0 & 1, x²<x

Question 12

If divisor > dividend, q=?, r=?

Answer 12

q=0, r=dividend

Question 13

Squaring both sides of an inequality

Answer 13

If both sides are +ve, then can square; If opp. signs, then can’t square

Question 14

Adding mean term to a list, shifts standard deviation

Answer 14

to LOWER value

Question 15

LCM & HCF

Answer 15

LCM=product of HIGHEST powers; HCF=product of LOWEST powers

Question 16

Perfect squares

Answer 16

The only integers with an ODD number of factors

Question 17

Numbers with 4 factors can be

Answer 17

Product of 2 prime numbers (1, p, q, pxq) / Cube of a prime number (1, p, p². p³)

Question 18

Always +ve

Answer 18

Factors of a +ve integer/ Remainders/ Prime numbers

Question 19

Always integers

Answer 19

Multiples of a +ve integer / Odd & even numbers

Question 20

[Exception] Quadratics have 2 solutions

Answer 20

(a-b)² = 0 & (a+b)² = 0 Yield only 1 solution

Question 21

A set of ‘n’ consecutive inegers will always contain one no.

Answer 21

Divisible by n (if n is odd, sum of n consecutive integers will be divisible by n)

Question 22

a⁰ = ?

Answer 22

1 (for all a except 0, i.e., 0⁰ = undefined)

Question 23

Addition with mod

Answer 23

|x+y| <= |x| + |y| (equal when x,y have same sign)

Question 24

Subraction with mod

Answer 24

|x-y| => |x| - |y| (equal when x,y have same sign & |x| >= |y|

Question 25

Impact of outliers on Mean

Answer 25

Changing highest/lowest no on a list, CHANGES mean

Question 26

Mutually exclusive events

Answer 26

2 events canNOT occur at the same time

Question 27

Independent events

Answer 27

One event remains UNAFFECTED by the occurence of the other event

Question 28

Data set values x -> ax+b, μ=? σ=?

Answer 28

a -> aμ + b; σ -> aσ

Question 29

If xᵃ = 1

Answer 29

then a=0 & x = any number (or) a = any number & x=1

Question 30

Data set that is symmetric about its average

Answer 30

Average = Average(least, greatest)

Question 31

Terminating decimal depends on

Answer 31

Factors other than 2 & 5 (i.e., fractions with 2s and 5s terminate, while others recur)

Question 32

Consecutive multiples of same number

Answer 32

μ = Median

Question 33

Consecutive integers

Answer 33

μ = Median

Question 34

Evenly spaced numbers / Any arithmetic sequence

Answer 34

μ = Median

Question 35

Symmetrical list

Answer 35

μ = Median

Question 36

If 2 series of consecutive multiples of 'p' have the same middle no

Answer 36

then the 2 series have the same μ

Question 37

If 2 series of consecutive multiples of 'p' have the same no of terms

Answer 37

then the 2 series have the same σ

Question 38

If |a| = b then

Answer 38

a = b (or) a = -b

Question 39

Even roots of

Answer 39

positive numbers -> +ve output; -ve numbers -> doesn't apply

Question 40

If (x+y) is divisible by d & x is divisible by d

Answer 40

y is divisible by d

Question 41

aˣ = ?

Answer 41

Every prime factor within the prime factorisation of that integer MUST have a power of x/its multiples

Question 42

Atleast 1 even factor in a product => product will be...

Answer 42

EVEN

Question 43

Fractions s ⁄ p & s ⁄ q where p>q [Bigger Dr make...]

Answer 43

s ⁄ p < s ⁄ q [...Smaller fractions]

Question 44

If x & y are each divisible by d

Answer 44

then (x+y) is divisible by d

Question 45

Fraction a/b; Adding p&q (a+p)/(b+q); result?

Answer 45

(a+p)/(b+q) will be closer to p/q than a/b; If a/b < p/q => a/b < resultant; If a/b > p/q => a/b > resultant

Question 46

[Exception] We need N equations to solve for N variables

Answer 46

Equations must be independent to count as separate / Cancellation of several variables at once helps

Question 47

Odd roots of

Answer 47

positive numbers -> +ve output; negative numbers -> -ve output

Question 48

x is what % of y

Answer 48

x/y * 100

Question 49

x is what % > or < y

Answer 49

(x/y - 1)*100 or (y/x - 1)*100

Question 50

If more than half the numbers in a list have the same value (x), median=?

Answer 50

x (regardless of values of remaining numbers)

Question 51

Product can be ODD if and only if

Answer 51

Every single factor is ODD

Question 52

Units digit of any product will be influenced by

Answer 52

ONLY the units digits of the 2 factors

Question 53

If Nr increases & Dr decreases, fraction?

Answer 53

Fraction increases

Question 54

p is a factor of q

Answer 54

q = kp

Question 55

q is a multiple of p

Answer 55

q = kp

Question 56

Inequality/Equality of type x-y & y-x on two sides

Answer 56

Unless x & y are equal +ve on one side & -ve on the other (opp signs)

Question 57

When a perfect square ends with an even number of zeros, the square root of such a perfect square will have exactly ___ of the number of zeros to the right of the final nonzero digit as the perfect square.

Answer 57

half

Question 58

If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly ___ of the number of decimal places. Thus, a perfect square decimal must have an ___ number of decimal places.

Answer 58

Half, Even

Question 59

If two absolute values are equal, it must be true that the expressions within the absolute value bars are either

Answer 59

equals or opposites

Question 60

If x² < |x| and x≠0, the range of x is

Answer 60

-1 < x < 1