Basic revision

Question 1

(a + b)²

Answer 1

a² + 2ab + b²

Question 2

a² - b²

Answer 2

(a - b)(a + b)

Question 3

fraction

Answer 3

a measure of how something is to be divided up or shared out

Question 4

numerator

Answer 4

the top number in a fraction

Question 5

denominator

Answer 5

the bottom number in a fraction

Question 6

proper fraction

Answer 6

a fraction in which the numerator is smaller than the denominator

Question 7

equivalent fractions

Answer 7

are two or more fractions that have the same value but are different in form eg

3/4, 6/8, 63/84, 75%, 0.75

all look different but they all have the same value

Question 8

product

Answer 8

the product is the result given by the operation of multiplication

Question 9

quotient

Answer 9

the quotient is the result given by the operation of division

32 divided by 8 is 4

the quotient is 4

Question 10

divisor

Answer 10

the number in a division sum that does the dividing

18 divided by 9 is 2

the divisor is 9

Question 11

test for dividing by 3

Answer 11

if the digits in the number add up to a multiple of 3

3597 is divisible by 3 since

3+5+9+7 = 24

Question 12

square – (as a verb)

Answer 12

to square a number means to multiply it by itself

Question 13

isosceles triangle

Answer 13

a triangle which has two sides with the same length

there will be two angles of the same size as well

Question 14

equilateral triangle

Answer 14

a triangle in which all three sides have the same length

therefore the angles in an equilateral triangle are the same

each is 60º

Question 15

negative times negative

Answer 15

positive

Question 16

4

Answer 16

• even
• square

Question 17

3, 4, ?

Answer 17

5 – 3, 4, 5 is a pythagorean triple ie when these 3 numbers are considered as lengths of the sides of a triangle the angle opposite the longest side will necessarily be a right angle

Question 18

5, 12, ?

Answer 18

13 – 5, 12, 13 is a pythagorean triple

Question 19

9

Answer 19

• odd
• square

Question 20

{1, 8, 27, 64, 125}

Answer 20

the set of the first 5 cube numbers

Question 21

16

Answer 21

• even
• square
• 2 to the power of 4

Question 22

25

Answer 22

• odd
• square

Question 23

{2, 3, 5, 7, 11, 13, 17, 19, 23}

Answer 23

the set of the first 9 prime numbers

Question 24

how to divide by a fraction?

Answer 24

• “kiss and flip”
• eg 8 divided by ½ is the same as 8 times 2

Question 25

mixed number

Answer 25

an improper fraction written as a whole number followed by a proper fraction

eg 2¾ = 11/4

Question 26

cancel – as a verb

Answer 26

to express a fraction in its simplest or lowest terms

eg 6/8 = 3/4 – we have cancelled the factor of 2 on the left hand side of the ‘=’ sign by dividing top and bottom of the fraction by 2 to get the fraction in its lowest terms (3 and 4 do not have any common factors)

Question 27

surd

Answer 27

a number that cannot be expressed as fraction, or ratio of whole numbers, hence it is sometimes called an irrational number

the square root of 2

the cube root of 5

3 + sqrt(2)

Question 28

negative divided by a negative

Answer 28

positive