Maths

Question 1

how to expand binomial products e.g. (a+b)(c+d)

Answer 1

use FOIL (first, outer, inner, last) e.g. ac + ad + bc + bd

Question 2

what are perfect squares? e.g. (a+b)²

Answer 2

a² + 2ab + b²

Question 3

factorising difference of squares e.g. a² - b²

Answer 3

(a-b)(a+b)

Question 4

what are monic quadratics

Answer 4

where a (coefficient of x²) = 1

Question 5

how to solve: ax² + bx + c

Answer 5

what two numbers multiply to give ‘c’ and add to give ‘b’?

Question 6

what do you if you have a monic with four terms?

Answer 6

group in pairs and factorise

Question 7

what are non-monic quadratics?

Answer 7

where a ≠ 1

Question 8

how to solve: ax² + bx + c

Answer 8

option 1. product, sum, factor - two numbers that give the product of ‘ac’, the sum of ‘b’, then break middle term, group in pairs and factorise. option 2. cross method

Question 9

how to simplify algebraic fractions (expressions)

Answer 9

factorise top and bottom first, then if it is +/-, common denominators then combine, if it is x/divide then you need to do that simplify

Question 10

how to solve algebraic fractions (equations)

Answer 10

multiply all terms by lowest common denominator

Question 11

adjacent angles have what?

Answer 11

a shared arm and vertex

Question 12

Z?

Answer 12

alternate angles equal in parallel lines

Question 13

F?

Answer 13

corresponding angles equal in parallel lines

Question 14

C?

Answer 14

co-interior angles are supplementary in parallel lines

Question 15

angle sum formula

Answer 15

(n-2) x 180

Question 16

regular polygon each angle formula

Answer 16

(n-2)x180/n

Question 17

angle sum of triangle

Answer 17

180

Question 18

angle sum of quadrilateral

Answer 18

360

Question 19

angle sum of pentagon

Answer 19

540

Question 20

exterior angle sum of polygon

Answer 20

360

Question 21

SSS?

Answer 21

Congruence proof, all corresponding sides are equal

Question 22

SAS?

Answer 22

Congruence proof, two pairs of corresponding sides and the included angle are equal

Question 23

AAS?

Answer 23

Congruence proof, right angle in both triangles and pair of hypotenuse and one other side are equal

Question 24

Name all similarity proofs

Answer 24

equiangular, all sides in same ratio, sides in same ratio about equal angle, right angle with hypotenuse and side in same ratio

Question 25

a quadrilateral is a trapezium if...

Answer 25

it has at least one pair of parallel sides

Question 26

a quadrilateral is a kite if...

Answer 26

two pairs of adjacent sides are equal and diagonals meet at right angles and of them is bisected by the other

Question 27

a quadrilateral is a parallelogram if...

Answer 27

both pairs of opp. sides are equal or both pairs of opp. sides are parallel or both pars of opp. angles are equal or one pair of opp. sides are equal AND parallel or the diagonals bisect each other

Question 28

a quadrilateral is a rectangle if...

Answer 28

if three (so all) angles are 90º or diagonals are equal AND bisect each other or it has two pairs of parallel sides AND one right angle

Question 29

a quadrilateral is a rhombus if...

Answer 29

all sides are equal or diagonals bisect each other at right angles

Question 30

a quadrilateral is a square if...

Answer 30

all sides are equal and one angle is 90º or diagonals are equal and bisect each other at right angles

Question 31

length ratio

Answer 31

x : y

Question 32

area ratio

Answer 32

x² : y²

Question 33

volume ratio

Answer 33

x³ : y³

Question 34

HOW TO SOLVE ALGEBRAIC EQUATIONS W/ FRACTIONS (HINT: NOT THE SAME AS EXPRESSIONS!!!)

Answer 34

multiply both sides (ALL TERMS) of the equation by the lowest common denominator (DO NOT MAKE EACH FRACTION HAVE THE LCD)

Question 35

How to simplify inequalities?

Answer 35

same as equations (do the same thing to each side) BUT if multiplying or dividing by a negative, flip the inequality sign

Question 36

how to graph greater/less than or equal to (≥)

Answer 36

fill in circle then draw line with arrow left for less than and right for greater than

Question 37

how to graph greater/less than

Answer 37

don't fill in circle, arrow left for less, arrow right for greater

Question 38

what question are simultaneous equations answering?

Answer 38

do these lines meet? if so, where?

Question 39

how can simultaneous equations be solved?

Answer 39

graphically (inefficient), or algebraically (efficient) - elimination or substitution

Question 40

how to do the elimination method for solving simultaneous equations

Answer 40

you need to first 'match' one of the variables (by multiplying or dividing) so that they cancel e.g. - 2y + 2y, then add or subtract the two equations then solve for the remaining variable

Question 41

how to do the substitution method for solving simultaneous equations

Answer 41

you need to make one variable the subject of the one equation then substitute the new equation in place of the variable in the other equation

Question 42

what is the null factor law?

Answer 42

if ab = 0, then a = 0, b = 0 or both = 0. remember with equations that = 0 don't divide by common factor, just factorise, otherwise you lose a sol'n.

Question 43

how to complete the square to solve (equations)? a² + 2ab + ? = (a + b)²

Answer 43

divide by common factor if non-monic, then add (2ab/2a)² to both sides .................... ? = (2ab/ab)² e.g. x² + 8x + ? --> x² + 8x + 4² = (x + 4)²

Question 44

what is (a + b)² expanded?

Answer 44

a² + 2ab + b²

Question 45

what is (a-b)² expanded?

Answer 45

a² - 2ab + b²

Question 46

how to complete the square to simplify (expressions)?

Answer 46

factorise if non-monic, then add and minus (2ab/2a)²

Question 47

what is the quadratic formula?

Answer 47

−b ± √(b² − 4ac) x = ———————————————— 2a