how to solve problems and some equations.

Question 1

how do you find the gradient from the graph?

Answer 1

(x₁ y₁) (x₂ y₂)
m=△y/ △x.
=y₂-y₁/ x₂-x₁

Question 2

what is the formula for rate of change?

Answer 2

rise/ run.

Question 3

how do you prove that (n+1)² -(n-3)² is always a multiple of 8. write down the steps and the answer?

Answer 3

expand first bracket and square the second one.
n²+2n+1- (n²-6n+9)
expand second bracket.
n²+2n+1-n²+6n-9.
simplify.
8n-8.
factorise.
8(n-1)
:8 is a multiple of 8.

Question 4

how do you work out the area of a semi-circle?

Answer 4

area of a sector= ⦵/360 × 𝝅r²

Question 5

how do you work out the missing length of a triangle which isn’t a right angle if your given 2 lengths and one angle?

Answer 5

1/2 absinC.

Question 6

how do you find the missing length of a triangle if its right angled, your given an angle and one length?

Answer 6

SOHCAHTOA.

Question 7

how do you find the angle of a triangle if its a right angles one and your given 2 lengths?

Answer 7

SOHCAHTOA.
sin/tan/cos -1.

Question 8

how do you solve algebraic fractions. work out this: 4/x+1 + 2/x-2 =3. give the steps and the answer?

Answer 8

(x+1×x-2) (x-2×x+1)
4(x-2)/(x+1)(x-2) + 2(x+1)/(x-2)(x+1) =3
4(x-2)+2(x+1)/ (x+1)(x-2) =3
4x-8+2x+2/x²-x-2 =3
(times x²-x+2)
6x-6=3x²-3x-6
(-6x+6)
0=3x²-9x
(÷3)
0=x²-3x
factorise.
0=x(x-3)
x=0, x=3.

Question 9

function transformations: what does f(x)+2 suggest about the graph?

Answer 9

moves up 2.

Question 10

function transformations: what does f(x)-2 suggest about the graph?

Answer 10

moves down 2.

Question 11

function transformations: f(x) has a minimum point at (0,3). find f(x)+4?

Answer 11

(0,1)

Question 12

function transformations: f(x) has maximum point at (-1,1). find f(x)-1?

Answer 12

(-1,1)

Question 13

function transformations: what does f(x+2) suggest about the graph?

Answer 13

it moves 2 to the left.

Question 14

function transformations: what does f(x-2) suggest about the graph?

Answer 14

it moves 2 to the right.

Question 15

function transformations: y=f(x) minimum point (4,0). co-ordinates of minimum point y=f(x+5)?

Answer 15

(-1,0)
moves 5 to the left.

Question 16

function transformations: y=f(x) maximum point (-1,-1). co-ordinates of maximum point y=f(x+5)?

Answer 16

(6,-1)
moves 5 to the left.

Question 17

function transformations: y=f(x). maximum (2,-2). co-ordinates of maximum point y=f(x-5)?

Answer 17

(7,-2)
moves 5 to the right.

Question 18

function transformations: what does the graph y=f(x) minimum pint (2,0). co-ordinates minimum point y=-f(x)?

Answer 18

reflected on a line under the curve.
maximum= (2,0)

Question 19

function transformations: what does the graph y=f(x) minimum (1,-3). co-ordinates minimum y=f(-x)?

Answer 19

reflected on a line next to the curve.
minimum=(-1,-3)

Question 20

how do you work out the area under a curve?

Answer 20

base × height/ 2

Question 21

vector: if 3 is on the top and 2 is on the bottom how would this line look?

Answer 21

2 up and 3 to the right.

Question 22

vector: if -3 is on top and -2 is on the bottom how would this line look?

Answer 22

go down 2 and 3 to the left.

Question 23

vector: how do you work out the magnitude of a vector?

Answer 23

make it into a triangle and use Pythagoras.

Question 24

vector: how do you work out: 3 on top and 2 on the bottom?

Answer 24

3²+4²=c²
9+16=c²
25=c²
square root.
c=5

Question 25

when adding vector together how do you do it?

Answer 25

add the top number together and then the bottom two and leave in the same format.

Question 26

how do you subtract vectors?

Answer 26

subtract the top number together and then the bottom two and leave in the same format.

Question 27

how do you add/ subtract vectors if there is a number outside of the brackets at the front?

Answer 27

multiply the vector (both top and bottom number) by the outside number then continue as normal.