Block Four

Question 1

What is a function notation

Answer 1

input value (usally x) then applies a rule to create an output value.
e.g the function y= 3x-1 has an input of x and output of y

Question 2

what do all these mean
f(x) = 3x -1

Answer 2

f = function
x= input
3x-1 = rule

Question 3

How to evaluate a function

Answer 3

when evaluating a function you must substitute a value for x and solve the equation from there
f(-2) = 2(-2) -1
= -4 -1
= -5

Question 4

How to find the input of a function

Answer 4

• you just work backwards and find the imput value
  -this is basically solving an equation question
• pay attention to the later used in the question

Question 5

What is the formula to find a y- intercept

Answer 5

y = mx + c
in this equation m is the gradient
and c is the y- intercept that means the line crosses the y axis at (0,C)

Question 6

What is the equation of a line through two points

Answer 6

y - b = m(x - a )

Question 7

how to find the gradient and y- intercept from an equation

Answer 7

if a straight line equation is in the form y= mx+c
if it is not written like this then you need to rearrange to y = mx+c

Question 8

Equations of parallel lines

Answer 8

y= mx+c
you must remember that parallel lines have an equal gradient

Question 9

formula volume of a cuboid

Answer 9

V = L x B x H

Question 10

formula volume of a prism

Answer 10

V = AH

Question 11

Formula Volume of a cylinder

Answer 11

V = 3.14 x radius squared x h

Question 12

Formula Volume of a pyramid

Answer 12

V = 1/3 of ( area of base ) x H
V = 1/3 AH

Question 13

Formula Volume of a cone

Answer 13

1/3 x 3.14 x radius squared x H

Question 14

what is a composite shape

Answer 14

large shape with a smaller shape cut away

Question 15

how to solve the volume of a composite shape

Answer 15

calculate the volume of the total shape and then calculate the volume of the smaller shape and take them away

Question 16

Formula Volume of a sphere

Answer 16

V= 4/3 x 3.14 x radius cubed

Question 17

Volume of a semi sphere

Answer 17

V= 1/2 of ( 4/3 x 3.14 x radius cubed )

Question 18

how to find the height from volume

Answer 18

• changing the subject
  H = v / 3.14 x radius cubed

Question 19

how to find the missing radius

Answer 19

change the subject
- R = cubed root ( 3V / 4x 3.14 )

Question 20

How to find the volume of a composite shape

Answer 20

Can be calculated by adding the volumes of the two individual shapes together

e.g Vcone + Vhemi

Question 21

How to solve equations with a bracket

Answer 21

begin by expanding the brackets and collect like terms

Question 22

How to solve an equation with fractions

Answer 22

remove the fraction by multiplying all terms by the denominator
if it involves more than one fraction you should multiply by the LCM of all denominators

Question 23

how to solve inequalities

Answer 23

• it is the same rules that apply
• if you multiply or divide by a negitive number change the direction of the inequality

Question 24

V of a cuboid

Answer 24

L x B x h

Question 25

V of a prism

Answer 25

A x h

Question 26

V of cylinder

Answer 26

pi x r x r x h

Question 27

V of a pyramid

Answer 27

1/3 x pi x A x h

Question 28

V of cone

Answer 28

1/3 x pi x r x r x h

Question 29

V of sphere

Answer 29

4/3 x pi x r 3

Question 30

V of hemi sphere

Answer 30

1/2 of 4/3 x pi x r 3