Finished: Math Practice Questions 25/05/2025
Here are 10 algebra practice questions tailored for a New Zealand student preparing for NCEA Level 1, incorporating Minecraft, football, and Greek philosophers:
Question 1 (Minecraft)
Steve is building a rectangular farm in Minecraft. The length of the farm is 3 blocks more than twice its width. The perimeter of the farm is 42 blocks. Find the dimensions of the farm.
Steps:
l=2w+3
P=2l+2w=42
changing 2(2w+3)+2w=42
4w+6+2w=42
6w+6=42
6w=42−6
6w=36
w=6/36
w=6
if w = 6 then L = 15
Answer: the dimensions are 6 X 15
Question 2 (Football)
In a football match, the number of goals scored by Team A is 5 less than double the goals scored by Team B. If the total goals scored by both teams is 19, how many goals did each team score?
Steps:
2x - 5 + x = 19
x = goals by team b
a=2x-5
x + (2x - 5) = 19 → 3x - 5 = 19 → 3x = 24 → x = 8.
goals by team a = 2x-5 = 16 -5 = 11
Answer: team a scored 11 and team b scored 8
Question 3 (Greek Philosophers)
Pluto has a collection of ancient Greek scrolls. He has twice as many Aristotle scrolls as Plato scrolls, and 5 more Socrates scrolls than Plato scrolls. If he has 37 scrolls in total, how many scrolls does he have for each philosopher?
Steps:
A= Aristotle
P=Plato
S=Socrates
A=2P
P+5=S
2p+p+p+5=37
4p=32
p=8
If= P=8 then A= 16
if P = 8 then S = 13
Answer: Pluto has 8 Plato scrolls, 13 Socrates scrolls and 16 Aristotle scrolls
Question 4 (Minecraft)
Alex mines 3 diamonds per hour and Steve mines 5 diamonds per hour. Together, they mine 24 diamonds in total after working the same amount of time. How many hours did each work?
Steps:
1 hour of mining = 3 diamonds + 5 diamonds => 8 diamonds
meaning 8 diamonds/hour
8x = 24 → x = 3
Answer: They worked 3 hours for 24 diamonds
Question 5 (Football)
A football club sells adult tickets for $12 and child tickets for $8. In one game, they sell 50 tickets and collect $480. How many adult and child tickets were sold?
Steps:
1 For every ticket sold to adult, $4 more is collected comparing to selling it to child.
2 let A be the tickets sold to adult, and C be the tickets sold to child.
if all tickets were sold to child, the total will be 8*50 = 400,
while the actual total amount is $480 meaning:
A*4 +400=480
A can be solved as 20, and C should be 30
Answer: they sold 20 adults tickets and 30 children's tickets.
Question 6 (Greek Philosophers)
Pythagoras has a number of students. If he adds 8 more students, the total becomes 3 times the original number. How many students did he originally have?
Steps:
Let ( x ) = original students. Then ( x + 8 = 3x ). Solve for ( x ).
8=2x
x=4
Answer: he had 4
Question 7 (Minecraft)
A creeper explosion destroys 4 blocks more than half the blocks in a structure. If 20 blocks are destroyed, how many blocks were in the structure originally?
Steps:
let total blocks be T,
4+T/2 = 20
T = 32
Answer: total blocks originally 32
Question 8 (Football)
A football is kicked upward with an initial speed. The height (h) in meters after t seconds is given by:
h = -5t² + 20t
At what time does the ball hit the ground?
Steps:
- Set ( h = 0 ): ( -5t² + 20t = 0 ) → ( t(-5t + 20) = 0 ) → ( t = 0 ) or ( t = 4 ).
Answer: 4 seconds
Question 9 (Greek Philosophers)
Socrates has twice as many books as Diogenes, and together they have 18 books. How many books does each have?
Steps:
S+D = 18
S=2D
d =6
S=12
Answer: Socrates had 12 and Diogenes have 6
Question 10 (Minecraft & Simultaneous Equations)
In Minecraft, 3 iron ingots and 2 gold ingots make 1 sword, while 1 iron ingot and 4 gold ingots make 1 shield. If a player has 14 iron ingots and 16 gold ingots, how many swords and shields can they craft?
Steps:
- Let ( x ) = swords, ( y ) = shields.
- ( 3x + y = 14 ) (iron)
- ( 2x + 4y = 16 ) (gold)
Solve to find ( x = 4 ), ( y = 2 ). The player can craft 4 swords and 2 shields.
Answer: the player can craft 4 swords and 2 shields