Finished:Math Practice Questions 14/07/2025
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. If the perimeter of the farm is 54 blocks, find the dimensions of the farm.
Steps:
Let width = W, length = 2W + 3. Perimeter = 2(W + 2W + 3) = 54 → 6W + 6 = 54 → W = 8, L = 19.
Answer: Width = 8 blocks, Length = 19 blocks.
Question 2 (Football)
A football team scores 3 goals for every 2 goals conceded. In a season, they conceded 24 goals. How many goals did they score in total?
Steps:
24/2 = 12
12x 3 = 36
they scored 36 goals
Answer: they scored 36 goals
Question 3 (Greek Philosophers)
Pluto has twice as many philosophy books as Aristotle, and together they have 36 books. How many books does each philosopher have?
Steps: 36/3 = 12
Aristotle has 12
and Pluto has 24
Answer: Aristotle has 12 and Pluto has 24
Question 4 (Minecraft & Simultaneous Equations)
In Minecraft, Alex collects diamonds (D) and emeralds (E). She has:
- D + E = 15
- D – E = 5
Find how many diamonds and emeralds she has.
Steps:
based on equation 2 D=5+E
putting this into equation 1
5+E+E=15
2E=10
E=5
and diamond = 10
Answer: E=5 and diamond = 10
Question 5 (Football & Linear Equations)
A football player runs x km in training. The next day, he runs 5 km more than half of the previous distance. If his total distance over two days is 23 km, find x.
Steps:
x + (0.5x + 5) = 23.
23-5
18/1.5
12
he ran 12kms
Answer: he ran 12kms
Question 6 (Greek Philosophers & Ratios)
Socrates, Plato, and Aristotle share gold coins in the ratio 2:3:5. If Aristotle receives 20 coins, how many coins do Socrates and Plato get?
Steps:
the total is 10 and Aristotle gets half there fore 20 gold coins was half
20/4 = 5
5 x3 - Plato
5x2 = Socrates
Plato got 15
Socrates got 10
and Aristotle got 20
Answer: Plato got 15 Socrates got 10 and Aristotle got 20
Question 7 (Minecraft & Expanding Brackets)
A Minecraft chest contains (3x + 2) stacks of cobblestone and (2x - 1) stacks of wood. Write and simplify an expression for the total stacks.
Steps:
3x+2 +2x-1
5x+1
Answer: 5x+1
Question 8 (Football & Substitution)
A football’s price is $5 more than twice a jersey’s price (J). If the football costs $35, find the cost of the jersey.
Steps:
35-5 = 30
30/2 = 15
the jersey is worth 15
Answer: the jersey is worth 15
Question 9 (Greek Philosophers & Equations)
Diogenes has x coins. After giving away 10 coins, he has half as many as Plato. If Plato has 30 coins, find x.
Steps:
30/2 = 15
15+10 = 25
Diogenes has 25 coins
Answer: Diogenes has 25 coins
Question 10 (Minecraft & Inequalities)
A Minecraft player needs at least 50 iron ingots to craft armor. If each iron block smelts into 9 ingots, write and solve an inequality to find the minimum number of blocks (B) needed.
Steps:
9x6=54
9x5 =45
meaning the least amount of iron blocks the player needs is 6
Answer: meaning the least amount of iron blocks the player needs is 6
Let me know if you'd like any modifications or additional explanations! Good luck with NCEA Level 1! by deepseek-chat