Finished:Math Practice Questions 20/07/2025
Here are 10 algebra practice questions tailored to your interests (Minecraft, football, and Greek philosophers) for NCEA Level 1 preparation:
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:
Width = 8, Length = 19.
( 2(W + 2W + 3) = 54 ) → ( 6W + 6 = 54 ) → ( W = 8 ), ( L = 19 ).
Answer: Width = 8, Length = 19.
Question 2 (Football)
During a football match, a player scores 3 more goals in the second half than in the first half. If the total goals scored are 11, how many goals did they score in each half?
Steps:
11-3 = 8
8/2=4
4 in the first half and 7 in the second half
Answer: 4 in the first half and 7 in the second half
Question 3 (Greek Philosophers)
Plato has twice as many books as Aristotle. Together, they have 24 books. How many books does each philosopher have?
Steps:
24/3 = 8
Aristotle has 8books
Plato has 16 books
Answer: Aristotle has 8 books and Plato has 16 books
Question 4 (Minecraft - Simultaneous Equations)
In Minecraft, Alex collects diamonds (D) and emeralds (E). She has:
- D + E = 12
- D – E = 4
Find how many diamonds and emeralds she has.
Steps:
based on equation 2
D = 4 +E
Putting this into equation 1
4+E+E=12
2E=8
D and E (D=8, E=4).
Answer: E=4 D=8
Question 5 (Football - Linear Equation)
A football team earns 2 points for a win and 1 point for a draw. If they played 10 matches and earned 16 points, how many matches did they win?
Steps:
if all the points were draws they would have only gotten 10 points
there is a 6 points difference
each win gives 2 more points
6/2 = 3
they won 3 matches
Answer: they won 3 matches
Question 6 (Greek Philosophers - Substitution)
Socrates has 5 more scrolls than Pythagoras. If Pythagoras has S scrolls, write an expression for the total number of scrolls they have together.
Steps:
2S+5
Answer: 2S+5
Question 7 (Minecraft - Expanding Brackets)
A Minecraft chest can hold (3x + 2) items, and another chest holds (2x – 5) items. Write a simplified expression for the total number of items both chests can hold.
Steps:
3X+2+2x-5=
5x-2
Answer: 5x-2
Question 8 (Football - Factorising)
The area of a football field is given by x² + 7x + 10. Factorise this expression to find possible dimensions of the field.
Steps:
(x+a)(x+b)
a+b=7
ab=10ab = 10ab=10
x2+7x+10=(x+2)(x+5)
(x+2) units and (x+5) units
Answer: (x+5)(x+2)).
Question 9 (Greek Philosophers - Solving Equations)
Aristotle says: "If you multiply my age by 3 and subtract 5, you get 40." How old is Aristotle?
Steps:
40+5 = 45
45/3 = 15
Aristotle is 15 at the time
Answer: Aristotle is 15 at the time
Question 10 (Minecraft - Simultaneous Equations)
A player mines stone (S) and coal (C). They collect:
- 2S + 3C = 26
- S – C = 3
Find how much stone and coal they mined.
Steps:
based on equation 2 s=3+c
putting this into equation 2
6+2c+3c=26
5C=20
c=4
Answer:c=4 and stone = 7
Let me know if you'd like any modifications or additional explanations! Good luck with your NCEA Level 1 prep! 🚀 by deepseek-chat