Finished:Math Practice Questions 16/07/2025
Here are 10 algebra practice questions tailored to your interests (Minecraft, football, and Greek philosophers) for NCEA Level 1 preparation:
Question 1 (Minecraft - Linear Equations)
Steve in Minecraft collects diamonds at a rate of 3 diamonds per hour. After 5 hours, he has a total of 20 diamonds (including some he already had). How many diamonds did Steve start with?
Steps:
5 times 3 = 15
20 - 15 = 5
Steve started with 5 diamonds
Answer: Steve started with 5 diamonds
Question 2 (Football - Substitution)
A football team scores 3 points for a win and 1 point for a draw. If they played 10 games and got 24 points, how many games did they win?
Steps:
if all 10 matches were draws the team would have only gotten 10 points
each win gives 2 more points. there is a 14 points difference.
14/2 = 7
the team won 7 matches
Answer: the team won 7 matches
Question 3 (Greek Philosophers - Simplifying Expressions)
Socrates has (2x + 5) books, and Plato has (3x - 2) books. Together, they have 18 books. Find the value of (x).
Steps:
2x+5+3x-2 = 5x+3
5x=15
x=3
Answer: x=3
Question 4 (Minecraft - Simultaneous Equations)
In Minecraft, Alex collects 5 wood blocks and 3 stone blocks in 26 minutes. Steve collects 2 wood blocks and 4 stone blocks in 20 minutes. How long does it take to collect 1 wood block and 1 stone block individually?
Let:
( w ) = time (minutes) for 1 wood block
( s ) = time (minutes) for 1 stone block
Equations:
1) ( 5w + 3s = 26 )
2) ( 2w + 4s = 20 )
Steps:
2(5w+3s)=2(26)⇒10w+6s=52(Equation 3)
5(2w+4s)=5(20)⇒10w+20s=100(Equation 4)
(10w+20s)−(10w+6s)=100−52 10w−10w+20s−6s=4810w - 10w + 20s - 6s = 4810w−10w+20s−6s=48 14s=48⇒s=4814=247≈3.43 minutes per stone block14s = 48 \Rightarrow s = \frac{48}{14} = \frac{24}{7} \approx 3.43 \text{ minutes per stone block}14s=48⇒s=1448=724≈3.43 minutes per stone block
5w+3s=26 5w+3(247)=26⇒5w+727=265w + 3\left(\frac{24}{7}\right) = 26 \Rightarrow 5w + \frac{72}{7} = 265w+3(724)=26⇒5w+772=26
5w=26−772=7182−772=7110
w=7⋅5110=35110=722≈3.14 minutes per wood block
Time per wood block: 227\boxed{\frac{22}{7}}722 minutes ≈ 3.14 minutes
Time per stone block: 247\boxed{\frac{24}{7}}724 minutes ≈ 3.43 minutes
Answer: Time per wood block: 227\boxed{\frac{22}{7}}722 minutes ≈ 3.14 minutes
Time per stone block: 247\boxed{\frac{24}{7}}724 minutes ≈ 3.43 minutes
Question 5 (Football - Expanding Brackets)
A football stadium has a seating capacity of (3(x + 4)) people. If (x = 5), how many seats are there?
Steps:
changing x to 5
(3(5+4))
3 x 9 =27 seats
Answer: 27 seats
Question 6 (Greek Philosophers - Solving Equations)
Aristotle says: "If you multiply my age by 2 and subtract 5, you get 17." How old is Aristotle?
Steps:
17+5=22
22/2 = 11
Answer: Aristotle is 11 at that time
Question 7 (Minecraft - Fractions)
A Minecraft creeper drops 3/4 of its gunpowder when defeated. If you get 9 gunpowder, how much did it originally have?
Steps:
9/3 = 3
3x4 = 12
Answer: 12 gunpowerder
Question 8 (Football - Rearranging Formulas)
The distance ( d ) a football travels is given by:
[ d = 5t^2 ]
where ( t ) is time in seconds.
If ( d = 80 ), find ( t ).
Steps:
( 5t^2 = 80 ) → ( t^2 = 16 ) → ( t = 4 ).
Answer: t=4
Question 9 (Greek Philosophers - Inequalities)
Pythagoras says: "Twice my number of students is less than 30." Write this as an inequality and solve for the maximum number of students.
Steps:
Sx2<30
s<15
Answer: s<15
Question 10 (Minecraft & Football - Word Problem)
In Minecraft, you earn 2 emeralds per goal scored in football. If you scored (x) goals and spent 10 emeralds on a diamond sword, you have 6 emeralds left. How many goals did you score?
Steps:
6+10 = 16
16/2 = 8
you scored 8 goals
Answer: you scored 8 goals
Let me know if you'd like any modifications or additional explanations! Good luck with your NCEA Level 1 prep! by deepseek-chat