Finished:Math Practice Questions 7/06/2025
Here are 10 algebra practice questions tailored for a New Zealand NCEA Level 1 student, incorporating Minecraft, football, and Greek philosophers:
Question 1 (Minecraft)
Steve is building a rectangular farm in Minecraft. The length of the farm is 5 blocks more than twice its width. The perimeter of the farm is 82 blocks. Find the dimensions of the farm.
Steps:
82/2
41
41-5=36
36/3=12
W=12
so L=29
Answer: 12 x 29
Question 2 (Football)
A football team scores 3 points for a win and 1 point for a draw. In a season, they played 20 matches and earned a total of 52 points. If they won ( w ) matches and drew ( d ) matches, write two equations to represent this situation and solve for ( w ) and ( d ).
Steps:
w+d=20
3w+d=52
(3w+d)−(w+d)=52−20
2w=32
w=16
16+d=20=>d=4
Answer: Wins (w) = 16 Draws (d) = 4
Question 3 (Greek Philosophers)
Plato has twice as many philosophy books as Aristotle. Together, they have 27 books. How many books does each philosopher have?
Steps:
27/3 = 9
A=9
P=2x9
p=18
Answer: Aristotle has 9 books Plato has 18 books
Question 4 (Minecraft)
A creeper explosion destroys a stack of blocks in the ratio 3:5 (stone to dirt). If 65 dirt blocks were destroyed, how many stone blocks were destroyed?
Steps:
65/5
=13
13 x 3 = 39
Answer: 39 were destroyed by the creeper
Question 5 (Football)
The number of goals scored by a striker in a season is given by ( 2x + 5 ), and the number of assists is ( x - 3 ). If the total contributions (goals + assists) is 17, find ( x ).
Steps:
3x+2=17
3x=15
x=5
Answer: x=5
Question 6 (Greek Philosophers)
Socrates has some olives. He gives away half of them to Plato and then loses 3 more. If he has 7 left, how many olives did he start with?
Steps:
7+3=10
10 x 2= 20
Answer: 10 x 2= 20
Question 7 (Minecraft)
A crafting recipe requires 4 iron ingots and 1 redstone dust to make a compass. If a player has 28 iron ingots and unlimited redstone, how many compasses can they make?
Steps:
28/4=7
Answer: the played can make 7 compasses
Question 8 (Football)
A football is kicked into the air. Its height ( h ) (in meters) after ( t ) seconds is given by ( h = -5t^2 + 20t ). At what time does the ball hit the ground?
Steps:
h(t)=−5t2+20t=0
−5t2+20t=0
t(−5t+20)=0
t=0
−5t+20=0⇒t=4
T=4
Answer: T=4
Question 9 (Greek Philosophers)
Pythagoras has a collection of right-angled triangles. The hypotenuse of one triangle is ( x + 2 ) cm, and the other sides are ( x ) cm and 6 cm. Find ( x ) using the Pythagorean theorem.
Steps:
(hypotenuse)2=(side 1)2+(side 2)2
(x+2)2=x2+62
(x+2)2=x2+36
x2+4x+4=x2+36
4x+4=36
4x=32
x=8
Answer: x=8
Question 10 (Minecraft & Simultaneous Equations)
Alex and Steve are mining diamonds. Alex finds 3 more diamonds than Steve. Together, they find 17 diamonds. Let ( A ) be Alex’s diamonds and ( S ) be Steve’s diamonds.
- Write two equations to represent this situation.
- Solve for ( A ) and ( S ).
Steps:
17-3=14
14/2=7
Steve finds 7 and Alex finds 10
Answer: Steve finds 7 and Alex finds 10
These questions integrate algebra with the student's interests while aligning with NCEA Level 1 standards. Let me know if you'd like any modifications! by deepseek-chat