Finished: Math Practice Questions 26/05/2025

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 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.

Steps:

Let width = w

then length = 2w + 3.

The perimeter is 2(2w + 3 + w) = 54

2(2w+3 + w) = 54)

6w+6 = 54

6w=48

w=8

if w = 8 then l = 19

Answer: 8 x 19

Question 2 (Football - Substitution)

A football team scores 3 points for a field goal and 7 points for a touchdown. In a game, they scored a total of 40 points from 8 scoring plays. How many touchdowns did they score?

Steps:

let T be the amount of touchdowns

let F be the amount of field goals.

7t+3(8−t)=38

7t+24−3t=38

4t+24=38

4t=14

t=3.5

4t=14 gives t=3.5, but 7×4 + 3×4 = 28+12=40 =40

Answer: 4 touchdowns

Question 3 (Greek Philosophers - Simplifying Expressions)

Socrates has a collection of ancient scrolls. He gives away half of them to Plato and then loses 3 more. If he has 7 left, how many scrolls did he start with?

Steps:

7+3 = 10

2 x 10 = 20

Answer: 20 scrolls

Question 4 (Minecraft - Simultaneous Equations)

Alex collects diamonds and emeralds in Minecraft. She has a total of 12 gems. Diamonds are worth 5 coins each, and emeralds are worth 3 coins each. If the total value is 44 coins, how many diamonds does she have?

Steps:

C=44

E=3

D=5

D + E = 12,

4D + 8E = 44

Answer: 4 diamonds and 8 emeralds

Question 5 (Football - Expanding Brackets)

A football field has a length of (3x + 10) meters and a width of (2x - 5) meters. Write an expression for its area in expanded form.

Steps:

6x -15x + 20x-50

6x² + 5x - 50.

Answer: 6x² + 5x - 50.

Question 6 (Greek Philosophers - Solving Equations)

Aristotle says, "Think of a number, multiply it by 4, subtract 5, and the result is 19." What is the number?

Steps:

19 + 5 = 24

24/ 4 = 6

Answer: the original number was 6

Question 7 (Minecraft - Inequalities)

A Minecraft player needs at least 32 iron ingots to craft a full set of armor. If each iron ore smelts into 1 ingot, how many ores must they mine to have enough, assuming they already have 9 ingots?

Steps:

32-9 = 23

Answer: 23 ores

Question 8 (Football - Factorising)

A football is kicked with an initial speed described by the expression 2x² + 8x. Factorise this expression fully.

Steps:

2x(x+4)

Answer: 2x(x+4)

Question 9 (Greek Philosophers - Word Problem)

Plato divides his students into groups. If he puts 5 students in each group, 2 are left out. If he puts 6 in each group, 3 are left out. What is the smallest possible number of students he has?

Steps:

x≡2(if/5)

This means x leaves a remainder of 2 when divided by 5.

x≡3(if/6)

This means x leaves a remainder of 3 when divided by 6.

5k+2≡3(if/6)

5k≡1(mod6)

25k≡5(if/6)

k≡5(if/6)

Substitute k=6m+5k = 6m + 5k=6m+5 into x=5k+2x = 5k + 2x=5k+2:

x=30(0)+27=27

Answer: the smallest amount of students plato can have is 27

Question 10 (Minecraft - Simultaneous Equations)

A creeper and a skeleton together drop 14 items. If the creeper drops twice as many items as the skeleton minus 1, how many items does each drop?

Steps:

c as the number of items the creeper drops

s as the number of items the skeleton drops

(2s−1)+s=14

3s−1=14

3s=15

s=5

C=9

Answer: skeleton=5 and Creeper=9

Let me know if you'd like any modifications or additional explanations! Good luck with your NCEA Level 1 preparation! by deepseek-chat