Math Practice Questions 21/07/2025

Here are 10 NCEA Level 1 Mathematics practice questions tailored to your interests in Minecraft, football, and Greek philosophers, aligned with the NCEA 91947 standard.

Number and Algebra (70%)

1. Relating Graphs, Tables, Equations, and Patterns

Question:
In Minecraft, Steve collects diamonds each day. The number of diamonds he collects follows the pattern:
Day 1: 3 diamonds
Day 2: 5 diamonds
Day 3: 7 diamonds
Write an equation for the number of diamonds ((D)) collected on day (n).

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2. Optimal Solutions (Linear Programming)

Question:
A football team needs at least 5 defenders and 3 attackers for a match. The coach wants to minimize costs, where defenders cost $50 each and attackers cost $70 each. Write the inequalities and find the minimum cost.

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3. Manipulating and Simplifying Expressions

Question:
Socrates simplifies the expression ((2x + 3)(x - 4) - (x^2 - 5x)). Show his working and simplify fully.

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4. Simultaneous Linear Equations (Two Unknowns)

Question:
In Minecraft, a diamond sword costs 2 diamonds and 1 iron ingot, while an iron sword costs 1 diamond and 3 iron ingots. If a player has 12 diamonds and 10 iron ingots, how many of each sword can they make?

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5. Relating Graphs and Equations

Question:
Plato draws a straight-line graph representing the distance a football travels over time. The line passes through points (2, 10) and (5, 25). Find the equation of the line.

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6. Simplifying Expressions

Question:
Aristotle simplifies (\frac{3x^2 - 12x}{x^2 - 16}). Show his working and simplify fully.

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7. Simultaneous Equations (Football Context)

Question:
A football team scores goals ((G)) and points ((P)) where:
[ 2G + P = 20 ]
[ G - P = 4 ]
Find the values of (G) and (P).

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Measurement & Geometry (30%)

8. Pythagoras’ Theorem (3D - Minecraft Context)

Question:
Steve builds a Minecraft tower that is 5 blocks tall. If he places a ladder diagonally from the base to the top, and the base is 12 blocks long, how long is the ladder?

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9. Trigonometric Ratios (SOHCAHTOA - Football Context)

Question:
A football is kicked at an angle of 30° with the ground. If the ball travels 50 meters horizontally, how high did it go?

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10. Pythagoras’ Theorem (2D - Greek Philosophers Context)

Question:
Pythagoras draws a right-angled triangle with legs of 6 cm and 8 cm. What is the length of the hypotenuse?

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These questions cover Number & Algebra (70%) and Measurement & Geometry (30%) while incorporating your interests. Let me know if you'd like any modifications! by deepseek-chat