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Questions and Answers
What is 324 expressed as the product of its prime factors?
What is 324 expressed as the product of its prime factors?
- $2 \times 3^4$
- $2^2 \times 3^4$
- $2^3 \times 3^3$
- $2^2 \times 3^3$ (correct)
Which of the following numbers is irrational?
Which of the following numbers is irrational?
- $\frac{22}{7}$
- 3.14
- $\sqrt{400}$
- $\frac{3\pi}{2}$ (correct)
Given the sequence 7, -1, 6, 0, 5, __, __, what are the next two numbers?
Given the sequence 7, -1, 6, 0, 5, __, __, what are the next two numbers?
- 1, 4 (correct)
- -1, 3
- 2, 5
- 1, 6
What is the formula for the nth term of the sequence 4, 7, 10, 13, ...?
What is the formula for the nth term of the sequence 4, 7, 10, 13, ...?
A cyclist is traveling at 10.5 m/s. State the limits of accuracy, including inequality signs, assuming the measurement is to the nearest 0.1 m/s.
A cyclist is traveling at 10.5 m/s. State the limits of accuracy, including inequality signs, assuming the measurement is to the nearest 0.1 m/s.
What fraction lies exactly halfway between $\frac{3}{14}$ and $\frac{1}{2}$?
What fraction lies exactly halfway between $\frac{3}{14}$ and $\frac{1}{2}$?
Divide $243 in the ratio 2:3:4. What is the largest share?
Divide $243 in the ratio 2:3:4. What is the largest share?
Simplify the ratio 24 : 30 : 45.
Simplify the ratio 24 : 30 : 45.
If five Chelsea Buns cost $11.75, what is the cost of 9 Chelsea Buns?
If five Chelsea Buns cost $11.75, what is the cost of 9 Chelsea Buns?
A brick wall is built by 3 builders in 10 days. Assuming all builders work at the same rate, how many days would it take 5 builders to complete the same wall?
A brick wall is built by 3 builders in 10 days. Assuming all builders work at the same rate, how many days would it take 5 builders to complete the same wall?
Flashcards
Prime Factorization
Prime Factorization
Expressing a number as a product of its prime number factors.
Irrational Numbers
Irrational Numbers
Numbers that cannot be expressed as a simple fraction; their decimal representation is non-terminating and non-repeating.
Number Sequence
Number Sequence
A list of numbers that follows a specific pattern or rule.
Formula for nth term
Formula for nth term
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Limits of Accuracy
Limits of Accuracy
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Fraction Half-Way
Fraction Half-Way
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Dividing in a Ratio
Dividing in a Ratio
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Simplifying Ratio
Simplifying Ratio
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Depreciation
Depreciation
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Original Price
Original Price
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Study Notes
- Auckland Grammar School Form 5Pre Q Common Test 1 2024 covers Arithmetic I, II, and III.
Prime Factorization
- Express 324 as the product of its prime factors.
Irrational Numbers
- Identify irrational numbers from the set: {3π/2, 3.14, 22/7, √122, √400}.
Number Sequences
- Determine the next two numbers in the sequence: 7, -1, 6, 0, 5, ...
Formula for nth Term
- Find the formula for the nth term of the sequence: 4, 7, 10, 13, ...
Limits of Accuracy
- State the limits of accuracy, including inequality signs, for a cyclist's speed of 10.5 m/s.
Fractions
- Calculate the fraction halfway between 3/14 and 1/2.
Ratios
- Divide $243 in the ratio 2:3:4.
- Simplify the ratio 24:30:45.
Cost Calculation
- Five Chelsea Buns cost $11.75; determine the cost of nine Chelsea Buns.
- Calculate the cost of 120 grams of brown rice at $5.60 per kilogram, rounded to the nearest cent.
Work Rate
- Three builders take 10 days to build a brick wall; find how long it would take five builders working at the same rate.
Depreciation
- A Nissan Leaf electric car costs $60,000 and depreciates by 12% each year; find its worth at the end of the 4th year.
Percentage Reduction
- A hat costs Pania $90 after a 40% reduction; calculate the original price of the hat.
Venn Diagram
- Complete the Venn Diagram for Winter Ski Sports, with 28 students watching Slopestyle, Ski Knuckle, and Super Pipe.
- Six students only liked Super Pipe, three only liked Slopestyle, and four only liked Ski Knuckle.
- Three students liked all three skiing styles.
- The number of students who liked exactly two skiing styles equals those who did not like any.
- Determine the number of students who did not like any skiing styles.
Simplification of Radicals
- Simplify the following expressions:
- 2√5 + 4√80 - 3√12
- 2√8 × 3√18
- √72 / √27
- √18(3√2 - 2√3)
- (2√3 - √7)(2√3 + √7)
- (3√2 - 2√5)²
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Description
Auckland Grammar School Form 5 Pre Q Common Test 1 2024 covers Arithmetic I, II, and III. Topics include prime factorization, irrational numbers, number sequences, limits of accuracy and ratios. It also test knowledge of fractions, cost calculation and work rate.
