Podcast
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?
- $2^2 \times 3^4$
- $2 \times 3^3$
- $2^2 \times 3^3$ (correct)
- $2 \times 3^4$
Which of the following numbers is irrational?
Which of the following numbers is irrational?
- 3.14
- $\frac{3\pi}{2}$ (correct)
- $\frac{22}{7}$
- $\sqrt{400}$
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
- 1, 5 (correct)
- 0, 3
- 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. Which of the following represents the limits of accuracy for this measurement, including inequality signs?
A cyclist is traveling at 10.5 m/s. Which of the following represents the limits of accuracy for this measurement, including inequality signs?
What fraction lies exactly halfway between $\frac{3}{14}$ and $\frac{1}{2}$?
What fraction lies exactly halfway between $\frac{3}{14}$ and $\frac{1}{2}$?
If $243 is divided in the ratio 2:3:4, what is the value of the largest share?
If $243 is divided in the ratio 2:3:4, what is the value of 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?
It takes 3 builders 10 days to complete a brick wall. Assuming the builders work at the same rate, how long would it take 5 builders to complete the same wall?
It takes 3 builders 10 days to complete a brick wall. Assuming the builders work at the same rate, how long would it take 5 builders to complete the same wall?
Flashcards
Prime Factorization
Prime Factorization
Expressing a number as a product of its prime factors (e.g., 12 = 2 x 2 x 3)
Irrational Number
Irrational Number
A number that cannot be expressed as a fraction of two integers.
nth term formula
nth term formula
A formula that defines a sequence using the position 'n' of a term.
Limits of Accuracy
Limits of Accuracy
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Midpoint (of two numbers)
Midpoint (of two numbers)
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Dividing in a Ratio
Dividing in a Ratio
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Simplifying Ratios
Simplifying Ratios
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Inverse Proportion
Inverse Proportion
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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
- Task is to write 324 as a product of its prime factors.
Irrational Numbers
- The problem requires identifying irrational numbers from a given set: {3π/2, 3.14, 22/7, √122, √400}.
Number Sequences
- The task is to state the next two numbers in the sequence: 7, -1, 6, 0, 5.
Formula for nth Term
- Task is to find a formula for the nth term of the sequence: 4, 7, 10, 13.
Limits of Accuracy
- Task is to state the limits of accuracy, including inequality signs, for a cyclist traveling at 10.5 m/s.
Fraction Midway
- Task is to find the fraction halfway between 3/14 and 1/2.
Ratio Division
- Task is to divide $243 in the ratio 2:3:4.
Ratio Simplification
- Task is to simplify the ratio 24:30:45.
Cost Calculation
- If five Chelsea Buns cost $11.75, calculate the cost of nine Chelsea Buns.
Builder Problem
- If 3 builders take 10 days to build a brick wall, determine how long it would take 5 builders working at the same rate.
Cost per Unit
- Find the cost of 120 grams of brown rice costing $5.60 per kilogram, rounded to the nearest cent.
Depreciation
- A Nissan Leaf electric car costs $60,000 and depreciates 12% each year; calculate its worth at the end of the 4th year.
Original Price
- A hat costs Pania $90 after being reduced by 40% from the original price; find the original price.
Venn Diagram Completion
- Complete the Venn diagram for Winter Ski Sports events (Slopestyle, Ski Knuckle, Super Pipe) based on the given information about student preferences.
- Six students liked Super Pipe only.
- Three students liked Slopestyle only.
- Four students liked Ski Knuckle only.
- Three students liked all three skiing styles.
- The number of students liking any pair of skiing styles (like Slopestyle and Super Pipe) is x.
- The total number of students that liked exactly two skiing styles equals the number of 4L students who didn't like watching any of the styles of skiing
Number of Students Disliking Skiing Styles
- The task is to find the number of students who did not like any of the skiing styles.
Expression Simplification
- Fully 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
Covers prime factorization, irrational numbers, and sequences. Includes finding the nth term and limits of accuracy. Also covers ratio divisions and cost calculations.
