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Number and Algebra Basics

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Number and Algebra Basics

Show your working where asked. Use clear mathematical notation.

Number structure and operations

1.Arrange these values from least to greatest: 10², 0.01, 10⁻¹, 1,000.

2.Write the prime factorisation of 60. Show how you split the number into factors.

3.What is the highest common factor of 30 and 45?

4.Find the lowest common multiple of 5 and 8.

5.Estimate 386 × 41 by rounding each number to the nearest 10. Write the rounded numbers and their product.

6.Calculate 3,762 ÷ 8. Give any remainder as a decimal.

7.Round 6,349 to the nearest hundred.

8.Round 14,752 to the nearest hundred.

9.Round 8,050 to the nearest hundred.

10.Which two strategies can help you find an approximate value for 62 × 39? Select all correct answers.

Round the factors to convenient values
Use place value to judge the size of the answer
Remove every digit and guess
Replace both factors with zero

Algebraic expressions

11.Simplify 8x − 3x + 4.

12.Simplify 6y + 7 − 2y + 3.

13.Simplify 7a + 3b − 2a + 5b.

14.Expand 4(x + 5).

15.Expand 3(2y − 7).

16.Expand 5(a + 3b).

17.Select every expression equivalent to 8x + 16.

8(x + 2)
4(2x + 4)
2(4x + 4)
x + 24

Solving equations and applying algebra

18.Solve x + 9 = 17. Show the inverse operation you use.

19.Solve 4y = 28. Show the inverse operation you use.

20.Solve 3x + 4 = 19.

21.Solve 5t − 6 = 24.

22.At a history museum, Mei says that five times a number, then adding 4, gives 29. Write an equation and solve to find the number.

23.A rectangular display has length (2x + 3) metres and width 5 metres. Write an expression for its perimeter and simplify it.

Mathematical vocabulary

24.Match each term with its meaning.

Variable
Prime factorisation
Distributive property
Like terms

Terms with the same variable part
Multiplying a factor by each term inside brackets
A letter used to stand for a number
Writing a number as a product of prime numbers

25.Complete the sentence with the correct term: inverse, estimate, exponent, simplify. To undo an operation when solving an equation, use its operation.

26.Complete the sentence with the correct term: inverse, estimate, exponent, simplify. Combine like terms to an algebraic expression.

27.Complete the sentence with the correct term: inverse, estimate, exponent, simplify. In 10⁴, the 4 is the .

28.Complete the sentence with the correct term: inverse, estimate, exponent, simplify. can help you decide whether a calculated answer is reasonable.

Problem-solving challenge

29.Keira has $50 to spend at the history museum shop. She buys several identical history books costing $9 each and has $14 left. Write and solve an equation to find how many books she bought.