Mathematics Stage 5 – Practice Test: Units 3 and 7

Instructions: Answer all 50 questions. Choose one answer for each question in Part I. Show your working and explain your thinking when asked in Part II.

PART I. MULTIPLE CHOICE

Câu 1. What is the term-to-term rule for the sequence $14, 21, 28, 35, \ldots$?

Câu 2. What is the next term in the sequence $18, 13, 8, 3, \ldots$?

Câu 3. A sequence starts at $4$ and increases by $3$ each time. What is its sixth term?

Câu 4. Which number is missing from the linear sequence $5, \square, 15, 20$?

Câu 5. Which number is a square number?

Câu 6. What is the next triangular number in the sequence $1, 3, 6, 10, \ldots$?

Câu 7. Which number is prime?

Câu 8. Which statement about number "$1$" is correct?

Câu 9. Which number is a multiple of both $3$ and $4$?

Câu 10. Which number is a factor of $36$?

Câu 11. Three cakes are shared equally among four children. How much cake does each child receive?

Câu 12. What is $\dfrac{3}{5}$ of $40$?

Câu 13. Which fraction is equivalent to $\dfrac{3}{4}$?

Câu 14. Which decimal is equivalent to $35\%$?

Câu 15. Which percentage is equivalent to $\dfrac{3}{5}$?

Câu 16. Which mixed number is equivalent to $\dfrac{11}{4}$?

Câu 17. Which improper fraction is equivalent to $2\dfrac{2}{5}$?

Câu 18. Which number is the greatest?

Câu 19. One quarter of a number is $7$. What is the number?

Câu 20. A shirt costs $80$ dollars. It is reduced by $25\%$. What is the sale price?

PART II. WRITTEN QUESTIONS

Show your working. Give an explanation whenever the question asks for one.

Unit 3. Numbers and sequences

Câu 1. A sequence starts at $9$. The term-to-term rule is “add $6$”.
a) Write the first six terms.

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b) Find the tenth term. Show how you found it.

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Câu 2. A sequence starts at $25$. The term-to-term rule is “subtract $8$”.
a) Write the first six terms.

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b) What are the first two terms less than zero?

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Câu 3. The numbers in this sequence increase by the same amount each time:
$7, \square, \square, \square, 31$.
Find the missing numbers and explain how you found the jump size.

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Câu 4. A sequence starts at $3$ and increases by $5$ each time. Will $58$ appear in the sequence? Explain your answer without listing every term.

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Câu 5. A sequence starts at $64$ and decreases by $6$ each time. Mia says, “The sequence will reach $0$.” Is she correct? Explain your answer.

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Câu 6. A theatre has $12$ seats in its first row. Each new row has $4$ more seats than the row before it.
a) How many seats are in the second, third and fourth rows?

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b) How many seats are in the eighth row? Show your working.

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Câu 7. Look at the sequence $2, 5, 9, 14, 20, \ldots$.
a) Write the next two terms.

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b) Is this a linear sequence? Explain your answer.

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Câu 8. A square pattern has $1$ dot in the first pattern, $4$ dots in the second and $9$ dots in the third.
a) Draw the fourth pattern as a square array of dots.

b) Write the number of dots in the fifth and tenth patterns.

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c) Explain why these numbers are called square numbers.

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Câu 9. The first four triangular numbers are $1, 3, 6, 10$.
a) Draw a dot pattern for the fifth triangular number.

b) Write the fifth and sixth triangular numbers.

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c) Describe how the sequence grows.

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Câu 10. Write all the square numbers greater than $40$ and less than $100$. Circle the even square numbers in your list.

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Câu 11. A number is greater than $20$ and less than $30$. It is prime and is also a factor of $46$. What is the number? Explain how you know.

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Câu 12. List all the factors of $24$. Explain why $24$ is a composite number.

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Câu 13. Leo says, “All odd numbers are prime.” Give a counterexample and explain why it shows that Leo is wrong.

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Câu 14. Use the digit cards $1$, $2$, $5$ and $9$. Use two different cards for each answer.
a) Make a two-digit prime number.

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b) Make a two-digit square number.

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c) Make a two-digit multiple of $3$.

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d) Make a two-digit factor of $36$.

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Câu 15. A row of joined squares is made from matchsticks. The first square uses $4$ matchsticks. Each new square shares one side with the previous square.
a) How many matchsticks are needed for $2$, $3$ and $4$ squares?

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b) How many matchsticks are needed for $10$ squares? Explain your method.

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Unit 7. Fractions, decimals and percentages

Câu 16. Five children share two identical cakes equally.
a) Write the division that shows the share for each child.

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b) What fraction of one cake does each child receive?

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Câu 17. A library has $48$ new books. It puts $\dfrac{3}{8}$ of them on a display. How many books are on the display? Show your working.

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Câu 18. A bottle contains $150$ ml of juice. This is $\dfrac{1}{4}$ of the amount it holds when full. How much juice does the full bottle hold?

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Câu 19. Three tenths of a number is $24$. Find the number and check your answer.

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Câu 20. Sam says, “To find $\dfrac{3}{5}$ of $45$, I divide $45$ by $3$ and then multiply by $5$.” Explain Sam’s mistake and find the correct answer.

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Câu 21. Complete each statement.
a) $\dfrac{3}{5}=\dfrac{\square}{10}$
b) $\dfrac{2}{3}=\dfrac{8}{\square}$
c) $\dfrac{\square}{12}=\dfrac{1}{4}$

Câu 22. Complete the table with equivalent fractions, decimals and percentages.

Câu 23. A rectangular card is divided into $20$ equal small squares. Seven squares are shaded.
a) What fraction of the card is shaded?

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b) Write the shaded fraction as a decimal and as a percentage.

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Câu 24. A bag contains $80$ beads. $50\%$ are red and $25\%$ are blue. The rest are white.
a) What percentage are white?

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b) How many beads are there of each colour?

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Câu 25. Write each improper fraction as a mixed number.
a) $\dfrac{13}{4}$ = _________
b) $\dfrac{17}{5}$ = _________
c) $\dfrac{20}{3}$ = _________

Câu 26. Write each mixed number as an improper fraction.
a) $1\dfrac{3}{4}$ = _________
b) $2\dfrac{2}{5}$ = _________
c) $3\dfrac{1}{3}$ = _________

Câu 27. Use $<$, $>$ or $=$ to complete each statement.
a) $\dfrac{3}{5}$ $\square$ $55\%$
b) $0.25$ $\square$ $\dfrac{1}{4}$
c) $\dfrac{7}{10}$ $\square$ $0.75$

Câu 28. Put these values in order from smallest to greatest:
$\dfrac{3}{4}$, $0.2$, $65\%$, $\dfrac{2}{5}$, $0.8$.
Show how you compared them.

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Câu 29. In a class survey, $8$ out of $40$ pupils choose football as their favourite sport. A pupil says, “That is $8\%$ of the class.” Explain the mistake and find the correct percentage.

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Câu 30. A shop reduces the price of a $60$-dollar backpack by $20\%$.
a) How much is the reduction?

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b) What is the sale price?

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c) A second backpack costs $48$ dollars and is reduced by $\dfrac{1}{4}$ of its price. Which backpack has the lower sale price? Show your working.

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Name: ................................................ Class: ........................