IB Primary Years Programme (PYP) · Mathematics

Generalizing patterns with expressions and equations: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Generalizing patterns with expressions and equations.

10 questions24 marksFree, no account

Question 1

1 mark

In the sequence: \( 4, 7, 10, 13, \dots \), what is the rule for finding the \( n \)-th term?

Question 2

1 mark

Solve for \( y \) in the equation: \( 4y - 6 = 18 \).

Question 3

1 mark

Which of the following expressions represents "5 more than 3 times a number \( n \)"?

Question 4

1 mark

A rectangular garden has a length of \( L \) meters. The width is 4 meters shorter than the length. If the perimeter of the garden is 32 meters, which equation can be used to find \( L \)?

Question 5

1 mark

If \( x + 7 = 15 \), what is the value of \( x \)?

Question 6

2 marks

If \(x + 5 = 12\), what is the value of \(x\)?

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Question 7

4 marks

The sum of three consecutive integers is 45. If the smallest integer is represented by \(n\), set up an equation and solve for \(n\).

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Question 8

5 marks

In a school library, the number of fiction books is 15 more than twice the number of non-fiction books. If there are 165 fiction books, find the number of non-fiction books by setting up an algebraic equation.

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Question 9

3 marks

Part a: A box contains some candies. If there are \( y \) candies in each box and Sarah has 5 such boxes, write an algebraic expression for the total number of candies she has.
Part b: If Sarah gives 12 candies to her brother, write an algebraic expression for the number of candies she has left in terms of \( y \).
Part c: If \( y = 20 \), calculate the actual number of candies Sarah has left after giving some to her brother. <\/p>

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Question 10

5 marks

A rectangle has a length that is 4 cm longer than its width. Let the width be \( w \) cm.
Part a: Write an algebraic expression for the length of the rectangle in terms of \( w \).
Part b: Write an algebraic expression for the perimeter of the rectangle in terms of \( w \) and simplify it.
Part c: If the width is 6 cm, find the actual perimeter of the rectangle.
Part d: If the perimeter is 40 cm, write an equation to represent this and find the value of \( w \).<\/p>

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