algebra problem solving questions year 7

Algebra Questions and Problems for Grade 7

Grade 7 algebra questions and problems with detailed solutions are presented. Questions on simplifying expressions, solving equations, factoring expressions,....are included.

• 12 x 3 + 5 x 2 + 4 x - 6 for x = -1
• 2 a 2 + 3b 3 - 10 for a = 2 and b = -2
• (- 2 x - 1) / (x + 3) for x = 2
• 2 + 2 |x - 4| for x = - 4
• - 2( x - 8) + 3 (x - 7)
• 2 (a + 1) + 5b + 3(a + b) + 3
• a (b + 3) + b (a - 2) + 2 a - 5 b + 8
• (1 / 2) (4x + 4) + (1 / 3)(6x + 12)
• 4 ( - x + 2 - 3(x - 2) )
• x / y + 4 / y
• (2 x / 4 ) × (1 / 2)
• (3 x / 5 ) ÷ (x / 5)
• 3 x 2 × 5 x 3
• [ (2 y) 4 9 x 3 ] ÷ [ 4 y 4 (3 x) 2 ]
• 24 x + 18 y
• 2 x + 5 = 11
• 3 x = 6 / 5
• 3 (2 x + 2) + 2 = 20
• Rewrite the expressions 3 × a × a × a - 5 × b × b using exponential.
• A rectangle has a length given by 2 x + 3 units, where x is a variable. The width of the rectangle is given by x + 1 units. Find the value of x if the perimeter of the rectangle is equal to 32.
• A rectangle has a length given by 2x - 1 units, where x is a variable. The width of the rectangle is equal to 3 units. Find the value of x if the area of the rectangle is equal to 27.
• 45% of the students in a school are male? Find the ratio of the number of female to the total number of male students in this school.
• A car travels at the speed x + 30 kilometers in one hour, where x is an unknown. Find x if this car covers 300 kilometers in 3 hours?
• Solve the proportion : 4 / 5 = a / 16
• Find a if the ordered pair (2 , a + 2) is a solution to the equation 2 x + 2 y = 10?
• Find the greatest common factor of the numbers 25 and 45.
• Write the number " one billion, two hundred thirty four million, seven hundred fifty thousand two " using digits.
• Write the number 393,234,000,034 in words.
• Find the lowest common multiple to the numbers 15 and 35.
• Find x if 2 / 3 of x is 30?
• What is 20% of 1 / 3?
• Order 12 / 5 , 250% , 21 / 10 and 2.3 from the smallest to the largest.
• The sum of 3 positive consecutive integers is equal to 96. Find the largest of these numbers.
• Dany scored 93 in physics, 88 in mathematics, and a score in chemistry that is double his score in geography. The average score of all 4 courses is 79. What were his scores in chemistry and geography?
• Linda scored a total of 265 points in mathematics, physics and English. She scored 7 more marks in mathematics than in English and she scored 5 more marks in physics than in mathematics. Find her scores in all three subjects.
• There are bicycles and cars in a parking lot. There is a total of 300 wheels including 100 small wheels for bicycles. How many cars and how many bicycles are there?
• The difference between two numbers is 17 and their sum is 69. Find the largest of these two numbers.

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15 Algebra Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

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Algebra questions involve using letters or symbols to represent unknown values or values that can change. Here you will find 15 algebra questions to test your knowledge and show you the different ways that algebra can be used to solve a problem to find an unknown value or to make generalisations.

Algebra in KS3 and KS4

Algebra questions ks2, you may also like:, algebra questions ks3: forming and solving equations, algebra questions ks3: graphs, algebra questions ks4: algebraic manipulation, algebra questions ks4: forming and solving equations, algebra questions ks4: graphs, looking for more algebra questions and resources, looking for more ks3 and ks4 maths questions.

Free GCSE maths revision resources for schools As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of free GCSE maths revision resources including: – GCSE maths past papers – GCSE maths worksheets – GCSE maths questions

There are many topics and techniques within algebra . In KS3 we learn to write and manipulate basic algebraic expressions and linear equations. In KS4 we develop these techniques to allow us to deal with more complicated algebra problems such as ones that involve quadratic equations or a system of equations.

How to solve algebraic questions

When you are presented with an algebraic problem it is important to establish what you are being asked to do. Here are some of the key terms along with what they mean:

• Solve the equation – find out the value of the unknown
• Substitute – put the values you have been given into the algebraic expression
• Simplify – collect together like terms to make the expression or equation look simpler
• Expand brackets – multiply out the brackets
• Factorise – put into brackets
• Make x the subject – rewrite the equation in the form x =…..

Remember, when working with algebra, we must still apply BODMAS / BIDMAS. i.e. B rackets, I ndices (powers, exponents, square roots), D ivision, M ultiplication, A ddition, S ubtraction.

When working with algebraic expressions and equations we must consider carefully which operations to deal with first.

Download this 15 Algebra Questions And Practice Problems (KS3 & KS4) Worksheet

Help your students prepare for their Maths GCSE with this free Algebra worksheet of 15 multiple choice questions and answers.

Algebra in KS2

The ideas of writing and simplifying expressions, solving equations and substitution are introduced in KS2. Here are some example KS2 algebra questions:

1. A chocolate bar costs c pence and a drink costs d pence. Write down an expression for the cost of 2 chocolate bars and 2 drinks.

2 chocolate bars would cost 2 lots of c, or 2c, and 2 drinks would cost 2 lots of d, or 2d.

2. Simplify the expression 4m+5+2m-1

We need to collect together like terms here so 4m + 2m = 6m and 5 – 1 = 4 (watch out for the negative).

Algebra questions KS3

In KS3 we learn a variety of different algebra techniques to answer algebra questions and to practise problem solving with algebra. These include:

• Simplifying algebraic expressions
• Expanding brackets and factoring
• Forming algebraic equations from word problems
• Solving algebraic equations and inequalities
• Substituting into expressions
• Changing the subject of an equation
• Working with real life graphs and straight line graphs

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Algebra questions KS3: basic algebra

1. In this pyramid, you add two adjacent blocks to find the value of the block above.

What expression will be in the top box?

2.  Brian is a window cleaner. He uses the following formula to calculate the amount to charge his customers:

Charge = £20 + 4n

Where n is the number of windows a house has.

If a house has 7 windows, how much would Brian charge?

In this question, n is 7 so we can substitute 7 into the formula.

Charge = £20 + 4 × 7

Charge = £48

3. The area of a rectangle is 4x-6.

Which of the following pairs could be the length and width of the rectangle?

2x and 2x-3

There are two ways of attempting this question. We know that area \;of \;a \;rectangle = length × width so we could multiply each pair together to see which pair makes 4x − 6.

Alternatively, if we factorise 4x − 6 we get 2(2x − 3) meaning the sides could be 2 and 2x − 3.

4.  The formula for changing degrees Celsius to degrees Fahrenheit is

F=\frac{9C}{5}+32

Rearrange this formula to make C the subject.

5. Work out the size of the smallest angle.

The angles in a triangle add up to 180^{\circ} therefore we can write

Now we have an equation we can solve.

The angles are :

The smallest angle is 34^{\circ} .

6.  Jamie’s dad is 4 times older than Jamie. In 14 years time, Jamie’s dad will be twice the age of Jamie.

What is the sum of Jamie’s age now and Jamie’s dad’s age now?

To solve this we need to write an equation.

Let Jamie’s age now be x . Then Jamie’s dad’s age is 4x .

In 14 years time Jamie’s age will be x + 14 and Jamie’s dad’s age will be 4x + 14 .

Since we know Jamie’s dad’s age will be two times Jamie’s age, we can write

4x+14=2(x+14)

Jamie is currently 7 years old meaning his dad is 28 years old. The sum of their ages is 35 .

7.  Which of the following lines passes through the point (2, 5)?

At the point (2, 5), x is 2 and y is 5. We can check which equation works when we substitute in these values:

Algebra questions KS4

Algebra is studied extensively in the GCSE and IGCSE curriculum.

In KS4 we build on the techniques learnt in KS3. Topics include:

• Expanding and factorising polynomials
• Solving quadratic equations
• Solving simultaneous equations
• Inequalities
• Algebraic fractions
• Further work on graphs

8. Which of the following expressions has the smallest value when a=5 and b=-3?

9. Find an expression in terms of x for the volume of this cuboid

Volume = (5x+1)(2x-3)(3x-1)

Volume = (10x^2+2x-15x-3)(3x-1)

Volume = (10x^2-13x-3)(3x-1)

Volume = 30x^3-39x^2-9x-10x^2+13x+3

Volume = 30x^3-49x^2+4x+3

10. The area of this triangle is 24cm^2 .

Work out the perimeter of the triangle.

The area of a triangle is area = \frac{1}{2} × b × h.

If we fill in what we know we get:

Since x = 3 , the side lengths are 6m, 8cm and 10cm .

The perimeter is 6 + 8 + 10 = 24cm .

11.  Solve the equation x+2-\frac{15}{x}=0

x=-2 or x=15

x=-3 or x=5

x=-5 or x=3

x=-15 or x=2

We can make this a bit easier by getting rid of the fraction involving x. We do this by multiplying each term by x.

12. At a theme park the Jones family purchased 2 adult tickets and 3 child tickets for £48 .  The Evans family purchased 3 adult tickets and 1 child ticket for £44 . 

Calculate the cost of one child ticket.

We can write simultaneous equations to solve this.

2a+3c=48 (Equation 1) 3a+c=44 (Equation 2)

Multiply equation 2 by 3 to make the coefficients of c equal: 9a+3c=132 (Equation 3)

Subtract equation 1 from equation 3: 7a= 84 a=12

Substitute a into equation 3: 3×12+c=44 36+c=44 c=8

The cost of an adult ticket is £12 and a child ticket is £8 .

13.  Which of these lines is parallel to the line 2y = x + 7

For two lines to be parallel, their gradient must be equal.

If we rearrange 2y=x+7 to make y the subject we get y=\frac{1}{2}x+\frac{7}{2}.

The gradient is \frac{1}{2}

14. Find the minimum value of the function f(x) = x^2+4x+5 .

To find the minimum value we need to complete the square.

The minimum value is 1. This occurs when (x+2) is 0.

15. The diagram shows the circle x^2+y^2=25 . The line is a tangent to the circle at the point (3,4) . Work out the equation of the line.

To work out the gradient of the line we need to work out the gradient of the normal.

We know that the normal goes through the points (0, 0) and (3, 4) so we can calculate the gradient: \frac{4-0}{3-0}=\frac{4}{3}.

The gradient of the tangent will be \frac{-3}{4}.

We can now use y=mx+c . We know the tangent goes through the point (3, 4) and that it’s gradient is \frac{-3}{4} .

Third Space Learning’s free GCSE maths resource library contains detailed lessons with step-by-step instructions on how to solve algebra problems, as well as worksheets with algebra practice questions and more GCSE exam questions.

Take a look at the Algebra lessons today – more are added every week.

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Solving Word Problems Using Algebra (Worksheet)

Related Topics & Worksheets: Algebra Worksheets Evaluate Algebraic Expressions by Substitution Worksheet

Objective: I know how to solve word problems using algebra.

Solve the following word problems: a) When 9 is subtracted from a number and then divided by 2, the answer is 4. What is the number? The number is b) The length of a rectangle is twice that of the width. The perimeter of the rectangle is 24 cm. What is the width of the rectangle? The width of the rectangle is cm c) Marcus, Sally and Sammy decided to share 20 sweets. Marcus took 8 sweets and Sally took three times as many as Sammy. How many sweets did Sammy receive? Sammy received sweets. d) If the sum of three consecutive numbers is 72, what is the largest number? The largest number is e) Andy is 2 times younger than his sister and his father is 25 years older than him. If the total of their ages is 53 years, what is Andy’s age and his father’s age? Andy is years old and his father is years old. f) The length and width of a rectangle are 7 cm and (x - 8) cm respectively. Find the value of x if the area of the rectangle is 42 cm2. The value of x is cm g) Carol is y years old and her daughter is 25 years younger. Find Carol’s present age if the sum of their ages in 6 years’ time is 75 years Carol’s age is h) Diana buys 20 apples at x cents each and 40 oranges at x + 10 cents. She packs them into bags containing 5 apples and 10 oranges and sells the bags for 20x cents each. Find out the amount that Diana paid for each apple if she obtained a total of $24 from selling all the fruits. The apple cost cents each

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Algebra Word Problems Worksheets

In algebra word problems worksheets, we will talk about algebra, which is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. They represent quantities without fixed values, known as variables. Solving algebraic word problems requires us to combine our ability to create and solve equations. Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems.

Benefits of Algebra Word Problems Worksheets

We use algebra in our everyday life without even realising it. Solving algebraic word problems worksheets help kids relate and understand the relevance of algebra in the real world. Algebra finds its way while cooking, measuring ingredients, sports, finance, professional advancement etc. They help in logical thinking and help students to break down a problem and then find its solution.

Download Algebra Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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Part 3: Algebraic Techniques | Free Worksheet

Guide Chapters

• 1. Fractions
• 2. Decimals and Percentages
• 3. Algebraic techniques
• 4. Angle Relationships
• 7. Data collection & representation
• 8. Pythagoras' theorem

Algebra is a central part of most Maths topics in High School. You’ve got to get it right early on. But don’t worry in this article, you’re going to learn all about Year 7 algebraic techniques!

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NSW Syllabus Outcome

This article deals with the following NESA Syllabus Outcomes:

In this article we’ll discuss:

We will be covering the following topics:

• Collecting Like Terms

Multiplication and Division

The distributive law.

And you can check your knowledge and skills on some:

• Checklist questions

Assumed knowledge

This guide lays the foundation for Algebraic Techniques.

To succeed in this topic, students should be comfortable computing with integers and fractions and have familiarity with basic index notation.

Test your knowledge of Algebra before we get started!

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Simplifying Expressions

Pronumerals essentially represent numbers, and, hence, they can be added, subtracted, multiplied and divided – the four number operations.

Let’s look at this in more detail.

Addition and Subtraction – Collecting like terms

Lengthy expressions such as \( 3a + 2a + a + b + 2b + 3b \) can be written in a much shorter form. This is known as simplifying the expression.

The key aspect of this process is that only like terms can be combined. Hence, the process is called “ collecting like terms” .

The below examples illustrate this process of simplification.

Simplify the following:

1. \( 3a + 2a + a + b + 2b + 3b \)

2. \( 4ab – 2ba \)

3. \( -5x^{2} + 3x – 2x^{2} + x \)

Common Mistakes

Expressions with unlike terms cannot be simplified further.

A common mistake is writing \( 2x + 3y \) as \( 5xy \). i.e. writing \( 2x + 3y = 5xy \).

\( 2x \)  and \( 3y \) are unlike terms. So, they must be kept as separate terms when added.

A good way to remember avoiding mistake is to note that \( x + y \) will not produce \( xy \).

Similar variants of the above mistake include:

• \( x + 5x^{2} = 6x^{3} \)
• \( x + 3 = 3x \)

Unlike addition and subtraction, like terms are not necessary for multiplication and division.

The rule for this process is to operate the numbers with the numbers, and the letters with the letters.

Let’s have a look at this in action.

1. \( 7a \times 9b \)

\begin{align*} \color{red}{7a \times 9b = 63ab} \end{align*}

2. \( 8u \times u \)

\begin{align*} \color{red}{8u \times u = 8u^{2}} \end{align*}

3. \( (5t)^{3} \)

\begin{align*} \color{red}{(5t)^3 = 5t \times 5t \times 5t = 125t^{3}} \end{align*}

Division can be written as a fraction. Fractions can be simplified by cancelling.

Remember that cancelling means to divide two terms by a common factor and that you can only cancel vertically or diagonally.

Let’s have a look at cancelling in action.

Simplify the following

1. \( 18b \div 3 \)

2. \( 15xy^{2}t \div 5xy \)

3. \( 25x^{7}y^{4} \div 5x^{3}y^{5} \)

4. \( \frac{2x^{3}y^{5}}{5z^{10}} \div \frac{6x^5y^2}{z} \)

Simplifying expressions should always be performed as it allows for questions to be handled more easily.

However, it is sometimes necessary to expand an expression, such as \( 2(3x + 5y) + 5(x – 2y) \) before like terms can be collected.

Expanding expressions involves using the distributive law:

Let’s see this at work.

Expand the following :

1. \( 5(a + 3) \)

\begin{align*} \color{red}{5(a + 3) = 5a + 15} \end{align*}

2. \( b(3b -a) \)

\begin{align*} \color{red}{b(3b -a) = 3b^{2} – ab} \end{align*}

3. \( -3(x-2) \)

A faster way is to do:

This method is used for the rest of this subject Guide.Note: \( -3 \times -2 = 6\)

4. \( -(x-5) \)

\begin{align*} \color{red}{-(x-5) = -x + 5} \end{align*}

Expand and simplify the following:

1. \( 3(x+4) + 2(x-3) \)

\begin{align*} \color{red}{3(x+4) + 2(3-3)} &\color{red}{= 3x + 12 + 2x – 6} \\ &\color{red}{= 5x+6} \end{align*}

2. \( 4(2a-3) – 3(2-a)\)

\begin{align*} \color{red}{4(2a-3) – 3(2-a)} & \color{red}{= 8a -12 -6 + 3a} \\ &\color{red}{= 11a – 18} \end{align*}

3. \( 3y(2x – 3) + \frac{2}{3}(3x-y) \)

\begin{align*} \color{red}{3y(2x – 3) + \frac{2}{3}(3x-y)} & \color{red}{= 2xy + 3y + \frac{2}{3}x – \frac{2}{3}y }\\ &\color{red}{= 2xy + \frac{2}{3}x + \frac{7}{3}y} \end{align*}

Now we’ve covered the skills, it’s time for you to put them into action!

Checkpoint Questions

1. Simplify  \( 6a + 4a – 3a \)

2.  Simplify  \( m^{2} + m + 3m^{2} + 4{m} \)

3.  Simplify \( -3a \times 2b \)

4.  Simplify  \( 4 \times -b \times -c \)

5.  Simplify  \( 12x^{2}y \div 4xy \)

6.  Simplify  \( 2x^{4}y \div 3x^{3}y^{2} \)

7. Expand \( -21(2-3a) \)

8. Expand and simplify  \( 5p(2p-1) – 3(p-2)\)

9.  Simplify \( \frac{(2x^{3})^{2}y^{5}}{5z^{5}} \div \frac {5x^{5}y^{2}}{3z} \div 2x\)

10.  Simplify  \( \frac{\frac{3}{2}x – \big{(}\frac{1}{3}x-2\big{)} + \frac{2}{5}x}{3 \big{(}\frac{2}{5}x-2\big{)} + 4\big{(}\frac{11}{120}x+2\big{)}} \)

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\begin{align*} 6a + 4a – 3a = 7a \end{align*}

\begin{align*} m^{2} + m + 3m^{2} + 4m = 4m^{2} + 5m \end{align*}

\begin{align*} -3a \times 2b = -6ab \end{align*}

\begin{align*} 4 \times -b \times -c \end{align*}

\begin{align*} 12x^{2y} \div 4xy = \frac{12x^{2}y}{4xy} = 3x \end{align*}

\begin{align*} 2x^{4}y \div 3x^{3}y^{2} = \frac{2x^{4}y}{3x^{3}y^{2}} = \frac{2x}{3xy} \end{align*}

\begin{align*} -2a(2-3a) = -4a+6a^{2} \end{align*}

\begin{align*} 5p(2p-1) – 3(p-2) &= 10p^{2} – 5p -3p + 6 \\ &= 10p^{2} – 8p + 6 \end{align*}

9. Note that \( (2x^{3})^{2} = 2x^{3} \times 2x^{3} = 4x^{6} \)

\begin{align*} ∴ \frac{(2x^{3})^{2}y^{5}}{5z^{5}} \div \frac{5x^{5}y^{2}}{3z} \div 2x &= \frac{4x^{6}y^{5}}{5z^{5}} \times \frac{3z}{5x^{5}y^{2}} \times \frac{1}{2x} \\ &= \frac{6y^3}{25z^{4}} \end{align*}

\begin{align*} \frac{\frac{3}{2}x \big{(}\frac{1}{3}x – 2 \big{)} + \frac{2}{5}x}{3\big{(}\frac{2}{5}x-2\big{)} + 4 \big{(} \frac{11}{120} + 2 \big{)}} & =\frac{\frac{3}{2}x – \frac{1}{3}x + 2 + \frac{2}{5}x}{\frac{6}{5}x – 6 + \frac{11}{30}x + 8} \\ &= \frac{\frac{45}{30}x – \frac{10}{30}x + 2 + \frac{12}{30}x}{\frac{36}{30}x – 6 + \frac{11}{30}x + 8} \\ &= \frac{\frac{47}{30}x + 2}{\frac{47}{30}x + 2} \\ &= 1 \end{align*}

Part 4: Angle Relationships

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