Grade 10 Maths Exam Paper
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GCSE Basic Algebra Questions

There are four basic parts in GCSE algebra that you should know when revising for the maths papers. They are:
  • 1. Substituting
  • 2. Expanding
  • 3. Factorising
  • 4. Solving
gcse basic algebra questions

GCSE Algebra Questions

Algebra is often regarded by both students and teachers as a tough topic to learn or teach.
Yet, you will do well if master the four skills. The skills are the same in primary (Years 5, 6, 8) and secondary (Years9, 10, 11, 12).
 

Basic Algebra Questions

Below you’ll find some basic algebra questions (and solutions) addressing the four skills. The questions were adapted from the UK GCSE maths exam papers.

 

SEE MORE ON GRADE 10 EXAM QUESTIONS HERE

 

1. Substitution

a. Write down the value of abc when a = 10, b = 2 and c = 0

The answer is 0

(Many students will write 20

Maths knowledge: any number multiplied by 0 is 0
b. Work out the value of 1/2x – 3y, when x= 10 and y= 2
 5 – 6 = – 1 (many students write 1 instead)
Concept tested: Addition and subtraction of -ve and +ve numbers. (Reinforce the differences between 6 – 5 and 5 -6 or ask students to think about the number line, starting at 5 and moving left 6 places)
2 marks
c. Find the
value of 3x + 2y when x = 4 and y = 5
 12 – 10 = 2 …………. 🙂
2 marks

2. Expanding Brackets

 Expand the following expressions
a. 3(2y – 5) =    (1 mark)
 6y – 15 ( many student forget to do 3 x – 15)
b. 4(2m + 3n) =   (1 mark)

8m + 12n

c. x(x – 10) =    (1 mark)
 x^2 – 10x

3. Factorising

Factorise the following expressions  (note that expanding and factorising are opposites)
a. 2a + 10 =   (1 mark)

Highest Common Factor (HCF) of 2a and 10 is 2
2(a + 10)

 

b. 4 + 6x =     (1 mark)

HCF = 2
2(2 + 3x)

c. 3x – 9=   (1 mark)

3 (x – 3)

d. 2x^2 + 4x
 HCF = 2x
2x (x + 2)
2 marks

4. Solving equation

Solve the following equations to find the value of x
a. 4x = 20     (1 mark)

x = 5

 

b. 3x – 7 = 8        (1 mark)
3x = 8 + 7 
3x = 15
  x = 5
Note: get the order 8 + 7 right and not 7 + 8. Even the answer is same, the answer may not be the same when – ing, see the example below
c. 8(x + 12) = 100
 8x + 96 = 100 ………………Expand the brackets
8x = 100 – 96………………. (subtract 96 on both sides (remember balancing equations?)
x = 4/8 (Why divide by 8? In order to find the value of x, you must divide LHS and RHS by 8)
x = 1/2 (or 0.5)
2 marks

Check out past algebra questions and maths resources here.

GCSE Foundation Maths Algebra Questions

Solve the following to find the value of y
a. y/3 = 9   (1 mark)
y = 27 ………….multiply 3 x 9 (you can use this to solve complex equations that have a divisor)
b. 2y/5 = 4   (1 mark)

2y = 20………. ( 20 = 5 x 4)
y = 10

 

c. 2y + 3 / 2 = 5
 2y + 3 = 10………. ( 10 = 2 x 5)
2y = 10 – 3 ………..( subtracting 3 on both sides of the equation)
2y = 7
y = 7/2
y = 3.5
2 marks

Where to get GCSE Maths Questions?

There are four GCSE exam boards where you can get the maths past paper Pdf for free AQA, Edexcel, SQA and OCR.
The exam boards also provide the marking schemes, examiner reports, and practice materials.
Check out the resources here for more information on GCSE maths exams, study guides and past papers.

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