GCSE Algebra Online test (H)

Year 10/11 maths revision


Simplify  Menu

a) 2a + 3b – 3a + a

b) a2 × 3a × 2a

c) 5s3p3 × 4s2p


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Simplify algebraic fractions  Menu
a)    b)
c)  d)
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Expand  Menu

a) 5a ( z – a )

b) t ( t4 – 3t)

c) 3n (4p3 – 5n )


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Factorise  Menu

a) y2 + 6y

b) 4y3 – 8xy

c) x2 – 25y2

d) 4x2 – 9y4


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Writing an equation  Menu

The rule below can be used to work out the cost, in pounds, of renting a computer projector.

Add two to the number of hours required
Multiply your answer by 20

The cost of renting a PC projector for n hours is C pounds.
Write down a formula for C in terms of n.

b) The rule below can be used to convert degrees Centigrade to Fahrenheit.

Multiply your temperature in centigrade by 9, then divide your answer by 5
Add 32 to your answer.

The temperature in centigrade is C. The conversion in Fahrenheit is F.
Write down a formula for F in terms of C

c) Using the formula in b), convert 100 centigrade to Fahrenheit


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Substitution - using given values in equations  Menu

The formula v = u + at gives the final velocity of an object as it accelerates.

a) Find the value of v when:
u = 100, a = –10 and t = 8.5

b) The formula v2 = u2 + 2as gives the final velocity of an object as it accelerates over a distance s.

Find v when: u = 5, a = 2 and s = 6

Find u when: v = 9 , a = 4.25 and s = 2


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Two bracket expansion  Menu

a) Expand and Simplify (y + 5)(y – 4)

b) Expand and Simplify (2a + 5)(3a – 2)

c) Expand and Simplify (2a2 + 2)(a – 2a2)

d) Expand and Simplify (a + 3)2


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Inequalities  Menu

a) Write down the integer values of x that satisfy the inequality
  – 4 ≤ x < 2

b) Solve the inequality   5a – 16 < 8 – a

c) Solve the inequality   4x ≥ x + 5

d) Solve the inequality   x > 3x + 10


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Subject of the Formula  Menu

a) Make a the subject of the formula
  4x = 3a + y

b) Make z the subject of the formula
  3x = 5z2 – 4y

c) Make x the subject of the formula
  6x – 3y = ax2 – 4

d) Make z the subject of the formula
rearrange


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Solving an equation  Menu

a) Solve  5t – 6 = 2t + 12

b) Solve   8 + x = 2(3 + 2x)

c) Solve   5(4x – 4) = 5(2x + 9)

d) Solve  7(x + 3) = 11x – 15


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Trial and Improvement  Menu

a) The equation x3 + 5x – 4 = 52
has a solution between 3 and 4
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.


b) The equation x3 – 3x2 + 7 = 6
Has a solution between 2 and 3.
Using trial and improvement find the solution to 1 decimal place.


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Powers or Indices  Menu

a) What is the reciprocal of 7?

b) Simplify
(y9)/ y3

c) Simplify a10 × a–5

d) Simplify fully  (3a3b4)5

e) Simplify fully   5h4 × 4h2 ÷ 2h3


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Graphs  Menu

a) Complete the table of values : y = 3x – 2

x –2–1 0  1  2  3 
y –8  –2   

b) Now get some graph paper and draw the graph of y = 3x – 2

c) What is the gradient of y = 3x – 2

d) Find the equation of the line passing through (6,5) and perpendicular to the line y = 3x + 4.

e) Find the equation of the line passing through (6,5) and (4,9)

f) Complete the table for: y = x2 + 4x– 1

x –5–4–3–2–1 0  1 
y –1 –4–5   

g) Get some graph paper and draw the graph of x2 + 4x– 1

h) Complete the table for: y = x3 + 2x – 1

x –2–1 0  1  2 
y –4  11

i) Get some graph paper and draw the graph of y = x3 + 2x – 1


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Graphing simultaneous equations  Menu

a) Complete the table for: 2y + 3x = 9

x–1 0  1  2  3 
y      

b) Now complete the table for: y = x + 2

x–2–1 0  1  2 
y      

c) Get some graph paper and draw the graph of y = x + 2 and 2y + 3x = 9

d) Using the graphs find the solution to the simultaneous equations
y = x + 2  and  2y + 3x = 9

e) Draw the graphs for these simultaneous equations and use them to find the solutions
x2 + y2 = 9
y = x + 1

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Finding angles using algebra  Menu
4 sided shape

Look at the angles in the above 4 sided shape.

a) Write an equation in terms of b, as simply as possible for these angles

b) Solve the equation in a) to work out the value of b


triangle

Look at the angles in the triangle

c) Write an equation in terms of x for these angles

d) Solve the equation in c) to work out the value of x

e) Show that the area of the shape above is given by the expression 10 x2 + 15x – 12


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Simultaneous equations  Menu

a) Solve the simultaneous equations
  5p + 3q = 25
  3p + 3q = 21

b) Solve the simultaneous equations
  6x + 5y = 15
  5x – 5y = 40

c) Solve the simultaneous equations
  6x – 4y = 19   12x + 12y = 18

d) Solve the simultaneous equations
  2x – 3y = - 5   3x + 2y = 38

e)Solve the simultaneous equations
  y = x2 – 6x + 24
  6x – y = 12


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Basic Quadratics - factorising & solve  Menu

a) Factorise x2 + 7x +10


b) Factorise x2 + 14 x – 15

c) Solve x2+ 10x – 39 = 0

d) Simplify fully quadratic


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Complex Quadratics - factorising  Menu

a) Factorise 2x2 – 10x + 8

b) Factorise 6x2 + 4x – 10

c) Hence or otherwise simplify
quadrativ


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Quadratics - completing the square  Menu

a) Factorise x2 + 10x + 24 by completing the square

b) Hence solve x2 + 10x + 24 = 0

c) Factorise y2 – 12y + 5 by completing the square.

d) Hence solve y2 – 12y + 5 = 0 correct to 2 d.p.


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Quadratics - The quadratic formula  Menu

Solve x2 – 7x - 9 = 0 using the quadratic formula. Answer to 3 sf

b) Solve x2 + 7x + 1 = 0 using the quadratic formula


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Linear equations  Menu

Solve the equation:
a)  linear equation
b)  linear equation

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