### GCSE Algebra Online test (H)

#### Year 10/11 maths revision

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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a) 5a ( z – a )

b) t ( t4 – 3t)

c) 3n (4p3 – 5n )

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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

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.

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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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

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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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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

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

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

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a) Factorise 2x2 – 10x + 8

b) Factorise 6x2 + 4x – 10

c) Hence or otherwise simplify

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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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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)
b)

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