GCSE Algebra online test (F)

Year 10/11 maths revision

Using letters instead of unknown numbers. Writing an equation  Menu

Kath is y years old. Her husband Bill is 4 years older.
Write down an expression, in terms of y, for Bill's age.

Cyril has n coins in his collection. His son David has three times as many coins
Write down an expression, in terms of n, for the number of coins in David's collection.

At a museum, the cost of child admission is C and the cost of adult admission is A.
Write an expression for the cost of 3 children and 2 adults to visit the museum

There are 100 sheets of paper in a box. There are x boxes
Write an expression, in terms of x, for the number of sheets of paper.


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Simplify  Menu

a) a + 3 + a + a

b) a × a × a

c) 6a × 2a

d) x + 4y + 5x – 2y

e) – 2p – 3q – 5q + 3p


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Expand  Menu

a) 4 ( b + 2 )

b) 4z ( z – 3)

c) 5a ( z – a )


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Factorise  Menu

a) 15y + 10

b) 4t – 20

c) ab – 3a

d) 4p – 12pq


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Writing an equation  Menu

I think of a number N, add six, and the answer is ten. Write an equation and solve it to find the number N

Kath is y years old. Her husband Bill is 4 years older. The total age of both Kath and Bill is 190 years.
Write an equation and solve it to find the value of y (Kath's age).

Cyril has n coins in his collection. His son David has three times as many coins Cyril and David have 200 coins altogether.
Write an equation and solve it to find the value of n (size of Cyril's coin collection).


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Formulas show how to do a calculation.  Menu

Here is a formula:
function machine


a) If the input is 4 what is the output

b) If the output is 31 what is the input

c) I work in a shop.
The pay per hour is £5.50. I also get a bonus each day of £3.00
If I work for 6 hours in a day how much will I get paid?

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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 = 25, a = 6 and t = 8

b) Find the value of u when
v = 45 , a = 3 and t = 5

c) The area of a circle is πr2
Use your calculator to find the area when
r = 2.5 cm and π= 3.142

d) If y = 3x - 5
What is the value of x when y = 19


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Two bracket expansion  Menu

a) Expand and Simplify (y + 2)(y + 3)

b) Expand and Simplify (y + 5)(y – 4)

c) Expand and Simplify (2a + 5)(a – 2)


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Inequalities  Menu

a) Write down the integer values of x that satisfy the inequality
  – 1 < x < 3

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

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


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Subject of the Formula  Menu

a) Make x the subject of the formula
  y = x + 10

b) Make r the subject of the formula
 C = 2πr

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

d) Make z the subject of the formula
  3x = 5z + 4y


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Solving an equation  Menu

a) Solve  7t – 6 = 29

b) Solve   2t + 6 = t + 8

c) Solve   5t – 6 = 2t + 12

d) Solve   5(2x – 3) = 3(2x + 1)

e) Solve  9(x + 2) = 7x + 25


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Trial and Improvement  Menu

a) The equation x3 + 2x = 58
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 – 5x = 8
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 × a5

d) Simplify   76 × 77

e) Simplify   75 ÷ 76


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Graphs  Menu

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

x –2–10123
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) Complete the table for: y = x2 + 4x– 1

x –5–4–3–2–101
y –1 –4–5   

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

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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


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