GCSE Higher - Algebra

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  1. A sequence starts:
    2, 7, 17, ...
    The rule for finding the next term is to multiply the previous term by 2 and then add on 3. 
    Work out the next term.
    37
  2. The rule for finding the next term in a sequence is to multiply the previous term by 2 and then add on a, where a is an integer.
    The first term is 8 and the fourth term is 127.
    8, ..., ..., 127
    Work out the value of a.
    • 2nd term = 16 + a
    • 3rd term = 2(16 + a) + a 
    •                         or
    •                 32 + 2a + a
    • 4th term = 2(32 + 3a) + a
    •                 64 + 7a = 127
    • so a = 9
  3. Factorise:
    a) Image Upload

    b) Image Upload

    c) Image Upload

    d) Image Upload
    a) Image Upload

    b) Image Upload

    c) Image Upload

    d) 10(x + 2y)(x - 2y)
  4. Two families go to a pantomime
    The Khan family of 2 adults and 3 children pay £69.
    The Lewis family of 3 adults and 5 children pay £109.
    Work out the cost of an adult ticket and a child ticket.
    • 2a + 3c = 69
    • 3a + 5c = 109

    Adult a = £18 and Child c = £11
  5. Solve this inequality 
    3x + 7 < x + 8
    x = Image Upload
  6. Make a the subject of the formula 

    Image Upload
    Image Upload
  7. Solve

     Image Upload
    x = 1.5 or Image Upload
  8. a) Factorise Image Upload

    b) Factorise Image Upload
    a) x(x + 10)

    b) (y + 6)(y - 6)
  9. Solve

    5w + 6 = 9 - w
    Image Upload
  10. Solve

    Image Upload
    2.9
  11. Katy is using the quadratic formula to solve a quadratic equation. 
    After correctly substituting the values, she writes:
    Image Upload
    a) What is the quadratic equation that Katy is trying to solve?
    b) Explain why Katy will not be able to find any solutions to the equation.
    a)Image Upload

    b) Can't square root a negative number
  12. a) Expand and simplify Image Upload

    b) Hence or otherwise, show that 
    Image Upload
    a) Image Upload

    b) Image Upload Image Upload Image Upload

    factorise Image Upload
  13. Solve the simultaneous equations:
    2x + 5y = 16
    4x + 3y = 11

    You must show working.
    Do not use trial and improvement.
    y = 3 and x = Image Upload
  14. Here are the equations of two straight lines:
    y = 7x - 6
    y = mx + c

    a) Write down the value of m if the lines are perpendicular

    b) Write down the values of m and if the lines are reflections of each other in the y axis.
    a) Image Upload

    b) m = -7 amd c = -6
  15. Simplify fully:

    Image Upload
    Image Upload
  16. Solve the equation Image Upload

    Give your answer to 2 decimal places.
    2.57 and -0.91
  17. Image Upload
    x = ∛(12V/π)
  18. You are given the identity Image Upload
    Work out the values of a and b
    a = -6

    b = -26
  19. Image Upload
    50cm
  20. 251 is a prime number
    (i) Write down the value of √251
        Give your answer to 1 decimal place
    (ii) Explain how to test that 251 is a prime number
    (i) 15.8

    (ii) Divide by numbers and reference to answers being whole numbersand/or decimal
  21. Image Upload
    4.6, 4.64, 4.65
  22. a) Simplify Image Upload

    b) Expand and simplify (x - 3)(x + 5)

    c) Rearrange the formula w = 3(2x + y) - 5 
    to make x the subject
    a) Image Upload

    b) Image Upload

    c) Image Upload
  23. Solve the equation Image Upload
    Give your solutions to 2 decimal places.
    2.82 and 1.18
  24. Andy and Ben both have some marbles.
    If Andy gives Ben 15 marbles, they will have an equal number.
    If Ben gives Andy 15 marbles, Andy will have four times as many as Ben.
    How many marbles does Andy have?
    Andy = 65
  25. a) Show that Image Upload

    b) p and q are two numbers.
       The sum of p and q is 10.
       The product of p and q is 18
       Work out the value of Image Upload
    • b) Image Upload
    •                   100 - 2 x 18 = 64
  26. Solve the simultaneous equations

    2x + 3y = 9
    3x + 2y = 1

    Do not use trial and improvement
    x = -3 and y = 5
  27. Find the values of a and b such that

    Image Upload
    a = 5 and b = -7
  28. Make x the subject of the formula

          Image Upload
    w = √(w - y)
  29. Simplify Image Upload
    Image Upload

    (5x -1)(x -3)
  30. Make x the subject of the formula
    Image Upload
    • y(x -3) = 3x + 4
    • yx -3y = 3x + 4
    • yx - 3x = 3y + 4
    • x(y - 3) = 3y + 4

    Image Upload
  31. Find the equation of the straight line passing through the point (0,5) which is perpendicular to the line 
    Image Upload
    Image Upload
  32. Image Upload
    x = 4.8
  33. Solve the simultaneous equations 

    y = x + 2
    Image Upload

    Do not use trial and improvement
    x = 1 and 2/3

    y = 3 and 4/3
  34. y is directly proportional to the square of x.
    When y = 5, x = 4
    Find the value of y when x = 8
    20
  35. Image Upload
    • Graph 1 = D
    • Graph 2 = A
    • Graph 3 = E
    • Graph 4 = C

Card Set Information

Author:
HLHSMaths
ID:
227918
Filename:
GCSE Higher - Algebra
Updated:
2013-07-30 11:45:35
Tags:
GCSE Higher Algebra
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Description:
GCSE Higher Algebra questions
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