Algebra & Numeracy

ALGEBRA AND NUMERACY20040306


An answer may well help in other questions. You are presumed able to think. Answers in your book for this one. Throughout this page, x is assumed to be an integer.

1    If x is even, is x² – 5x + 6 even? Any idea why?

2    If x² – 5x + 6  is odd, is x odd or even? Any idea why?

3    Solve      x² = 16  giving both answers

4    Solve       x² –9 = 16

5    Multiply out (x-2)(x-3)

6    If x=6, find the value of     a)  2x²       b)  4x²       c)  (-2x)²       d)  -3x²    

7    Which of these gives an integer (whole number) solution when you square root it? a)  9x²    b)  3x²    c)   9x² –4x²     d)  9x² –6x +1         e)   9x² +6x – 1

8    Sketch 2x + 3y = 9   and  x – 4y = 8   on one pair of axes, showing intercepts and intersection. Give the intersection to the nearest half or third.

9    If 2 < x ≤ 5 and x is an integer, list the possible values of x.

10    If the word WIT can be be rearranged in 6 ways {wit, wti, iwt, itw ,tiw, twi} and note 3! = 6, then in how many ways can the letters of these words be arranged?  a)  FRED  b)  FOOL  c)  FREDA  d)  IDIOT  e) M I SS I SS I PP I  or mississippi.




If you’ve missed it, 3! means 3x2x1 and is called three factorial. Your calculator (use the n! key) probably tells you  69! but not 70! Why is that? A fairly simple homework asks you to find the value of 73! to, say, 8 sig.fig.


1&2. x even, 5x even, x² even, Therefore the expression is even.   If x is odd then 5x is odd, x² is odd , Therefore the expression is odd-odd+6, which is even. 

3. x=±4   4. x=±5    5. as in Q1   6.  72, 144, 144, -108   7.  a & d

8.  Intercepts are at (0, 3) & (4.5, 0), at (8, 0) & (0, 2). They meet at a calculated (12/5, 7/5). Expect intersection to be drawn and seen as perhaps (2.5, 1.5), acceptable.

9.  x is 3 or 4 or 5

10.   a   24,    b   12=4!/2!,    c   120,    d   60 = 5!/2!,    e   11! / (2!x4!x4!) = 34650

73! = 73x72x71x70x69! = 4.4701155x 10^105 = 4.4701155x 10105    to 8s.f.

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