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.
