O-LevelMathematicsVectors and transformations4024/21 · Oct/Nov 2015 · Q310 Marks
A=(1 3 / -2 2) B=(-1 2 / -3 2)
- (a)(i)Find 2A-B,[2]
- (a)(ii)Find B⁻¹.[2]
- (b)The matrix C satisfies the following equation. 3C+4(-2 1 / 0 3)=C Find C.[2]
- (c)(i)Theresa sells raspberries and blackcurrants. The first matrix shows the number of kilograms of each fruit she sells during three different weeks. The second matrix shows the price per kilogram, in cents, of the fruit Theresa sells. raspberries blackcurrants Week 1: 3, 2 Week 2: 1.5, 3 Week 3: 2, 2.5 price/kg 650 (raspberries) 580 (blackcurrants) D = (3 2 / 1.5 3 / 2 2.5) (650 / 580) Find D.[2]
- (c)(ii)Explain the meaning of the information given by matrix D.[1]
- (c)(iii)Find the total amount, in dollars, that Theresa gets for the fruit she sells.[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] (3 4 / -1 2)
- B1 for one row or one column correct
- [2] (1/4 * (2 -2 / 3 -1)) oe isw
- B1 for det = 4 soi
- or for (2 -2 / 3 -1)
- [2] (-2 4 / 0 6) oe
- B1 for one row or one column correct
- Or M1 for 2C = - 4 (-2 1 / 0 3) oe
- or for -1/2 C = (-2 1 / 0 3)
- [2] (3110 / 2715 / 2750)
- B1 for 2 elements correct in a 3 by 1 matrix or all 3 values correct in dollars
- or M1 for (1950+1160 / 975+1740 / 1300+1450)
- [1] Amount [in cents] for each week
- [1] 85.75 cao
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