O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2017 · Q39 Marks

Anya makes T-shirts. The matrix, M, shows the number of T-shirts of different types she makes in one week. M = ( 10 25 30 ) Men ( 20 40 25 ) Women

(a)Anya sells all of these T-shirts to a shop. She charges $5 for each small T-shirt, $6 for each medium T-shirt and $8 for each large T-shirt. Represent these amounts in a 3 × 1 column matrix N.[1]
(b)(i)Work out P = MN.[2]
(b)(ii)Explain what the elements in matrix P represent.[1]
(c)(i)The shopkeeper sells all sizes of men's T-shirts at $10 each. He sells all sizes of women's T-shirts at $9.50 each. He sells all of these T-shirts. Work out (10 9.50) M.[2]
(c)(ii)Work out the percentage profit the shopkeeper makes when he sells all of the T-shirts.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] (a) (5 6 8)ᵀ cao
[2] (b)(i) (440 540)ᵀ cao
B1 for one element correct
[1] (b)(ii) The amount Anya makes for men's T-shirts and women's T-shirts
[2] (c)(i) (290 630 537.5[0])
B1 for two correct values seen in a row of 3 elements or column of 3 elements isw
[3] (c)(ii) 48.7%
M1FT for their (440 + 540) and their (290+630 + 537.5)
and M1 for (their 1457.5 – their 980) ÷ their 980 ое

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.