O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2021 · Q313 Marks
p = (3q+5)/r² Calculate p when q = 15 and r=-4.
- (a)p = (3q+5)/r² Calculate p when q = 15 and r=-4.[2]
- (b)Expand and simplify 3 (2x+1)+4(x-5).[2]
- (c)Solve (3-k)/4 = 1.[2]
- (d)x⁶/xᵐ = x⁻³ Find m.[1]
- (e)(i)A rectangular piece of card measures 30 cm by 24 cm. The net of an open box is made by removing a square from each corner of this piece of card. Each square that is removed has side x cm. The area of the net is 576cm². Form an equation in x and solve it to find the value of x. [Figure 3.1][3]
- (e)(ii)The net is made into an open box. 1000 cm³ of sand is placed inside the box. Find the fraction of the box that is filled with sand. Give your answer in its simplest form.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [2] 3.125 or 3 1/8 or 25/8
- [2] M1 for [p =] (3×15+5)/(-4)² or better
- [2] After 0 scored, SC1 for answer -3.125 or -25/8 or -3 1/8
- [2] 10x - 17 final answer
- [2] B1 for 6x + 3 + 4x - 20 soi or answer 10x + k or kx – 17
- [2] -1
- [2] M1 for 3-k = 1×4 oe
- [1] 9
- [M1] 24 x 30 – 4xxxx = 576 oe
- [M1 FT] x² = k from their equation
- [B1] 6
- [3] 125/162 cao nfww
- [3] M2 for 1000 / ((30-2×their 6)(24-2×their 6)(their 6))
- [3] or M1 for (30-2 × their 6)(24 – 2 × their 6)(their 6)
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