6 The base of a cuboid is a square with side length 4 cm. The volume of the cuboid is 48 cm3. On the grid, complete the accurate drawing of the net of the cuboid. The base is drawn for you. [3]

6 Correct net 3 M2 for 3 or 4 faces correct size and position or M1 for height 3 soi or for net of 4 by 4 by n cuboid drawn where n ≠ 3 To get full marks, you need to draw the complete and correct net of the cuboid. You can earn partial marks for drawing 3 or 4 faces of the correct size and in the correct position, or for correctly determining the height of the cuboid as 3 cm, or for drawing a net of a 4 by 4 by n cuboid where n is not 3.

7 A B D C 10 7 NOT TO SCALE h The diagram shows trapezium ABCD. AB = 7 cm and DC = 10 cm. The area of ABCD is 85cm2. The perpendicular height of the trapezium is h cm. Find the value of h. h = … [2]

7 10 2 M1 for ½ ( 7 + 10) × h = 85 or better To earn full marks, you must correctly state the value of h. You can earn one mark by setting up the correct equation for the area of a trapezium, such as ½ (7 + 10) × h = 85.

3 (a) p r q 3 5 2 = + Calculate p when q 15 = and r 4 =- . p = … [2] (b) Expand and simplify ( ) ( ) x x 3 2 1 4 5 + + - . … [2] (c) Solve k 4 3 1 - = . k = … [2] (d) x x x m 6 3 = - Find m. m = … [1] (e) NOT TO SCALE 24 30 x 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 576 cm2. (i) Form an equation in x and solve it to find the value of x. x = … [3] (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]

3(a) 3.125 or 25 8 or 1 38 2 M1 for [p =] ( ) 2 3 15 5 4 × + − or better After 0 scored, SC1 for answer –3.125 or – 25 8 or – 1 38 3(b) 10x – 17 final answer 2 B1 for 6x + 3 + 4x – 20 soi or answer 10x + k or kx – 17 3(c) –1 2 M1 for 3 – k = 1 × 4 oe 3(d) 9 1 3(e)(i) 24 × 30 – 4 × x × x = 576 oe M1 x2 = 36 M1 FT x2 = k from their equation 6 B1 3(e)(ii) 125 162 cao nfww 3 M2 for 1000 (30 2 6)(24 2 6)( 6) −× −× their their their or M1 for (30 – 2 × their 6)(24 – 2 × their 6)(their 6) (a) To earn marks, you must substitute the given values of q and r into the formula and correctly calculate p. (b) To earn marks, you must correctly expand both sets of parentheses and then combine like terms to simplify the expression. (c) To earn marks, you must correctly rearrange the equation to solve for k. (d) To earn marks, you must correctly identify the exponent m by simplifying the expression involving x. (e)(i) To earn marks, you must set up an equation for the area of the net by subtracting the area of the four removed squares from the total area of the card, and then solve this equation for x. (e)(ii) To earn marks, you must calculate the volume of the box using the value of x found in part (i), and then express the amount of sand as a fraction of this volume in its simplest form.

Cambridge O Level Mathematics (Syllabus D) · 4024

O-Level Mathematics (Syllabus D) (4024) Mensuration past paper questions

Revise O-Level Mathematics (Syllabus D) (4024) — Mensuration with real Cambridge past-paper questions grouped by topic, each shown with its marking scheme. Working one topic at a time targets exactly the skill each question tests.

95 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.