Chapter 2 Practice Paper: Integers, Rational Numbers and Real Numbers — mark scheme (print)

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QuizQuipPractice Series

QQ/S1MATH/CH2

Secondary 1 · Lower Secondary Mathematics (G2 / G3)

Mark scheme

Integers, Rational Numbers and Real Numbers

Chapter 2 Practice Paper · Maximum mark: 30

Notes for markers

Award one mark for each point marked [1], up to the marks shown for the part.
Accept answers worded differently that show the same understanding.
Units are required where the answer line shows one. ecf: allow an error carried forward.

Section A: Multiple-choice questions[10 marks]

Question	Answer
1	BNegative numbers get smaller as they move left on the number line, so -12 is less than -5, -1 and 0.	1
2	AA negative times a negative gives a positive: 3 × 6 = 18.	1
3	D22 is larger than 15, so the answer is negative: the difference is 7 below zero, which is -7.	1
4	A5 ÷ 8 = 0.625 exactly, since 5/8 = 625/1000.	1
5	CUse the common denominator 15: 6/15 + 5/15 = 11/15.	1
6	CThe square root of 5 cannot be written as a fraction of whole numbers; its decimal never terminates or repeats. The others are fractions or recurring decimals, so they are rational.	1
7	D1 1/2 = 6/4, and 6/4 - 3/4 = 3/4.	1
8	D(-4) × (-4) × (-4): the two positives from the first pair multiply with the remaining negative to give -64.	1
9	B5/7 is a fraction of two whole numbers, which is exactly what rational means. The other three describe irrational numbers.	1
10	CFalling 9 degrees from 4 °C: 4 - 9 = -5 °C.	1

Section B: Structured questions[20 marks]

Question	Answer and marking points	Marks
1(a)	-2.5, -1, 0.6, 3/4, 2 Negatives in the right order (-2.5 before -1) [1] All five numbers in the correct order [1] Accept 0.75 written as 3/4 in any position where 3/4 would be correct.	2
1(b)	The largest number is 2. [1]	1
1(c)	Only -1 and 2 are integers. -1 and 2, and no others [1]	1
1(d)	(-2.5 + 0.6) ÷ 2 = -1.9 ÷ 2 = -0.95 -0.95, with the averaging seen [1]	1
	Total for Question 1	5
2(a)	9/12 + 10/12 = 19/12 = 1 7/12 Common denominator 12 seen [1] 19/12 or 1 7/12 [1]	2
2(b)	(7 × 4)/(8 × 21) = 28/168 = 1/6 Multiplies numerators and denominators [1] 1/6 [1] Award the second mark for 1/6 however it is obtained; cancelling before multiplying is fine.	2
2(c)	5/2 × 8/5 = 40/10 = 4 [1]	1
	Total for Question 2	5
3(a)	(-7) + 15 = 8 [1]	1
3(b)	(-6) × (-3) = 18, and 18 - 20 = -2. Product 18 seen [1] -2 [1]	2
3(c)	-3 + 8 = 5 °C at noon, and 5 - 12 = -7 °C at the second midnight. Noon temperature 5 °C [1] -7 °C [1] Award the final mark only for a negative answer that follows a rise then a fall.	2
	Total for Question 3	5
4(a)	A rational number can be written as a fraction of two whole numbers. A recurring decimal can always be converted: 0.363636... = 36/99, which simplifies to 4/11. States the definition (a fraction of two whole numbers / an integer over an integer) [1] Gives a fraction such as 36/99 = 4/11 [1]	2
4(b)	Any integer n can be written as n/1, a fraction with whole-number top and bottom. So every integer is rational. Writes the integer over 1 (or equivalent fraction form) [1] Concludes with the definition of rational [1]	2
4(c)	The square root of 5 (about 2.236), or any other non-terminating, non-recurring decimal such as 2.505005000... Any valid irrational number strictly between 2 and 3 [1] Accept the square root of 5, 6, 7 or 8, or a described non-repeating decimal. Reject 2.5 (rational) and fractions.	1
	Total for Question 4	5

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