Sec 1 G2 Maths Integers, rational and real numbers worksheet with answers
A free Sec 1 G2 Maths worksheet on integers, rational and real numbers: 6 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.
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Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.
Section A
1
(a)State whether −7 is a rational number or an irrational number.
Answer (a)[1]
(b)State whether 0 is a rational number or an irrational number.
Answer (b)[1]
2
(a)Express 265 as an improper fraction.
Answer (a)[2]
(b)Calculate 21+107, giving your answer in its simplest form.
Answer (b)[2]
3
(a)Without using a calculator, find the value of 0.4×0.9.
Answer (a)[2]
(b)Express 165 as a decimal.
Answer (b)[2]
Section B
4
(a)(i)Arrange the following numbers in descending order: 3,−2,−10,6,−5
Answer (a)(i)[1]
(a)(ii)At 6 a.m., the temperature in Moscow was 7∘C. By noon, it had fallen by 12∘C. Find the temperature at noon.
Answer (a)(ii)°C[1]
(b)Calculate 1−8−(−12).
Answer (b)[2]
5
(a)(i)Write < or > in the box to make the statement correct: −15□−4
Answer (a)(i)[1]
(a)(ii)Arrange the following numbers in descending order: −1,−7,4,−12,9
Answer (a)(ii)[1]
(b)(i)Use a calculator to arrange the following numbers in ascending order: P =2, Q =1.4, R =1.4˙, S =710. Write down the letters in order, starting with the smallest.
Answer (b)(i)[2]
(b)(ii)Ahmad writes: "The sum of two irrational numbers is always irrational." State whether the statement is true or false. If it is false, give a counterexample. Choose the answer with its reason.
Answer (b)(ii)[1]
(c)(i)Calculate 8.3+0.904.
Answer (c)(i)[1]
(c)(ii)Express 0.875 as a fraction in its simplest form.
Answer (c)(ii)[2]
6
(a)Without using a calculator, find the value of 2.4×3.5.
Answer (a)[2]
(b)(i)Calculate −15+6.
Answer (b)(i)[1]
(b)(ii)Calculate (−4)×(−9)÷6.
Answer (b)(ii)[1]
(c)(i)Calculate 30−5×4+12÷3.
Answer (c)(i)[2]
(c)(ii)Calculate 16−2×9+15÷5.
Answer (c)(ii)[2]
END OF PAPER
Answers and worked solutions
Question 1
(a)Answer: RATIONAL[1]
−7=1−7, a fraction of two integers.So −7 is rational.
(b)Answer: RATIONAL[1]
0=10, a fraction of two integers.So 0 is rational.
Question 2
(a)Answer: =617[2]
265=62×6+5=617
(b)Answer: =151[2]
21+107=105+107=1012=56=151
Question 3
(a)Answer: 0.4×0.9=0.36[2]
4×9=36Decimal places: 1+1=20.4×0.9=0.36
(b)Answer: =0.3125[2]
165=16×6255×625=100003125=0.3125
Question 4
(a)(i)Answer: 6>3>−2>−5>−10[1]
6>3>−2>−5>−10
(a)(ii)Answer: =−5 °C[1]
Temperature at noon =7−12=−5 °C
(b)Answer: =5[2]
1−8−(−12)=1−8+12=5
Question 5
(a)(i)Answer: <[1]
On the number line, −15 is to the left of −4.−15<−4
(a)(ii)Answer: 9>4>−1>−7>−12[1]
9>4>−1>−7>−12
(b)(i)Answer: QPSR[2]
P: 2=1.4142 (4 d.p.)Q: 1.4=1.4000 (4 d.p.)R: 1.4˙=1.4444 (4 d.p.)S: 710=1.4286 (4 d.p.)In order: Q, P, S, R
(b)(ii)Answer: R[1]
The statement is false.10 and −10 are irrational, but their sum is 0, which is rational.
(c)(i)Answer: =9.204[1]
8.300+0.904=9.204
(c)(ii)Answer: =87[2]
0.875=1000875=1000÷125875÷125=87
Question 6
(a)Answer: =8.4[2]
24×35=840Decimal places: 1+1=22.4×3.5=8.40=8.4
(b)(i)Answer: =−9[1]
−15+6=−9
(b)(ii)Answer: (−4)×(−9)÷6=6[1]
Number of negative numbers: 2So the answer is positive.(−4)×(−9)÷6=6