Sec 1 Maths Integers, rational and real numbers worksheet with answers
A free Sec 1 Maths worksheet on integers, rational and real numbers: 8 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
Calculate 25−3×6+20÷4.
Answer[2]
2
(a)Write < or > in the box to make the statement correct: −4□1
Answer (a)[1]
(b)Arrange the following numbers in descending order: −13,8,−3,−20,1
Answer (b)[1]
3
(a)State whether 30 is a rational number or an irrational number.
Answer (a)[1]
(b)Wei Jie 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)[1]
4
(a)Calculate −11+15−10.
Answer (a)[2]
(b)Calculate (−48)÷(−6).
Answer (b)[1]
Section B
5
(a)Express 4027 as a decimal.
Answer (a)[2]
(b)The points P, Q, R and S are marked on the number line. Which point represents 6?
Answer (b)[2]
6
(a)(i)Calculate −8+(−9).
Answer (a)(i)[1]
(a)(ii)Calculate (−120)÷6÷(−4).
Answer (a)(ii)[1]
(b)(i)Calculate 0.45+1.385.
Answer (b)(i)[1]
(b)(ii)Without dividing, state whether 5017 is a terminating decimal or a recurring decimal.
Answer (b)(ii)[1]
7
(a)The number line is divided into equal parts. Write down the number that the point P represents.
Answer (a)[2]
(b)(i)Without using a calculator, find the value of 9.5÷0.19.
Answer (b)(i)[1]
(b)(ii)Express 0.875 as a fraction in its simplest form.
Answer (b)(ii)[2]
8
(a)(i)Calculate 21+52, giving your answer in its simplest form.
Answer (a)(i)[2]
(a)(ii)Calculate 221×54, giving your answer in its simplest form.
Answer (a)(ii)[2]
(b)(i)Calculate (−2+7)2×3−(−2)3.
Answer (b)(i)[2]
(b)(ii)Calculate 41+32×83, giving your answer as a fraction in its simplest form.
Answer (b)(ii)[2]
END OF PAPER
Answers and worked solutions
Question 1
Answer: =12[2]
25−3×6+20÷4=25−18+5=12
Question 2
(a)Answer: <[1]
On the number line, −4 is to the left of 1.−4<1
(b)Answer: 8>1>−3>−13>−20[1]
8>1>−3>−13>−20
Question 3
(a)Answer: IRRATIONAL[1]
30 is not a perfect square, so 30 is a non-terminating, non-recurring decimal.So 30 is irrational.
(b)Answer: R[1]
The statement is false.6 and −6 are irrational, but their sum is 0, which is rational.
Question 4
(a)Answer: =−6[2]
−11+15−10=−11+15−10=−6
(b)Answer: (−48)÷(−6)=8[1]
So the answer is positive.(−48)÷(−6)=8
Question 5
(a)Answer: =0.675[2]
4027=40×2527×25=1000675=0.675
(b)Answer: Q[2]
4<6<92<6<36=2.44…So 6 is nearer to 2.The point is Q.
Question 6
(a)(i)Answer: =−17[1]
−8+(−9)=−8−9=−17
(a)(ii)Answer: (−120)÷6÷(−4)=5[1]
Number of negative numbers: 2So the answer is positive.(−120)÷6÷(−4)=5
(b)(i)Answer: =1.835[1]
0.450+1.385=1.835
(b)(ii)Answer: TERMINATING[1]
50=2×52The denominator has no prime factor other than 2 and 5, so 5017 is a terminating decimal.
Question 7
(a)Answer: =−11[2]
From −12 to −7 there are 5 divisions.One division =5−7−(−12)=1P=−12+1×1=−11