Page 32 - vectormsint_catalogue

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Maths
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More Exercises
Exercises
1 Three diff erent bulbs light up at diff erent times. Bulb A lights up every 20 seconds. Bulb B lights up

1 The Olympic Games are held in the years that are multiples of 4. Give the every 54 seconds. Bulb C lights up every 1 minute 15 seconds. If all three bulbs first flash together

years in which the next three consecutive Olympic Games were held after at 07:30, find the time when the bulbs flash together again.
the year 2000.
2 A man sold lollipops at 40 cents each. He used all the money from selling the lollipops to buy
2 Factorise each number into a product of its prime factors. several bottles of mineral water which cost 70 cents per bottle. Find the lowest number of lollipops
(a) 90 (b) 198 (c) 294 (d) 1089 (e) 3087 he could have sold.
3 Write the HCF for each group of numbers. 3 Find the value of the digit k if the number 14 k if the number 14 k k95 is divisible by 11.
(a) 147 and 294 (b) 30, 48 and 72 (c) 132, 390 and 212
Maths as language
4 Write the LCM for each group of numbers. Let’s Explore! Maths 1, Student’s Book Let’s Explore! Maths 1, Student’s Book
(a) 16, 24 and 32 (b) 54, 72 and 162 (c) 126, 168 and 567
3 2 square of 3 / 3 to the power of 2 / 3 squared
5 Find the square root of the numbers using prime factorisation. 4 3 cube of 4 / 4 to the power of 3 / 4 cubed
(a) 1024 (b) 1521 (c) 4225 (d) 5929
9 square root of 9
6 Find the cube root of the numbers using prime factorisation. 3 8 cube root of 8
(a) 729 (b) 2744 (c) 3375 (d) 5832

7 Find the difference between the first two perfect squares that end with the
digit ‘9’. Unit at a glance
8 There are two metal bars of length 72 cm and 96 cm. Short bars of equal 1 The factors of a number divide the number exactly.
length are cut from both metal bars. Find the largest possible length of
each short bar. 2 Prime numbers are numbers which have exactly two factors, the number 1 and the number itself. 1 is
not a prime number.
9 4 clocks ring at intervals of 6, 11, 15 and 24 minutes respectively. If they
ring together at 5 p.m. on a Tuesday, when will they next ring together 3 Prime factorisation is the method of expressing a number as the product of its prime factors.
again?
4 The HCF is the largest common factor among all the common factors of two or more numbers.
10 Find the HCF and the LCM of the following, giving your answers as a
product of prime factors in index notation. 5 Multiples of a number are produced by multiplying the number by positive integers.
(a) 2 2 × 3 3 and 2 3 × 3 2 × 5 (b) 2 2 × 3 3 × 7 and 2 3 × 3 2 × 5
6 The LCM is the smallest common multiple among all the common multiples of two or more numbers.
11 Find the smallest possible integer which can be divided by 2, 5, 6 and 8.
7 When we multiply a number by itself, the product is a square number. Squaring integers produces
12 Express 2880 as the product of its prime factors in index notation. perfect squares. The square root of a perfect square is the absolute value of the integer before
squaring it.
13 Two numbers are greater than 15 and smaller than 25. Given that their

HCF is 1 and their LCM is 391, find the two numbers. 8 When we multiply a number three times by itself, the product is a cube number. The cube root of a
cube number is the integer before it is multiplied by itself three times.
14 During the students՚ fi rst day at school, the school shared 825 books, 495
pencils and 660 erasers equally between the students. Find the largest 9 Useful properties: For any numbers a, b and for n ≠ 0 and m ≠ 0, it is true that:
and
m
and
possible number of students at school that day. a n × b n = (a × b) n and a n×m = (a n ) m .
38 39
2 2 2 Factors and multiples Glo s s ar y
Glossary
Assessment abbreviation a brief way to write something
absolute value
the distance of any number a from 0 on a number line; |a|
Read the questions carefully. For each question, 4 options are given. Circle the correct one. adjacent angles two angles that have the same vertex, one common side and nothing else in
common
1 What is the HCF of 63, 105, 42 and 294?
(a) 20 (b) 21 (c) 22 (d) 23 algebraic expression a mathematical expression that includes variables
2 What is the LCM of 216 and 144? alternate angles a pair of equal angles formed between two parallel lines and a transversal with
the angles on opposite sides of the transversal line that crosses the parallel lines
(a) 354 (b) 495 (c) 432 (d) 583 approximation an answer we get by rounding numbers up or down either before calculating or
3 What is the square root of 8649? after calculating
(a) 93 (b) 94 (c) 95 (d) 96 ascending from the smallest to the greatest
4 What is the cube root of 3375? Let’s Explore! Maths 1, Student’s Book Let’s Explore! Maths 1, Student’s Book associative property for any numbers or variables, a, b and c, it is true that (a + b) + c = a + (b + c)
(a) 13 (b) 19 (c) 16 (d) 15 and (a × b) × c = a × (b × c)
5 How many factors does the number 99 have? bar chart an organised way to represent data by using rectangular bars proportional to the Let’s Explore! Maths 1, Student’s Book Let’s Explore! Maths 1, Student’s Book
(a) 6 (b) 7 (c) 8 (d) 9 values that the bars represent
6 Which number is prime? bisect to cut something into two equal parts
(a) 25 (b) 58 (c) 47 (d) 93 bisector (of an angle) a ray with its end point on the angle’s vertex that divides an angle into two parts
7 Which are cube numbers between 150 and 1000? equal in value
(a) 216, 343, 2500, 3600 (b) 216, 343, 512 (c) 169, 225, 324 (d) 289, 324, 361 class a way to group data, each group may include just one data value or each group
8 Which are the common factors of 27 and 42? may include an interval of data values

(a) 2, 3 (b) 3, 7 (c) 1, 3 (d) 3, 9 coefficient the number that multiplies the variables of a term
9 What is the first common multiple of 6 and 8? column a part of a table where people vertically write numbers, words, etc.

(a) 42 (b) 36 (c) 56 (d) 24 *combine to join two or more things or ideas together
it is true that
it is true that
a
10 What is the product of the HCF and LCM of 24, 45 and 75? commutative property for any numbers or variables a and b it is true that a + b = b + a and a × b = b × a
(a) 5400 (b) 3600 (c) 1800 (d) 2500 complementary angles two angles that have a sum of 90°
11 What is √7056 in index notation? complete angle an angle equal to 360°
√
√
(a) 3 × 5 × 7 (b) 23 × 52 × 7 (c) 2 2 × 3 × 7 (d) 2 × 33 × 7
*complex not simple, having variables related in complicated ways
concave being a polygon that has at least one interior angle greater than 180°
*concept an idea
consecutive one after the other, as they appear in order
constant something that does not change; a term in an algebraic expression that doesn't
have variables
*context the environment or situation in which something occurs
conversion the process of changing something into something else
40 convex being a polygon that has all the interior angles less than 180° 191
convex
being a polygon that has all the interior angles less than 180°
convex
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