Year 7 Mathematics
Week Review 4
Revision and Consolidation
Divisibility tests
1 All numbers are divisible by 1.
2 All even numbers are divisible by 2. Last digit must be a 0, 2, 4, 6 or 8.
3 The sum of the digits must be divisible by 3.
4 The number formed from the last two digits must be divisible by 4.
5 The last digit must be a 0 or 5.
6 Must pass the divisibility tests for 2 and 3.
7 There is no easy divisibility test for the numeral 7.
8 The number formed from the last three digits must be divisible by 8.
9 The sum of the digits must be divisible by 9.
10 The last digit must be 0.
1.
Which three divisibility tests involve calculating the sum of the digits?
2.
If you saw only the last digit of a 10-digit number, which three divisibility tests could you
still apply?
3.
Determine whether or not the following calculations are possible without leaving a remainder.
a 54 327 ÷ 3
b 765 146 ÷ 8
4.
Give the remainder when 326 is divided by 3.
Fluency and Understanding
5.
Simplify the following expressions by writing them in index form.
a 5×5×5×5×5×5
b
3×3×2×3×2×3
6.
Expand and evaluate 23  52
7.
Write 6785 in expanded form.
8.
State whether 21 is a prime or composite number.
9.
91 is not a prime numbers, yet it is the product (×) of two primes.
Find the two prime numbers.
Modelling and Problem Solving
Problem Solving
10.
Twin primes are pairs of primes that are separated from each other by only one even number;
for example, 3 and 5 are twin primes. Find three more pairs of twin primes.
11.
A text message is sent to five friends. Each of the five friends then forwards it to five other
friends and each of these people also sends it to five other friends. How many people does the
text message reach, not including those who originally forwarded the message?
Reasoning
12.
a.
Is the number 968 362 396 392 139 963 359 divisible by 3?
b.
Many of the digits in the number above can actually be ignored when calculating the digit
sum. Which numbers can be ignored and why?
c.
To determine if the number above is divisible by 3, only five of the 21 digits actually need to
be added together. Find this ‘reduced’ digit sum.
NAPLAN ( NON-CALCULATOR)
13.
This jug has some milk in it.
If Tom adds an extra 500 mL of milk to the jug,
how many millilitres (mL) of milk will then be in the jug?
14.
37.9 × 10 =
mL
15.
Jill lives in a street that runs directly north–south.
Her house is north of the park and west of the school.
What street does Jill live in?
16.
These are four number cards.
Use each card once to make this number sentence true.