Assignment 1

Write your answers in the spaces provided. Show all your working because this will tell your teacher if you understand each question.

1 Translate each of the following word sentences into a number sentence. The first one has been done for you. You may use your calculator to find the answer.

Word sentence / Number sentence / Answer
Evaluate the difference between 165 and 88. / 165 – 88 / 77
(a) Double 18 then divide by 9.
(b) Find the square of 8.
(c) Take 10 away from the product of 19 and 2.

2 Answer ‘true’ or ‘false’. You may use a calculator to help you.

(a) 123 + 76 is bigger than 341 – 115. ______

(b) The sum of 11 and 22 is equal to the product of 3 and 11. ______

(c) 200 – 40 ´ 2 = 320 ______

(d) 3 ¸ 4 = 4 ¸ 3 ______

3 A real estate agent sold three units last Saturday. The total value of the sales was$584000.

(a) If the first two units cost $129 000 and $210 000, how much did the third unitcost?

(b) What is the price difference between the highest-priced unit and the lowest-priced unit?

4 Read the instructions and fill in the missing numbers (the first column has been completed as an example).

Instructions / Number / Number / Number
Start with a two-digit number that has different digits / 83 / 74 / 51
Reverse the digits / 38
Find the difference / 83 _
38
45
Divide the difference by 9 / 45 ¸ 9 = 5
Is it exactly divisible by 9? / Yes

5 (a) List all the prime numbers less than 20.

(b) A German mathematician named Goldbach found that every even number greater than two can be expressed as the sum of two primes. For example:

4 = 2 + 2
and
8 = 3 + 5

Test this by choosing two even numbers between 10 and 20 and expressing each number as the sum of two primes.

6 Complete the following:

eq1

eq2

ag fo1co

(b) Write this fraction as a decimal.

(c) Write this fraction as a percentage.

8 (a) Write the following numbers using index notation:

(i) Four squared

(ii) Five cubed

(b) Write the number 26 using multiplication symbols.

9 In a javelin-throwing competition, the following results were recorded:

Sue 21.06 m
Ryan 21.04 m
Benjamin 21.16 m
Thanh 21.105 m

Arrange the competitors in order, from 1st place to 4th place.

10 A survey of traffic in the main street stated:

‘There are 5 trucks for every 14 cars’.

(a) What is the ratio of trucks to cars?

(b) Does the statement mean that only 5 trucks and 14 cars were counted? Yes □ No □

11 (a) A human heart beats 360 times in 5 minutes. Find how many times the heart beats in one minute.

(b) Heartbeat is one example of a rate; it is measured in beats per minute.
Write two more everyday examples of rates.

12 A student used a calculator to calculate the following:

eq3

Estimate the answer by following these steps:

Step 1: round off each of the numbers in the numerator to the nearest hundred.

556.8 is rounded to ______

205.2 is rounded to ______

Step 2: round off the denominator to the nearest ten.

36 is rounded to ______

Step 3: use the rounded numbers to estimate the answer:

13 Complete the statements below to describe the first step in converting the following powers to ordinary numbers.

(a) 2.456 ´ 106 means move the decimal point ______places to the ______.

(b) 3.8 ´ 10 –5 means move the decimal point ______places to the ______.

14 (a) Life started on Earth about 3.8 ´ 109 years ago. Write this number out in full.

(b) Red light has a wavelength of 0.000 000 7 m. Write this wavelength in standard form.

15 Use your calculator to calculate the following. Write your answer correct to 2 decimal places, where necessary.

eq4
eq5
eq6
eq7
(e) 25 –34

16 Find the meaning of these words from Section 1 of your module notes. You may use an example to help in your explanation.

Word / Meaning
place value / The position of a numeral determines its value.
For example in the number 623, the digit 6 has a place value of ‘hundreds’.
(a) denominator
(b) estimate
(c) divisible
(d) index (or power)
(e) square root

4930CD: Assessment guide Page XXX

Ó DET NSW, 2005/008/012/06/2006 P0025399