44723382 Mathematics Worksheet 3a3t70

CICERON SECONDARY SCHOOL MATHEMATICS WORKSHEET 1. Express the following as a single fraction in its lowest :

2. Evaluate the following (a) 18.75 – (2.11)2

(b) 2 – 0.24

(C) 5.3 × 2.5 ÷ 0.04

(d) 5.68 + 7.12

0.15

3.2 × 0.04

3. The cash price of a bicycle is $319.95. It can be brought on hire purchase by making a

deposit of $69.00 and monthly installments of $28.50 each. i.

What is the TOTAL hire purchase price of the bicycle?

ii.

Calculate the difference between the total hire purchase price and the cash price.

iii.

Express your answer in (ii) above as a percentage of the cash price.

4. A piece of ribbon 81cm long is divided into three pieces in the ratio 1:3:5. Calculate the

length of the longest piece of ribbon.

5. A loan of $12 000.00 was borrowed from a bank at 14% per annum. Calculate: i.

The interest on the loan at the end of the first year

ii.

The total amount owing at the end of the first year

A repayment of $7 800.00 was made at the start of the second year Calculate: iii.

the amount still outstanding at the start of the second year

iv.

the interest on the outstanding amount at the end of the second year

6. (a) Given that m = -2, n = 4 Calculate ( 2m + n)(2m – n) (b) Solve the simultaneous equations i. 5x + 6y= 37 ii. 2x + 3y = 4

(c) Factorize completely i. 4x2 – 25

ii. 6p – 9ps + 4q – 6qs iii. 3x2 + 4x -4

7. (a) On a certain day, 300 customers visited a bakery that sell bread and cakes 70 customers bought cakes 80 customers bought neither bread nor cakes. 2x customers bought bread only. x customers bought both bread and cakes.

U

B

C

i.

U represents the rest of customers visiting the bakery on that day, B represents the set of customers who bought bread, and C represents the set of customers who bought cake. Copy and complete the Venn diagram to illustrate the information.

ii.

Write an expression in x to represent the TOTAL number of customers who visited the bakery on that day.

iii.

8. The diagram below shows a pattern made of congruent right-angled triangles. In each

triangle, the sides meeting at a right angle 1 unit and 2 units long.

B H C

L

F

G

i.

Describe FULLY the single transformation that will map triangle BCL onto triangle FHL.

ii.

DESCRIBE FULLY the single transformation that will map triangle BCL onto triangle HFG.

iii.

Using a ruler , a pencil and a pair of comes construct parallelogram WXYZ in which WX = 7.0 cm , WZ =5.5 cm and ZXWZ = 600

iv.

Measure and state the length of the diagonal WY

9. The data below are the lengths to the nearest centimeter of the right foot of the 25

students in a class.

14 18 20 22 24 15 18 20 22 25 16 18 21 22 25 16 19 22 23 26 17 19 22 23 27 (a) Copy and complete the following grouped frequency table for the data above.

Length of Right Foot (cm) 14 – 16

Frequency

17 – 19

………….

20 – 22

8

…………….

5

26 - 28

2

4

(b) State the lower boundary of the class interval 14 – 16 (c) Sate the width of the class interval 20 – 22 (d) A student’s right foot measured 16.8cm. State the class interval in which this length we lie. (e) A student was chosen at random from the group, and the length of his right foot was

measured. Calculate the probability that the length was GREATER THAN or EQUAL to 20cm. (f) State the modal length of a student’s right foot

10. (a) The volume V, of gas varies inversely as the pressure P when the temperature is held constant. i.

Write an equation relating V and P

ii.

If V = 12.8 when P = 500 determine he constant of variation

iii.

Calculate the value of V when P =480

(b) the lengths in cm of the sides of the right angled triangle shown below are a a(a – 7) and (a + 1)

a-7

a+ 1

a i.

Using Pythagoras theorem write an equation in of ‘a’ to represent the relationship among the three sides.

ii.

Solve the equation for a

iii.

Hence state the lengths of the THREE sides of the triangle