math corrections log.

d

Determine whether 1457 is a prime or composite number (mistake 5)- flawed foundation

composite (put prime at first)

the numbers 1575 and 42 , written as the product of their prime factors are-

1575=3²×5²×7

42=2×3×7\

find the largest integer which is a factor of both 1575 and 42 rule 1-careless

21 . (answer at first was 7)

given the set of numbers:

27 cubed, one over 3, 64 cubed, -4 over -2, 2 squared

*****find the difference between the smallest rational number and the largest rational number** (rule 2) misread mistakes

smallest rational number = one over 3

largest rational number = 64 cubed which is 4

differnce = 3 and 2 over 3

A helicopter hovered at 985 m above sea level.

(b) The set of binoculars then bounced off the jetty and sank to the seabed, 15 m below sea-level. What was the vertical distance between the helicopter and the set of binoculars?

rule 3 -concept mistake

985-(-15)=1000m ( i put 970m)

Lamp posts are positioned at intervals of 120 m along a road and pots of bougainvillea plants are placed at intervals of 96 m. The first pot of bougainvillea plant is placed at the foot of the first lamp post.

(b) Find the total number of lamp posts and pots of bougainvillea plants within this road segment. rule 1, careless(

corect answer 11, i put lp-5, bp-6 (forgot to add dint know we had to ) *

City W at 12 p.m.- 4 °C

City W at 12 a.m. -7.5 °C

City X at 12 p.m. -10 °C

City X at 12 a.m.- 3 °C

City Y at 12 p.m.- 27 °C

City Y at 12 a.m. -32.5 °C

City Z at 12 p.m. -10.5 °C

City Z at 12 a.m. -12 °C

(c) Find the change in temperatures from 12 a.m. to 12 p.m. for each city. Which city experienced the greatest change in temperature between 12 a.m. and 12 p.m.?

(d) The temperature at 12 a.m. in one of the cities had been taken wrongly. Which city do you think it is? Give a reason for your answer.

©Change in temperature for City W 11.5 °C (From -7.5 °C to 4 °C)

Change in temperature for City X 7 °C (From 3 °C to 10 °C)

Change in temperature for City Y 5.5 °C (From 32.5 °C to 27 °C)

Change in temperature for City Z 22.5 °C (From -12 °C to 10.5 °C)

City with the greatest temperature change City Z (with a change of 22.5 °C)

(d)City with the wrongly recorded temperature City Y

Reason why City Y's temperature is wrong The midnight temperature (32.5 °C) should not be much hotter than the noon temperature (27 °C) in December.

Subtract 5x² + 8x - 3 from 9x² - 16x + 6 careless

4x² - 24x +9

Express (3x - 2)/4 - 2(x - 7)/5 as a fraction in its simplest form. careless

7x+46 over 20

Oranges are sold at r cents each. Pears are sold at 4 for p dollars. Apples are each sold at 30 cents cheaper than each orange.

(a) Express the cost of an orange in dollars in terms of r.

(b) Express the cost of 6 pears in dollars in terms of p.

(c) Express the cost of an apple in dollars in terms of r.

(d) Express the cost of buying 5 oranges, 6 pears and 7 apples in dollars, in terms of p and r, and simplify it.

(e) If r = 60 and p = 3, find the cost of buying 5 oranges, 6 pears and 7 apples in dollar.*unsure*

(a) - 0.01r

(b)1.5p

© 0.01r -0.30

(d) 0.12r+1.5p-2.10

(e)9.60

The perimeter of a rectangle is (10x + 4y - 8) cm and its breadth is (2x + y) cm.

(a) Find the length of the rectangle in terms of x and y.

(b) If x = 6 and y = -2, find the area of the rectangle. careless

(a) 3x + y -4

(b)120

if x=3(y-2z), find the value of z when x=21 and y=42 careless

17.5

PQRS is a rectangle and H is a point on QR. PQ = (5x+2)cm, HR = (6-x) cm and the perimeter of the rectangle is (17x+1) cm

(a) find in terms of x , an expression for

(i) PS

(ii) QH

(b) given that the length of QH is twice the length of HR, find

(i) an equation in terms of x

(ii) the value of x by solving the equation from part (b)(i)

(iii) the area of rectangle PQRS

dk how to do

(a)(i) 7x-3 over 2 / 3.5x - 1.5

(ii) 9x -15 over 2 / 4.5x -7.5

(b)(i) 9x-15 over 2 = 2(6-x) / 4.5x-7.5 = 2(6-x)

(ii) x=3

(iii) 153 cm²

Ben drove for a distance of 135km at a certain speed. Lindsey drove for a distance of 120km at a speed of 10km/h slower than ben . given that the time taken by both of them were the same, find the speed at which each of them drove. not sure how to do

bens speed- 90km/h

Lindseys speed- 90-10 =80km/h

Given the linear function 3 over 2 y-6x =9, find

(a) the gradient ^ make y 1^

(b) the y-intercept hint

^dont know how to do^

gradient - 4

y-intercept-6

x- (-1) 0 2 3

y - 5 ? ? -11

(a) Using the values given in the table above, find the gradient of the straight line.

(b) Hence, given that the equation of the straight line is \(y = -kx + 1\), where \(k\) is an integer, write down the value of \(k\).

(c) Complete the table above.

(d) Using 2 cm to represent 1 unit on the \(x\)-axis and 1 cm to represent 1 unit on the \(y\)-axis, draw the graph of \(y = -kx + 1\) for \(-1 \le x \le 3\). ( chapter 6 qn 51 - check assessment book on the graph)

(a) 4

(b) 4

( c ) 1,-7 (left to right)

30 workers need 6 days to paint a building. If only 10 workers are available to work, find the number of days the remaining workers will need to paint the building.

Workers and days are inversely proportional.

Total work = Workers × Days

= 30 × 6

= 180 worker-days

If only 10 workers are working:

Days = 180 ÷ 10

= 18 days

Answer: 18 days

2. Convert the Following Speeds

(a) 75 m/s to km/h

(b) 90 km/h to m/s

©(c) 84 000 cm/min to m/s

@1 m/s = 3.6 km/h

75 × 3.6 = 270 km/h

Answer: 270 km/h

(b)90 × 1000 ÷ 3600

= 25 m/s

Answer: 25 m/s

©84 000 cm = 840 m

Convert minutes to seconds:

840 ÷ 60

= 14 m/s

Answer: 14 m/s

A piece of rope is divided in the ratio

5 over 12 , one over 6, 1 over 9

Given that the difference between the longest and the shortest piece is 75 cm, calculate the length of the rope.

Hint* take LCM

200

Tom , Dick and harry work for a company which requires them to pack hampers for a festive event. Working at constant rates, tom ,Dick, and harry can pack the hampers, each on their own in 8h, 9h and x hours respectively,

(i) when tom and harry work together, they can pack the hampers in 3h . find the time taken by harry when he packs the hampers alone

(ii) hence, find the time taken to pack the hampers when tom, dick and harry work together.

(i) 4.8h

(ii) 2h15min

Car A travelled at a speed 15% faster than Car B and Car C travelled at a speed 10% faster than Car A. By what percentage did Car C travel faster than Car B?

26.5%

b) Complete the table below.

Figure number (\(n\))	Number of black triangles (\(b\))	Total number of triangles (\(t\))
1	0	1
2	1	4
3	3	9
4
5

(c) Write down the formulae for the following:

• (i) \(b\) in terms of \(n\)

• (ii) \(t\) in terms of \(n\)

(d) Find the total number of triangles in the figure which has 66 black triangles.

(b) - 16,25

(c) Formulae

• (i) \(b = \frac{n(n-1)}{2}\) (or \(0.5n^2 - 0.5n\))

• (ii) \(t = n^2\)

(d)Final Answer: 144

(c) Cedric took up the following hire purchase plan for a year to buy another

laptop at $1899.90.

Downpayment = 20% of the cash price

Interest = 3.5% per year

Calculate the monthly payment Cedric must pay for the laptop.

Downpayment = 20% × $1899.90 = $379.98

Interest = 3.5% × (1899.90 − 379.98) = $53.20

Monthly payment 1899.90−379.98+53.20

12

= $131.09

2 (a) An alcohol solution is a mixture of water and alcohol.

A chemist has 8 litres of 15% alcohol solution.

How much water must she add to the alcohol solution to reduce the

concentration to 10%?

4 litres

4 Mr Tan travelled from Town A to Town B at an average speed of 40 km/h. He rested at Town B

for 8 minutes before travelling to Town C.

(a) If Mr Tan took 1 hour 20 minutes to travel from Town A to Town C on an average speed of

60 km/h, find the distance between Town A and Town C.

80km

(b) Given that the distance between Town A and B is 2 fifth of that between Town A

Town C, find Mr Tan’s average speed, in km/h, from Town B to Town C.

120km/h