math corrections log.

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Types of mistakes.

1. The "Careless" Mistakes (Execution Errors)

You understood the math, but your brain or hand slipped. [1]

• Arithmetic Slips: Adding 2+3 and writing 6.

• Copying Errors: Writing a number incorrectly from the question line to your working line.

• Sign Flips: Dropping a negative sign (e.g., changing -3x to 3x halfway through).

• Calculator Miskey: Punching the wrong numbers into your device. [1, 2]

2. The "Misread" Mistakes (Interpretation Errors)

You knew how to do the math, but you solved the wrong problem.

• Missed Constraints: Ignoring words like positive integer, exact value, or in terms of π.

• Units Mismatch: Giving the answer in hours when the question asked for minutes.

• Wrong Target: Solving for x when the question asked for 2x+5. [1]

3. The "Concept" Mistakes (Knowledge Gaps)

You did not know how to approach the problem because you lack the underlying knowledge.

• Formula Blank: Forgetting the actual formula or theorem needed.

• Misapplied Rules: Using a rule where it does not apply (e.g., trying to use the Pythagorean theorem on a non-right-angled triangle).

• Weak Foundation: Not understanding the theory behind a topic (e.g., how logarithms actually work).

4. The "Strategy" Mistakes (Application Errors)

You know the formulas and concepts, but you could not connect the dots to start or finish.

• Pattern Blindness: Not recognising that a complex-looking question is just a simple concept in disguise.

• Dead-End Path: Choosing a long, complicated method instead of a faster, cleaner algebraic shortcut.

• Time Crunch Panic: Rushing and choosing a poor strategy because you ran out of time.

5.The "Flawed Foundation" Mistake

• those that u thought u knew but got it wrong and dint understand the answe5.r

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