QR- quick retrieval flashcards

1. What is 1/5 as a percentage?

2. What is 1/8 as a percentage?

3. What is 2/3 as a percentage?

4. What is 1/3 as a percentage?

5. What is 1/6 as a percentage?

6. What is 1/9 as a percentage?

7. What is 1/7 as a percentage?

8. What is 1/10 as a percentage?

9. What is 3/8 as a percentage?

1. 20%

2. 12.5%

3. 66.7%

4. 33.3%

5. 16.7%

6. 11.1%

7. 14.3%

8. 10%

9. 37.5%

Percentage Change- What is the Joyel shortcut and work it out for this example: “price went from 80 to 100. What's the % change?”

Joyel Shortcut - (Final / Initial) − 1, then read the decimal.

100 / 80 = 1.25 → subtract 1 → 0.25 → × 100 = 25%

What formula is used for these types of percentage questions?

1. Find a % of a value - "What is 15% of 300?"

2. Find what % one value is of another - "120 is what % of 480?"

1. Value × (% / 100) → 300 × 0.15 = 45, or 300 * 15 %

2. (Part / Whole) × 100 → (120 / 480) × 100 = 25%

How would you work out a reverse percentage question for an increase? Work it out for this example: “A laptop costs £360 including 20% VAT. What was the price before VAT?"

divide by 1 + the percentage (20% = 0.20, 0.20 + 1 = 1.2)

• 360 / 1.2 = £300

How would you work out a reverse percentage question for a decrease? Work it out for this example: “A laptop is sold in a clearance sale after its price is reduced by 20%. The sale price is £640”

divide by 1 - the percentage (20% decrease = 100 - 20 = 80, becomes 0.80)

• 640 / 0.80 = £800

In the percentages questions, what are synonyms for increase and decrease that could be used in the question?

Price includes an increase- VAT, markup, addition

Price reflects a decrease - discount, reduction/reduced

1. What is the decimal for 1/2?

2. What is the decimal for 1/5?

3. What is the decimal for 2/3?

4. What is the decimal for 4/5?

5. What is the decimal for 1/3?

6. What is the decimal for 1/6?

7. What is the decimal for 2/5?

8. What is the decimal for 3/5?

9. What is the decimal for 5/6?

10. What is the decimal for 1/8?

11. What is the decimal for 3/8?

12. What is the decimal for 5/8?

13. What is the decimal for 7/8?

1. 0.5

2. 0.2

3. 0.667

4. 0.8

5. 0.333

6. 0.167

7. 0.4

8. 0.6

9. 0.833

10. 0.125

11. 0.375

12. 0.625

13. 0.875

Ratios: Simplifying them quicker - “What is the ratio of 480 to 360?”

1. 480 / 360 = 1.333…
2. Recognise 1.333 = 4/3
3. Ratio = 4 : 3

If you don't recognise the decimal, divide both numbers by the smaller one: 480 / 360 = 1.333 and 360 / 360 = 1 → ratio = 1.333 : 1 = 4 : 3.

Ratios: Work this question out using the Delta Shortcut - “Boys and girls are in ratio 9 : 1. There are 40 more boys than girls. How many boys?”

Delta Shortcut:

• ratio difference = 9 − 1 = 8 parts.

• 8 parts = 40 people → 1 part = 5 people

• Boys = 9x5 = 45

1. What is 6 mins in a fraction of an hr

2. What is 10 min in a fraction of an hr

3. What is 12 min in a fraction of an hr

4. What is 15 min in a fraction of an hr

5. What is 20 min in a fraction of an hr

6. What is 30 min in a fraction of an hr

7. What is 45 min in a fraction of an hr

6 min	0.1 hr (1/10)
10 min	0.167 hr (1/6)
12 min	0.2 hr (1/5)
15 min	0.25 hr (1/4)
20 min	0.333 hr (1/3)
30 min	0.5 hr (1/2)
45 min	0.75 hr (3/4)

Rates

1. What does “per” refer to?

2. Label the triangle for rate, total and units

3. Label the triangle for distance, time and speed

1. "Per" = division

2. Total on top, Rate × Units below

3. Distance on top, Speed x Time below

1. Convert 1/7 into a decimal

2. Convert 1/8 into a decimal

3. Convert 1/9 into a decimal

4. Convert 1/11 into a decimal

5. Convert 1/12 into a decimal

6. Convert 2/7 into a decimal

7. Convert 3/7 into a decimal

8. Convert 2/9 into a decimal

Fraction	Decimal	Fraction	Decimal
1/7	0.143	1/12	0.083
1/8	0.125	2/7	0.286
1/9	0.111	3/7	0.429
1/11	0.091	2/9	0.222

Averages & Statistics: What are the formulas for mean, sum, n and change in mean? Answer a change in mean question such as: “A warehouse has 5 crates. 6 kg is added to each of 4 crates. By how much does the mean weight of the 5 crates change?”

• Mean = Sum / n

• Sum = Mean × n

• n = Sum / Mean

• Change in mean = Change in Sum / n

Change in sum = 6 × 4 = 24 kg (added 6 to each of 4 crates)
n = 5 crates (total number stays the same)
Change in mean = 24 / 5 = 4.8 kg

Averages & Statistics: When items are added or removed, you go through the sum. Mean × n = Sum is the bridge.

1. Adding an item: "Mean of 8 values is 25. A 9th value of 34 is added. New mean?"

2. Removing an item: "Mean of 10 values is 50. Value of 20 is removed. New mean?"

1. Current sum = 25 × 8 = 200. New sum = 200 + 34 = 234. New mean = 234 / 9 = 26

2. 50 × 10 = 500. New sum = 500 − 20 = 480. New mean = 480 / 9 = 53.3

Averages & Statistics: Median & Mode - Find the median from these values: 23, 17, 31, 8, 42, 15, 29, Tell me what a mode is.

Round 1: remove 8 (lowest) and 42 (highest) → 23, 17, 31, 15, 29
Round 2: remove 15 and 31 → 23, 17, 29
Round 3: remove 17 and 29 → 23

(THE MODE IS THE MOST OCCURING NUMBER)

Geometry: What is the area and perimeter for the 2D shapes such as rectangle, square, triangle, circle and trapezium?

Shape	Area	Perimeter / circumference
Rectangle	l × w	2(l + w)
Square	s²	4s
Triangle	½ × base × height	a + b + c (all sides)
Circle	π × r²	π × d (or 2 × π × r)
Trapezium	½ × (a + b) × h	sum of all sides

Geometry:

1. What is the volume of the 3D shapes such as cuboid, cube, cylinder and any prism?

2. What is the formula for surface area?

Shape	Volume
Cuboid	l × w × h
Cube	s³
Cylinder	π × r² × h
Any prism	base area × height (length)

2. SA = 2 × (base area) + (base perimeter) × height

Geometry: What is the formula for Pythagoras and “Find c when a = 3, b = 4"

Pythagoras = a² + b² = c²

3 * * = 9 (a²) → press P (store in memory)
4 * * = 16 (b²) → + C = 25 (add memory: 9 + 16)
√ = 5 (square root)